Abstraction and Intermediation: The Implications of Behavioral Decision Making

for Three Applications in Finance

A dissertation submitted to the

Department of Social and Decision Sciences in partial fulfillment of the requirements

for the degree of

Doctor of Philosophy in Social and Decision Sciences

by

David C. Rode

Dissertation Committee:

Paul Fischbeck (Chair) Baruch Fischhoff

Jay Apt Eric Gold

Carnegie Mellon University Pittsburgh, Pennsylvania

October 2017

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Table of Contents

TABLE OF CONTENTS ................................................................................................................................. i 

TABLE OF EXHIBITS .................................................................................................................................. iii 

ACKNOWLEDGEMENTS ........................................................................................................................... vi 

PRÉCIS .......................................................................................................................................................... viii 

INTRODUCTION ........................................................................................................................................ 1-1 

LITERATURE REVIEW ............................................................................................................................ 2-1 

2.1  ABSTRACTION ................................................................................................................................... 2-1 2.2  INTERMEDIATION .............................................................................................................................. 2-4 2.3  RESEARCH QUESTIONS & PREVIOUS WORK ...................................................................................... 2-6 

2.3.1  Descriptive Models of Choice and Securities Design ............................................................. 2-6 2.3.2  Expert Judgment and Regulatory Decision-Making ............................................................... 2-8 2.3.3  Computational Modeling of Risky Intertemporal Choice ....................................................... 2-9 2.3.4  Presentation Compression and Complexity Reduction ......................................................... 2-12 

CATASTROPHIC RISK AND SECURITIES DESIGN ........................................................................... 3-1 

3.1  INTRODUCTION .................................................................................................................................. 3-1 3.2  THE PC INDUSTRY AND THE NATURE OF CATASTROPHIC RISKS ....................................................... 3-7 

3.2.1  The Insurance Market ............................................................................................................. 3-8 3.2.2  Regulation ............................................................................................................................... 3-9 3.2.3  Intra-Industry Competition ..................................................................................................... 3-9 3.2.4  Definitions ............................................................................................................................. 3-11 3.2.5  Estimating the Risks of Catastrophic Events ......................................................................... 3-12 

3.3  STRUCTURE OF CATASTROPHE BONDS ............................................................................................ 3-15 3.4  HUMAN BEHAVIOR AND CATASTROPHE BONDS .............................................................................. 3-19 

3.4.1  Cognitive Complexity ............................................................................................................ 3-21 3.4.2  Exaggerated Comprehensiveness .......................................................................................... 3-23 3.4.3  Illusion of Control ................................................................................................................. 3-23 3.4.4  Reliance on Availability ........................................................................................................ 3-24 3.4.5  Overweighting Small Probabilities ....................................................................................... 3-24 3.4.6  Violations of Extensionality .................................................................................................. 3-25 3.4.7  Dimensions of Risk ................................................................................................................ 3-27 3.4.8  Asymmetric Information ........................................................................................................ 3-28 

3.5  MARKET EQUILIBRATION ................................................................................................................ 3-29 3.5.1  Immature Market Structure ................................................................................................... 3-29 3.5.2  A Dual Equilibrium ............................................................................................................... 3-30 

3.6  CONCLUSIONS AND IMPLICATIONS FOR SECURITIES DESIGN ........................................................... 3-32 3.7  EPILOGUE ........................................................................................................................................ 3-33 

REGULATED EQUITY RETURNS: A PUZZLE .................................................................................... 4-1 

4.1  INTRODUCTION .................................................................................................................................. 4-1 4.2  REGULATED EQUITY RETURNS AND THE CAPM ............................................................................... 4-3 4.3  REGULATED ELECTRIC UTILITY RETURNS ON EQUITY SINCE 1980 ................................................... 4-6 

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4.3.1  Historical Authorized Return on Equity Data ......................................................................... 4-6 4.3.2  The Regulated Equity Premium............................................................................................... 4-9 

4.4  POTENTIAL THEORETICAL EXPLANATIONS FOR THE PREMIUM ....................................................... 4-12 4.4.1  Capital Structure Effects ....................................................................................................... 4-12 4.4.2  Asset-Specific Risk ................................................................................................................ 4-14 4.4.3  The Market Risk Premium ..................................................................................................... 4-15 4.4.4  Testing a Theoretical Model of the Risk Premium ................................................................ 4-17 

4.5  POSSIBLE IMPLICATIONS ................................................................................................................. 4-21 4.5.1  Potential Alternative Finance Explanations ......................................................................... 4-23 4.5.2  Potential Public Policy Explanations ................................................................................... 4-25 4.5.3  Potential Behavioral Economics Explanations ..................................................................... 4-27 4.5.4  Potential Public Choice Explanations .................................................................................. 4-29 

4.6  CONCLUSION ................................................................................................................................... 4-31 

A COMPUTATIONAL FRAMEWORK FOR RISKY INTERTEMPORAL CHOICE ....................... 5-1 

5.1  INTRODUCTION .................................................................................................................................. 5-1 5.2  LITERATURE REVIEW ........................................................................................................................ 5-2 

5.2.1  Choice Under Risk and Uncertainty ....................................................................................... 5-3 5.2.2  Choice Over Time ................................................................................................................... 5-4 5.2.3  Risky Intertemporal Choice ..................................................................................................... 5-5 

5.3  SIMULATING THE POPULATION OF DECISION MAKERS ...................................................................... 5-7 5.3.1  Parameterization and Decision Demographics ...................................................................... 5-7 5.3.2  Decision Processes and Sequencing ..................................................................................... 5-17 

5.4  ANALYSIS AND FINDINGS ................................................................................................................ 5-18 5.4.1  Incorporating Probabilistic Information into Decision Problems ........................................ 5-20 5.4.2  Evaluating Novel and Complex Problems ............................................................................. 5-23 

5.5  APPLICATIONS AND IMPLICATIONS .................................................................................................. 5-34 

PRESENTATION COMPRESSION: INVESTMENT METRICS & HEURISTICS ............................ 6-1 

6.1  INTRODUCTION .................................................................................................................................. 6-1 6.2  THE LEVELIZED COST OF ENERGY IN THEORY AND PRACTICE .......................................................... 6-3 

6.2.1  The Levelized Cost of Energy .................................................................................................. 6-3 6.2.2  Levelized Cost vs. Levelized Cash Flow .................................................................................. 6-6 

6.3  THE DECISION PROBLEM ................................................................................................................... 6-7 6.3.1  Decision Problem Structure .................................................................................................. 6-11 

6.4  ANALYSIS AND FINDINGS ................................................................................................................ 6-14 6.4.1  Power Investments as Intertemporal Lotteries ...................................................................... 6-14 6.4.2  Basic Prospect Structures and Design Elements................................................................... 6-15 6.4.3  Compression and Different Prospect Designs ...................................................................... 6-21 6.4.4  Compression and a Heterogeneous Population of Decision Makers .................................... 6-33 

6.5  APPLICATIONS AND IMPLICATIONS .................................................................................................. 6-39 6.5.1  Compression as a Tool for Debiasing ................................................................................... 6-42 

FINAL THOUGHTS & FUTURE DIRECTIONS .................................................................................... 7-1 

7.1  SECURITIES DESIGN........................................................................................................................... 7-1 7.2  REGULATORY INTERMEDIATION........................................................................................................ 7-3 7.3  TOWARD A COMPUTATIONAL APPROACH TO BEHAVIORAL DECISION THEORY ................................ 7-7 7.4  PRESENTATION COMPRESSION IN RISKY INTERTEMPORAL CHOICE ................................................... 7-8 

REFERENCES ............................................................................................................................................. R-1 

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Table of Exhibits

Exhibit A: Catastrophe-Risk Financial Instruments as of 1997 ......................................... 3-5 Exhibit B: Three Examples of Early Catastrophe Bond Offerings .................................... 3-7 Exhibit C: Natural Catastrophes in 1995, 1996, and 1997 ............................................... 3-13 Exhibit D: Contingent Surplus Note (CSN) Cash Flow Structure ................................... 3-15 Exhibit E: Catastrophe Insurance Index Basis Comparisons ........................................... 3-17 Exhibit F: GCCI versus PCS Coverage in Index-based Contracts .................................. 3-18 Exhibit G: Behavioral Anomalies and Implications for Catastrophe Bonds ................... 3-20 Exhibit H: The St. Paul Re Pro Rata Capital Note Cash-Flow Structure ........................ 3-22 Exhibit I: Comparing and Contrasting Cat Bonds with Conventional Securities ............ 3-26 Exhibit J: Development Scenario for ART Products ....................................................... 3-30 Exhibit K: Actual vs. Projected Issuance of Cat Bonds ................................................... 3-34 Exhibit L: Contemporary Standardized Cat Bond Structure............................................ 3-34 Exhibit M: Qualifying Rate Cases Filed per State for the Ten Most Frequently- and Least

Frequently-Filing States, 1980-2015 .......................................................................... 4-7 Exhibit N: Risk Premium Growth by Frequency of Case Filing. Gaps in the series reflect

years in which no rate cases were filed for the subject group .................................... 4-7 Exhibit O: Range of Risk Premium Growth Across States. States with highest and lowest

rates of growth (among states with at least 5 rate cases) are highlighted .................. 4-8 Exhibit P: Filing Frequency by Year ................................................................................. 4-9 Exhibit Q: Authorized Return on Equity vs U.S. Treasury and Investment Grade Corporate

Bond Rates ............................................................................................................... 4-10 Exhibit R: Distribution of Premium Across All Years .................................................... 4-10 Exhibit S: Authorized Return on Equity Premium, 1980-2015 ....................................... 4-11 Exhibit T: Authorized Rate-of-Return Premium vs. Utility Leverage ............................. 4-13 Exhibit U: Authorized Rate-of-Return Premium vs. the Hamada Capital Structure

Parameter ................................................................................................................. 4-14 Exhibit V: Authorized Rate-of-Return Premium vs. Industry Average Asset Beta ........ 4-15 Exhibit W: Market Risk Premium Trends over Time by Historical Window ................. 4-16 Exhibit X: Authorized Rate-of-Return Premium vs. Ex Ante Estimated Market Risk

Premium ................................................................................................................... 4-17 Exhibit Y: Regression Results for CAPM-based Risk Premium Model.......................... 4-19 Exhibit Z: Actual vs. Regression-Model Risk Premium Spreads .................................... 4-19 Exhibit AA: Regression Results for a Two-Period CAPM-based Risk Premium Model 4-20 Exhibit BB: Actual vs. Two-Period Model-Predicted Risk Premium Spreads ................ 4-21 Exhibit CC: Wholesale Fuel and Power Price Trends, 2007-2015 .................................. 4-22 Exhibit DD: Wholesale vs. Retail Power Prices, 2007-2015 ........................................... 4-23 Exhibit EE: Comparability of Spreads Measured with Authorized and Earned Rates of

Return and Utility Net Income ................................................................................. 4-25 Exhibit FF: Authorized Rates of Return on Equity and Skewness .................................. 4-28 Exhibit GG: Rate of Return Authorized as a Percent of Rate of Return Requested ........ 4-30 

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Exhibit HH: Summary of Studies Estimating Cumulative Prospect Theory Parameters .. 5-8 Exhibit II: Parameter Estimates by Country from Rieger, Wang, and Hens [2017] .......... 5-9 Exhibit JJ: Empirical Distributions of Cumulative Prospect Theory Parameters ............ 5-10 Exhibit KK: Descriptive Statistics and Correlations for the Cumulative Prospect Theory

Parameters ................................................................................................................ 5-11 Exhibit LL: Parameter Space for the Value Function ...................................................... 5-12 Exhibit MM: Parameter Space for the Probability Weighting Function (Gains) ............. 5-12 Exhibit NN: Parameter Space for the Probability Weighting Function (Losses) ............ 5-13 Exhibit OO: Time Discounting Model Hierarchy ............................................................ 5-15 Exhibit PP: Distribution of Hyperbolic Present Bias Parameters .................................... 5-16 Exhibit QQ: Summary of Decision Maker Parameter Bounds ........................................ 5-16 Exhibit RR: Basic Taxonomy of Decision Processes ...................................................... 5-17 Exhibit SS: Probabilistic Representation of the Probability Weighting Function for Gains

for the Simulated Population of Decision Makers ................................................... 5-21 Exhibit TT: Probabilistic Representation of the Probability Weighting Function for Losses

for the Simulated Population of Decision Makers ................................................... 5-21 Exhibit UU: Probabilistic Representation of the Value Function for the Simulated

Population of Decision Makers ................................................................................ 5-22 Exhibit VV: Population Decision Demographics for a Choice Problem ......................... 5-22 Exhibit WW: Percent of Population Exhibiting Certainty-Risk Asymmetry .................. 5-25 Exhibit XX: Percent of Population Exhibiting Certainty-Risk Asymmetry with State 1

Adjustment at Zero, Using “Uncertainty First” Decision Sequence, and Varying Decision Process ...................................................................................................... 5-26 

Exhibit YY: Logistic Regression Results for Certainty-Risk Asymmetry. Case used is p = 0.5, Δ = 3, and = 0 for HDPT, Uncertainty First. ................................................ 5-27 

Exhibit ZZ: Percent of Population Exhibiting Short-Long Asymmetry .......................... 5-29 Exhibit AAA: Classification Tree Analysis Illustrating Quasi-Complete Separation. Case

used is p = 0.05, Δ = 10, t = 1, and Premium = 100 for HDPT, Uncertainty First. . 5-31 Exhibit BBB: Bayesian Logistic Regression Results for Short-Long Asymmetry. Case used

is p = 0.05, Δ = 10, t = 1, and Premium = 100 for HDPT, Uncertainty First. .......... 5-32 Exhibit CCC: Bayesian Logistic Regression Results for Short-Long Asymmetry. Case used

is p = 0.05, Δ = 10, t = 1, and Premium = 100 for HDPT, Time First. .................... 5-33 Exhibit DDD: Diagram of Choice Rule and Presentation Relations ................................. 6-8 Exhibit EEE: Presentation-Heuristic Pairing Agreement Classification ......................... 6-13 Exhibit FFF: Full and Compressed Presentation Forms .................................................. 6-13 Exhibit GGG: Typical Power Project Cash Flow Derivation .......................................... 6-15 Exhibit HHH: Four Example Cash Flow Profiles ............................................................ 6-16 Exhibit III: Four Power Plant Classes and Class-Specific Information ........................... 6-17 Exhibit JJJ: Capacity-Factor Levels for Each Type of Power Plant Included ................. 6-18 Exhibit KKK: Capacity Factor and Energy Price Multiplier Curves ............................... 6-19 Exhibit LLL: Energy-Price Trajectories with Multipliers Relative to Average Price ..... 6-20 Exhibit MMM: Comparison of Two Stylized Projects with Different Lifespans for which

Compression is a Useful Heuristic ........................................................................... 6-24 Exhibit NNN: Interpretation of Hypothesis Tables ......................................................... 6-24 Exhibit OOO: Relative Life Hypotheses and Short-Long Asymmetry ........................... 6-26 

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Exhibit PPP: Population Classification According to the Relative Lifespans of the Prospects, Measured as Longer Lifespan Divided by Shorter Lifespan .................. 6-26 

Exhibit QQQ: Cash Flow Framing Hypotheses and Gain-Loss Asymmetry .................. 6-27 Exhibit RRR: Population Classification According to Cash Flow Profile Framing ........ 6-27 Exhibit SSS: Incentive Hypotheses and Short-Long Asymmetry ................................... 6-28 Exhibit TTT: Population Classification According to Use of Incentives ........................ 6-28 Exhibit UUU: Project Type Hypothesis and Gain-Loss and Magnitude Asymmetries ... 6-29 Exhibit VVV: Population Classification Across vs. Within Project Types ..................... 6-29 Exhibit WWW: Refining the Population Classification Across Project Types by

Controlling for Renewable Power Types ................................................................. 6-31 Exhibit XXX: Influence of Prospect Characteristics on Decision Problems with

Compression ............................................................................................................. 6-32 Exhibit YYY: Percentage Variation of Subgroup Mean Coefficient Value from Population

Coefficient Means .................................................................................................... 6-34 Exhibit ZZZ: Example of De Minimis Impact on from Further Dividing the Group ... 6-34 Exhibit AAAA: Connection of Decision Maker Characteristics ( ) to Project

Characteristics for the Simplifying and Useful Outcome Classes ........................... 6-36 Exhibit BBBB: Connection of Decision Maker Characteristics ( ) to Project

Characteristics for All Outcome Classes.................................................................. 6-37 Exhibit CCCC: Connection of Decision Maker Characteristics ( ) to Project

Characteristics for All Outcome Classes.................................................................. 6-38 Exhibit DDDD: Information Consumer Choice Strategy Outcomes ............................... 6-43 Exhibit EEEE: Heuristic Map of Change-in-Choice Consequences ................................ 6-46 Exhibit FFFF: Rule Accuracy by Prospect and Decision Maker Characteristics ............ 6-47 Exhibit GGGG: Gross Margin Trends in California, Pennsylvania, and Texas ................ 7-4 Exhibit HHHH: Regression Results Examining Commission Reputation on Spreads ...... 7-6 

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Acknowledgements

Forsan et haec olim meminisse iuvabit Virgil (The Aeneid)

Although perhaps Aeneas’s journey was longer, both it and this process have stretched to epic proportions and have involved adventures with a myriad of characters. These acknowledgements do little justice to the number or influence of that group. I can but therefore offer, with deep humility, my gratitude to the following people, who must serve as proxies for the larger, unnamed cast.

There is easily no person who has had a greater influence on my arrival at this moment than Paul Fischbeck. I owe Paul thanks for seeding my path with interesting problems and clearing the roadblocks so that I could—eventually—reach my destination. He has been a trusted advisor, an influential mentor, a favorite research co-conspirator, and a good friend. Paul provided me with opportunities that literally changed my life (and my views on hyphenation) and did so while making the whole process (or maybe 95% of it) fun.

I am grateful, also, to my committee members: Baruch Fischhoff, Jay Apt, and Eric Gold. Baruch was officially my introduction to SDS, having called to inform me that I was admitted many, many years ago. I was fortunate to have been his TA during my first semester in the department and to have benefitted from his influence on my qualifying exam committee. Despite our seemingly different interests and approaches, I have been impressed frequently over the years—such is the breadth of his influence—by the number of times Baruch has said something or I have read something he’s written that has struck a chord, resonated, and provided the spark that lit the way down an interesting path. Jay has been an encouraging supporter of mine since his installation as director of CEIC, and has generously provided me numerous opportunities to share my work with CEIC and its advisory board over the years. With Eric, my connection to SDS spans the entire history of the department. Eric was SDS’s first graduate student, and defended the year I arrived in the department. To each of them, I am deeply appreciative of their support, their insight, and their patience.

Two teachers from my distant past must also be acknowledged, as my arrival at this moment is due in part to their influence. The late Jim Robinson was my Latin and English teacher in high school. A Renaissance man in the truest sense, his gift to me was a classical education. It was only with age that I have come to see, and continue to see, the expansiveness of this gift, as items he planted in my head decades ago appear with surprising regularity. I have a wider, richer, and more profound appreciation for our Western inheritance than I could have imagined three decades ago, and he is to thank for it. Subsequently, Jim Laing, now emeritus at Wharton, changed my thinking as an undergraduate. Yes, finance has always remained of central interest to me, but Jim Laing

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was responsible for my introduction to decision sciences, to behavioral decision theory, to game theory, to social choice theory, and to evolutionary computation methods. He is the one who inspired me to add Decision Processes as a second concentration. He is the one who suggested that perhaps considering graduate school would be of interest. He is the one who encouraged the finance practitioner in my head to make room for the researcher, and I am better for it. I truly would not be who I am today without their influence and support.

I was grateful to have a job that, for 15½ out of 16 years, was deeply satisfying. That was in no small part due to it providing long relationships with valued colleagues. Tony, Alex, Jen, Pete, and Lisa made for a great team over the years, and I was lucky enough to get to know and appreciate their families as well. Of the many decisions I made throughout that time, bringing on Tony and Alex were two of the best. I have been (and continue to be) so proud of them both. I couldn’t have asked for better colleagues or friends.

I am not—let’s be honest—the easiest person to get to know. I am thus grateful to a small, loyal group whose friendship has meant so much to me: my very long-time friends, Robert Rissman and John Forté, with whom I share a history of unmatched duration; my Pittsburgh family, Lisie (my “spark”) and Jeff Lipsitz; my soulmate, John Nulty; and last, but certainly not least, the Waldorf to my Statler, the Liz to my Karen, and the one who got away, Tim Zinn. Kuckleffel

There has been no greater surprise in my life than my discovery that I am so deeply in love with two wonderful kids. Tony and Sarah Páez could have given me no greater gift than sharing their wonderful children, Claire and Antonio, with me. They stole my heart early on and never gave it back. No one brightens my day the way they can. And no one is ever so excited to see me (and I them). They lift my heart. Claire and Antonio: I love you, I love you, I love you! Never forget that. I hope I can help to provide you both with bright futures as partial repayment for how each of you has added to the substance of my life.

Finally, I must offer my thanks to my family, which has supported my endeavors, whichever direction they took me. I have benefited from a mother and father whose support and encouragement have been complete and unconditional. I only wish my father could have lived to see my various graduations. I know he would have been proud of me, but they are still moments I’d have liked to have shared with him. I owe my sister thanks as well, for putting up with a curmudgeonly brother and a polar opposite. She’s seen the good, the bad, and the ugly, and yet she still talks to me. It is only with the passage of so much time that I have come to appreciate the entirety of my family’s legacy in the traits and behaviors and culture for which they were (and are) the guardians. I am certainly myself, but I have become what I am through their collective influence. And I am glad of it.

To each of these people, and to those unnamed behind them, I offer my profound thanks.

Remember me, but forget my fate Dido’s Lament (Henry Purcell, Dido & Aeneas)

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Précis Modern financial theory and practice make extensive use of the concepts of

abstraction and intermediation. Securities are designed, valued, and allocated within

portfolios based on characteristics that contain little of the richness of the actual assets

underlying their claims. Corporate financial decisions and policy analyses evaluate choices

based on comparing abstract metrics that ignore or minimize the myriad attributes belonging

to such choices. In many cases, these evaluations and choices are made by intermediaries

(whether human experts or heuristic rules) that either offer specialized information or serve

as a proxy for competitive markets. While economic theory has addressed issues in

abstraction and intermediation that arise from incentive problems and information

asymmetries directly, most approaches have maintained the traditional assumption of

rational agents free of cognitive constraints and biases. This dissertation illustrates, through

three applications, that abstraction and intermediation are at significant risk of suboptimal

operation when faced with certain limitations prevalent in the behavioral decision-making

literature.

The three diverse applications include the design of financial securities, the rate-

making practices of utility regulators, and the use of metrics and heuristics by intermediaries

in corporate finance and policy analysis. Well-established areas in the behavioral decision-

making literature, such as risk perception, communication about uncertainty, and heuristic

choice and expert judgment are shown to challenge the application of these core principles

of economics in practice. This dissertation develops a methodology for evaluation and

demonstrates the practical consequences of behavioral decision-making in each of the three

applications and examines possible responses and interventions to mitigate their effect.

1-1

1 Introduction

The Oxford English Dictionary defines “abstraction” as “the process of considering

something independently of its associations or attributes.” In finance, “intermediation”

generally refers to the role played by banks or brokers acting as a bridge between investors

and companies or lenders and borrowers [Allen and Santomero, 1997]. In a similar vein, in

regulatory economics, regulators are tasked with standing in for competitive market forces

in instances where market failures are likely or the government has permitted a monopoly to

exist. Although modern economic theory has come to see intermediation as an issue

primarily of information asymmetries in a principal-agent setting (e.g., Diamond [1984]),

Schumpeter, had a more expansive definition:

“…the banker must not only know what the transaction is which he is asked to finance and how it is likely to turn out but he must also know the customer, his business and even his private habits, and get, by frequently ‘talking things over with him’, a clear picture of the situation.” [Schumpeter, 1939: p. 116]

That is, successful intermediation involves a richness of detail regarding not just the

information itself, but how it is communicated and how it is received by transaction

stakeholders who are subject to cognitive constraints and behavioral biases. These two

concepts—abstraction and intermediation—play an enormous role in modern financial

theory. They also pose significant challenges, however, to a world faced with the numerous

findings of the behavioral decision-making literature.

Abstraction can, in theory, allow diverse securities to be priced using common

theoretical constructs built up from the treatment of Arrow-Debreu securities—highly-

stylized state-contingent claims—that contain none of the richness of actual securities, which

reflect specific firms and are targeted at specific clienteles. Intermediation, or the placing of

a person or rule in between an actor and an investment or policy, is commonplace in

corporate finance and regulation, where various metrics (e.g., Net Present Value (“NPV”),

1-2

Levelized Cost of Electricity1 (“LCOE”)) serve as proxies for projects and policies, and

regulators are called upon to take the place of competitive markets. But metrics, like heuristic

decision rules in general, are imperfect, and regulators can be subject to biases in judgment.

Given the importance of these concepts to modern financial practice, it is important to

identify what implications the behavioral decision-making literature has for them.

In this dissertation, I explore three specific areas in finance that represent archetypal

examples of abstraction and intermediation, I develop a method for exploring decision-

making behavior in novel environments, and I illustrate the challenges to their practical

application introduced by widely-known behavioral decision-making findings.

The first essay addresses abstraction in the context of securities design. Finance

theory generally, and structured finance practice in particular, operate on the premise that

cash flows can be extensively manipulated and “reconfigured” to exploit clientele effects

(or, as Merton [1989] described it, the bundling and unbundling of risks). Behavioral

decision theory suggests that there are limits to such reconfiguration, in particular when

involving high consequence, low probability events, and when violations of extensionality

and the multidimensional nature of perceived risk confound risky choice. My first essay

“Catastrophic Risk and Securities Design,” published in the Journal of Psychology and

Financial Markets2, analyzes a novel financial instrument (so-called “cat bonds”3) by

examining the complications that arise from attempting through abstraction to design

securities for investor clienteles without acknowledging their cognitive limitations and

biases in dealing with the richness of detail actually present in real examples of such

securities.

1 The LCOE is a calculation that spreads the fixed and variable costs of generating electricity from a particular source evenly over a period of time, such that the NPV of the actual cash flows and the NPV of the “levelized” cash flows are equal. In this formulation, as is traditional in finance, uncertainties are intended to be captured in the selection of a discount rate. 2 Now the Journal of Behavioral Finance. 3 A catastrophe (or “cat”) bond is a security issued by an insurance company whose principal and/or interest is reduced in the event of a pre-defined catastrophic loss (e.g., hurricane, earthquake).

1-3

The second essay addresses intermediation in the context of regulation. Regulators

are often called upon to stand in for the discipline of a competitive market in setting rates of

return for regulated industries. Governments, for example, have granted monopolies (or

“franchises”) to electric utilities to prevent costly duplication of services [Kahn, 1970]. In

return for the grant of an exclusive franchise, however, utilities are subjected to rate

regulation by regulators that seek to impose the discipline of competitive markets (by

limiting the rates that utilities are allowed to charge to those deemed to be competitive or

“just and reasonable”) in spite of their de jure monopoly status. Regulators seek to estimate,

therefore, the rate of return that such a business would earn if it were not granted a monopoly,

and therefore if its investors were compensated solely on the basis of the risks they would

assume under competitive operation. Although financial theory provides clear guidance in

this area in the form of normative asset pricing models, the evidence involving electric

utilities suggests that the judgment of regulators in this area deviates from those outcomes

and also from the decisions of regulators that default to formulaic approaches. In particular,

a “money illusion” effect appears to be present.4 The second essay uses a unique data set of

electric utility rate cases to test competing hypotheses about the existence of regulatory

biases and finds that the normative finance model is deficient in explaining observed rate-

setting behavior and that utilities appear to be earning excess returns as a result.

The third essay develops a method for exploring decision-making behavior in novel

or complex environments under uncertainty and over time. Behavioral decision-making

research has made extensive use of experiments with human subjects in identifying a variety

of anomalies regarding risky intertemporal choice. These models, at a very general level,

have tended to converge to a small set of functional forms, separated only by varying

parameterization. There remains a difficulty, however, in applying these models and their

various parameterizations to many complex and domain-specific problems. Human subject

pools have typically involved students, and more recently have involved online labor

markets, such as Amazon.com’s Mechanical Turk (“MTurk”). As such, many experimental

tasks must be reduced to very generic or “abstract” levels, resulting in a general difficulty in

4 In behavioral economics, the “money illusion” refers to the tendency of people to misperceive nominal price changes as real price changes.

1-4

exploring many complex, or domain-specific decision tasks. The third essay develops a

computational framework for extending behavioral decision-making research in risky

intertemporal choice into such domains that is based on the general decision-making

characteristics identified in the literature.

The fourth essay addresses both abstraction and intermediation in the use of metrics

by heuristic investment decision makers and policymakers. Finance theory operates on the

basis that certain decision problem presentations I shall refer to as “metrics” (such as NPV

or LCOE) are extensionally equivalent for choice purposes to the cash flows from which

they are derived. For example, Project A is preferred to Project B if NPV(Project A) >

NPV(Project B) or Policy X is preferred to Policy Y if LCOE(Policy X) < LCOE(Policy Y).

But these metrics are the product of “lossy compression.” Information is “lost” or abstracted

away in the process of “compressing” project details to create the metric. In particular,

lotteries are replaced with expected values (compression across risk) and events unfolding

over time are replaced with present values (compression across time). This lost information

is deemed to have no normative value beyond what is captured in the compressed forms.

This information may, however, contain attributes that influence actual decision making.

One such metric, the Levelized Cost of Energy, is commonly used to represent

competing choices in policy analysis (e.g., for ranking tasks, such as determining the optimal

response to environmental regulation [Bruckner et al., 2014; Anderson et al., 2016]),

regulatory economics, forecasting [EIA, 2016], and even investment decision-making (such

as determining the preferred long-term capital investment strategy for regulated utilities

[USAID, 2009; Tucson Electric Power, 2016]). LCOE is perceived as a normative means of

spreading the cost (or value) of a project over its estimated life. Notwithstanding its

normative positioning, Joskow’s [2011] critique of LCOE focused on its exclusion of certain

practical considerations (such as time-of-use) for some technology types. Restated in

different terms: Joskow argues that the use of LCOE as a heuristic could lead to preference

reversals because the compression process omitted information that did, in fact, have

normative relevance. That is, it is flawed as a normative measure.

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The premise of the fourth essay has an analogous basis: the act of compression that

creates LCOE can lead to a violation of extensionality in that decision makers make different

choices than they would if presented with the uncompressed information. If the use of LCOE

as a presentation form in certain environments impairs decision making (in the sense that

compressing a project cash flow profile triggers heuristics that bias the choices made by

decision makers), then there is value in being able to identify those environments and

understand how such biases can be mitigated. However, if the information lost to

compression would otherwise have itself triggered a bias, then its removal in the process of

levelizing may actually improve decision making. Although this work identifies classes of

project types where the use of LCOE leads heuristics to become unreliable, it also illustrates

the value of LCOE as a debiasing technique for cognitively-constrained decision makers. In

many cases, having less detailed information results in such decision makers making better

choices.

In Chapter 2, I review the literature on abstraction and intermediation in finance in

the context of relevant previous work in the behavioral decision-making literature and

outline the research questions examined herein. In Chapter 3, I present the first application,

which involves securities design for risks involving catastrophic insurance losses. In Chapter

4, I present the second application, which is an empirical examination of electric utility rate

case data between 1980 and 2015. In Chapter 5, I develop a computational approach to

investigate novel decision-making environments for which reliance on human subjects may

be problematic. In Chapter 6, I present the third application, which uses the approach

developed in Chapter 5 to identify classes of decision problems and types of decision makers

for which compression through the use of LCOE creates violations of extensionality in

choice and to illustrate the usefulness of compression as a debiasing technique for

cognitively-constrained decision makers. In Chapter 7, I provide concluding thoughts on the

three applications and discuss suggestions for future research in this area.

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2 Literature Review 2.1 Abstraction

Financial theory and practice have often proceeded along two parallel tracks. While

considering a security or an investment abstractly, or independent of its associations and

attributes has been at the core of financial theory, innovation in the design of financial

securities has increased steadily over time. The process of valuation may be based on

abstraction, but Wall Street sells (and buys) descriptive richness.

The theory of general equilibrium was built up in part from Arrow-Debreu securities,

which are state-contingent claims that pay one unit of the numeraire commodity in one state

of the world and zero in all other states [Arrow, 1964]. The dynamic spanning of these

securities ensures market completeness and the existence of an equilibrium [Arrow and

Debreu, 1954]. As such, these securities abstract away from corporate details, projects,

government policies, investor preferences, and other descriptive factors. This lack of

descriptive richness continued into modern portfolio theory, as Markowitz [1952] and Tobin

[1958] showed that the von Neumann-Morgenstern [1947] axioms were consistent with

mean-variance preferences if utility functions were quadratic. That is, if investors cared only

about the mean and variance of wealth (or returns), then optimal portfolios could be

determined. But if quadratic utility admits only mean and variance preferences, then no other

attributes could be influential to decision makers (at least within the von Neumann-

Morgenstern axiomatization).

The consequences of this development of portfolio theory were that securities were

reduced to a probabilistic characterization of their expected return, its variance, and its

covariance with other returns. Tobin [1958] further extended this result by demonstrating

what is now known as one-fund separation: that all investors should hold a combination of

the market portfolio and the riskless asset. In such a world, investors need only hold an index

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fund and need not concern themselves with the makeup of the underlying index or the nature

of the companies composing it. Abstraction provides simplicity. Security analysis, or the

evaluation of individual investments based on their unique characteristics, is largely

irrelevant in such an environment [Fama, 1970; Malkiel, 1973].5 The preeminence of

abstraction continued into the world of corporate finance as well. Projects could be reduced

to a simple metric (NPV) and decisions made solely based on that metric were shown to

produce optimal choices in the sense of maximizing firm value [Hirshleifer, 1958]. Discount

rates could be determined by simple formulas (such as the Capital Asset Pricing Model

(“CAPM”)) that would result in asset market clearing [Sharpe, 1964; Lintner, 1965; Mossin,

1966].

The securities we observe in the real world, however, look nothing like the theoretical

Arrow-Debreu securities. Over time, more complex and descriptively rich securities have

emerged, prompting a search for an explanation of this emergence. In an early and

exhaustive study of historical security issuance, Dewing [1934: pp 236-237] noted that our

basic security concepts—debt and equity—arose from distinctions in Anglo-Saxon law

regarding debtors and creditors. But even among those two classes, Dewing catalogued a

diverse array of variations and hybrid securities. Although many of the securities he

identified at the time eventually fell out of use, financial innovation resulted in a steady

stream of new security types over time [Allen and Gale, 1994].6

The process of “securitization,” or “structured finance,” that began in the late 1970s

has only accelerated these trends. If cash flows and risks are fungible, they can be—in

theory—almost infinitely bundled and unbundled [Merton, 1989]. To put this evolution in

context, the total market capitalization of all global stock markets is approximately $69

trillion (World Federation of Exchanges, 2015) and the total face value of all outstanding

public and private debt is approximately $223 trillion (ING, 2013). However, the total

5 But see the paradox created by this assumption identified by Grossman and Stiglitz [1980]. They show that it is technically impossible for markets to be informationally efficient if no one does security analysis. 6 Many early securities fell prey to changes in tax law or regulation. Others, such as “guaranteed stock” and “participating bonds,” fell out of common usage because they were unattractive hybrids of other existing securities [Dewing, 1934].

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notional value of all derivative securities (that is structured securities derived from

underlying equity and/or debt holdings) is more than $550 trillion (Bank for International

Settlements, 2015). The collective value of “innovated” securities is nearly twice that of all

“basic” securities (on which they are theoretically based). Clearly, there is a strong demand

for financial innovation. This demand exists to adapt to changing regulations (e.g., changing

definitions of bank capital), to create markets for risks that were previously not easily traded

(e.g., cat bonds), and to attract new sources of capital by attempting to appeal to investors

not previously interested (e.g., market-linked certificates of deposit).

This returns us to the two parallel tracks of finance and their reconciliation. The

descriptive sparseness of asset pricing theory and the creative efficiency of financial

engineering have given rise, ironically, to a diverse ecosystem of complex securities. The

ease with which many securities, on paper, can be modified and redesigned has resulted in

their proliferation. In light of market frictions and in seeking to appeal to as many investor

clienteles as possible, this process is reasonable and (largely) harmless. For many structured

securities, their replicability from simpler securities provides arbitrage bounds on pricing

and liquidity because they can always be “unbundled” into simpler instruments. Many

options can be decomposed into stocks or bonds and cash [Black and Scholes, 1973], zero-

coupon bonds can be created from coupons “stripped” from traditional government bonds

[Fabozzi and Fabozzi, 1995], and index funds can be synthetically created by acquiring all

of the index components.

Many other structured securities, however, have no directly-traded constituent

components. In such cases, the assembly of these instruments from their abstract components

may work on paper, but are not guaranteed of price or liquidity in practice. In those cases,

the structuring entities seek to maintain a matched book of buyers and sellers, but imbalances

in those matched books can create sudden and dramatic swings in price and liquidity (see

Salmon [2009] for an example related to mortgage-backed securities and the financial crisis

of 2007-2009). These securities, then, depend crucially on the ability of investors to

understand their characteristics, to perceive their risks, and to interpret communications

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about them clearly and “rationally.” Abstraction, absent arbitrage, creates a direct reliance

on investor rationality—a subject to which we shall return in Section 2.3 below.

2.2 Intermediation

The classical model of intermediation was that of the banker, who collected deposits

from customers and lent those deposits out to businesses. The banker assumed the credit risk

and profited from scale economies and informational asymmetries by charging the borrower

more than the banker paid the depositors. It was this world that Schumpeter had in mind in

the description of intermediation that I cited previously.

This model was about resolving informational asymmetries [Diamond, 1984] and

minimizing transaction costs [Gurley and Shaw, 1960] in a world of imperfect markets.

Frictions in the form of transaction costs could be minimized by an intermediary dividing

fixed costs over individuals. Frictions caused by information asymmetries could be resolved

by intermediaries with specialized knowledge that were subjected to “delegated monitoring”

in a principal-agent setting.

Since that original research, however, transaction costs have fallen dramatically and

large amounts of information are increasingly available. Contrary to those theories, however,

the quantity of, and activity by, intermediaries has increased substantially. As a result, there

has been a significant re-thinking of intermediation theory in finance. Merton [1989] and

Allen and Santomero [1997] highlight two previously overlooked functions of

intermediaries: risk transfer and complexity reduction. These functions involve the ability to

evaluate risks, the willingness to accept and manage risks, and the ability to communicate

risks and complex structures to less-informed market participants. In many respects, the

increased complexity borne of structured finance and discussed in Section 2.1 has created a

demand for more and more intermediation.

These demands have also expanded the role of intermediaries far beyond the

commercial banks identified nearly a century ago. Allen and Santomero [1997] in particular

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note the significant growth in non-bank intermediaries, such as insurance companies,

pension funds, investment banks, advisors and consultants, and institutional investors and

asset managers. I focus on this expanded treatment to consider as an intermediary “any

evaluator or rule-processor that stands between actors.” This definition is purposefully

cumbersome so as to include non-human intermediaries, such as automated rules.

Let us consider the two functions advanced by Allen and Santomero [1997]. First,

the risk transfer function can take two forms: risk minimization and risk allocation. The role

of an intermediary can be to allow smaller investors or lenders to diversify their exposures

across multiple investments at low cost. Even corporations may wish to diversify

investments across multiple parties so as to avoid the costs of financial distress [Warner,

1977] or purely out of managerial self-interest [Ross, 1977; Stulz, 1984; DeMarzo and

Duffie, 1995]. The second form, risk allocation, is that of intermediary as risk “traffic cop.”

Once risk has been minimized, a decision as to who is best able to bear the remaining risk

must be made. This is a function performed, in my interest here, by regulators who are tasked

with both providing utilities (for example) a reasonable profit so as “to preserve the financial

soundness of the utility” [Bluefield Water Works & Improvement Co. v. Public Service

Commission of West Virginia (262 U.S. 679 (1923))] and also “protecting the public interest”

[Federal Power Commission v. Hope Natural Gas Company, 320 U.S. 591 (1944)]. This

twin mandate requires regulators to apportion costs and risks of certain investments to the

various stakeholders involved as they act as proxies for the discipline of competitive markets

in mediating between firms and consumers.

The second function advanced by Allen and Santomero [1997], complexity

reduction, can also be divided into two forms: delegation and simplification. The traditional

role of intermediaries involved delegation. In other words, complexity was addressed by

delegating decisions entirely to parties with specialized information or abilities [Diamond,

1984]. Complexity reduction can also be achieved by intermediaries that simplify the

decisions to be made. This is what may be considered the “satisficing” approach [Simon,

1947; 1956] and involves choices informed by (simple) heuristic rules [Simon, 1979].

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2.3 Research Questions & Previous Work

In both abstraction and intermediation in finance, there is a tension between

simplification and “complexification,” between theoretical purity and practical relevance.

As Simon [1979] noted nearly forty years ago in his Nobel Prize lecture: “[d]ecision makers

can satisfice either by finding optimum solutions for a simplified world, or by finding

satisfactory solutions for a more realistic world.” My interest is in the latter: how can

financial decision-making be improved while maintaining a practical level of descriptive

richness? I explore three questions with real-world applications:

1. How can descriptive models of choice be used to improve securities design

and guide financial innovation?

2. How can the expert judgment of regulators be improved in the performance

of their role as risk-allocating mediators?

3. How does problem presentation affect the performance of heuristics used in

risky intertemporal choice?

In each of these questions, the tension is manifest in the struggle to find a balance between

seeking missing (or hidden) information that would make for “better” (and different)

decisions (either normatively better or better justified or communicated) and suppressing

information that would make decision-making “worse” because of biases or cognitive

limitations.

2.3.1 Descriptive Models of Choice and Securities Design

Often, financial securities are designed exclusively to meet the needs of the issuer or

seller. However, if insufficient attention is given to the preferences of potential buyers, the

issuer may not realize the level of funding anticipated, may face a higher cost, or after-market

liquidity may be nonexistent. While not every security will appeal to every investor, I focus

here on two other issues: (i) potential investors may not understand the novel security, and

(ii) potential investors may not believe the information they’re given about the novel

security.

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As I noted previously, the design of new securities has progressively become more

complex over time. There is an abundant literature on the challenges of decision-making in

novel and complex environments [Simon et al., 1987]. In such environments, individuals

tend to default to heuristic reasoning and automated “rule-based” responses [Newell and

Simon, 1972; Cross, 1983; Albers and Laing, 1991; Becker, 1993]. They may misapply these

decision schemata because they disagree even about what the attendant risks are [Fischhoff,

1985]. They may suffer from cognitive dissonance when presented with normatively optimal

choices that appear “unpalatable” [Fisher and Statman, 1997].

Koonce, McAnally, and Mercer [2005] provide experimental evidence concerning

how investors actually judge the risks of financial instruments, showing that additional

explanatory power is provided by incorporating “behavioral” variables in addition to what

they term “decision-theory” variables (information about probabilities and payoffs). In

attempting to reason about complex investment decisions, even trained experts have

exhibited high rates of requests for useless information [Kroll, Levi, and Rapoport, 1988].

This finding is often confounded by regulatory requirements (e.g., the Security and

Exchange Commission’s Regulation FD) for increased disclosure of information, resulting

in many firms providing “kitchen sink” disclosures out of an abundance of caution. Lo,

Mamaysky, and Wang [2000] also note that the jargon and “patois” common to securities

disclosures often distort meaning and can produce disagreement even when the intent of the

disclosures is the same. MacGregor [1989] demonstrated (in reference to consumer

products) that inferences about risks were linked closely to interpretations of words and

phrases contained in product warnings. All of these factors challenge potential investors’

understanding of novel securities, and that lack of understanding may either dissuade them

from investing, or prompt investment under mistaken premises.

Even for those investors who do understand the securities in question, they may not

trust the information they’re given, or may simply have different estimates of the risks and

values involved. If additional discounting is undertaken by prospective investors to

compensate for such doubts or differences of belief, the result is likely to be a bid-ask spread

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that is sufficiently wide so as to limit liquidity or lead to a breakdown in trading altogether.

Duffie and Rahi [1995] have noted that even the perception of large information

asymmetries can lead investors to reject certain investments, feeling that they would be

hopelessly disadvantaged. But trust issues may not arise solely from intentional

asymmetries. They can also emerge from different estimates of the problem parameters.

Biases in judgment have been exhibited when dealing with probabilities, including the

overweighting of small probabilities [Kahneman and Tversky, 1979] and overestimating

probabilities involving especially “vivid” or relatively publicized events [Tversky and

Kahneman, 1973; Lichtenstein et al., 1978; Combs and Slovic, 1979].7 Even the values

involved may be perceived differently. Slovic [1964] and Fischhoff et al. [1978] have

illustrated that perceptions of risk may vary widely from the single-factor ideals so common

in finance.

As a result of these findings, the presumption of understanding should be questioned

even among domain experts, and care should be taken not only in the provision of

information, but also in how such information is communicated to potential investors. A

central question in this line of inquiry is whether or not the provision of additional or

different information leads to better decisions. Would investors make “better” decisions

(about novel securities, for example) if they were provided with greater information about

probabilities and diverse risks in an attempt at debiasing, or when they are not distracted by

the additional information provided and focus instead on a simplified presentation?

2.3.2 Expert Judgment and Regulatory Decision-Making

Regulators, despite having domain expertise, are not immune from many of the

decision-making biases identified above. Slovic [1972] noted that even with accurate models

and good judgment, experts are unable to apply what they know consistently. Imperfect

expert judgment has also been shown to permit suboptimal choices in difficult and

7 For example, attempts to sell contingent convertible notes (known as “CoCos” or “bail-in bonds”), which are used to bolter bank regulatory capital positions, often follow well-publicized concerns about bank solvency. The disproportionate availability of information about banking systems risks may lead potential investors to overestimate the risks associated with a particular bank’s issuance.

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consequential tasks [Dawes, Faust, and Meehl, 1989; Mowen, 1994; Thaler, 1994; Kammen

and Hassenzahl, 1999]. Dawes [1979], in particular, has demonstrated that even simple

linear models tend to outperform experts on issues of “clinical intuition.”

One of the activities that regulators are tasked with performing is setting rates of

return for regulated industries. Their twin mandate is to provide for rates that are sufficient

to maintain the utility in a financially-sound state, while also protecting the public interest

from excessive costs. In the U.S., rates of return have typically been set in nominal terms.

For example, a utility may be granted the approval to charge rates intended to provide a

return on equity of 10%. The underlying cost of that utility’s capital, however, varies not

only with the perceived risk of the firm, but also macroeconomic conditions, including

inflation. In the 1970s and early 1980s, many utilities suffered from “regulatory lag” because

regulators were unable to adjust their nominally-denominated authorized rates of return

quickly enough to accommodate rising inflation.

This problem is an example of money illusion, or the tendency to misperceive

nominal price changes as real price changes [Shafir, Diamond, and Tversky, 1997]. Thaler

and Tversky [1996] note that the presence of money illusion can also impact risk aversion.

Kahneman, Knetsch, and Thaler [1986] show that judgments of fairness are based on

evaluation of nominal (as opposed to real) changes as well. Because evaluation of risk and

fairness are both solidly within the purview of regulators, there is concern that decisions by

regulators may be subject to such biases in a way that results in suboptimal regulatory

decision-making—a consequence that may be exceedingly costly for consumers and/or

firms. In this situation, the public interest may be better served by advocating for the use of

heuristic rules by regulators, in lieu of detailed evaluation and fact-finding during rate cases.

2.3.3 Computational Modeling of Risky Intertemporal Choice

Almost all the major findings in the behavioral decision-making literature have

emerged from experiments with human subjects. These experiments, often out of necessity,

have typically involved highly-stylized decision-making tasks. Although “natural”

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experiments have been conducted when feasible (for example, Lichtenstein and Slovic

[1973] studied actual behavior in casinos, Odean [1999] examined actual brokerage records

for individual investors, and Chetty et al. [2014] studied labor market and retirement saving

behavior using detailed household balance sheet and employment data), the ability of

researchers to test decision making experimentally in complex or novel environments has

been limited.

Notwithstanding these limitations, a large and robust literature on human decision-

making behavior under uncertainty and over time has emerged. The behavioral decision-

making literature has established a collection of anomalies and alternative theories of risky

choice [Kahneman and Tversky, 1979; Tversky and Kahneman, 1992] and of intertemporal

choice [Thaler, 1981; Loewenstein, 1988; Kirby and Maraković, 1995; Read, 2001]

supported by extensive experimental results. These alternative theories have been codified

into certain generally-accepted stylized models of decision making. Further, a significant

effort has been made to estimate the parameters of these models and evaluate differences

between various populations of decision makers.

Most of the experimental work, however, has been carried out using college students

and, more recently, using online labor markets such as MTurk. Scholars have rightly

questioned the generalizability of results obtained from these populations. Although for

many generic decision tasks, these groups are representative of the population as a whole,

there are also clear exceptions. Shuptrine [1975] compared experimental results from student

to those from actual consumers and found the results “inconclusive,” “strongly suggest[ing]

that investigators attempt in every way possible to test the population that they are interested

in studying.” Similarly, Peterson [2001] concluded that “caution must be exercised” when

attempting to extrapolate results to non-student populations. More recently, Goodman,

Cryder, and Cheema [2013] noted that MTurk participants exhibit many similarities to the

general population, but have important differences as well. In particular, they are “less likely

to pay attention to experimental materials.”

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Even samples of experts or professionals exhibit behavior not perfectly aligned with

the general population. Albert [1967] noted that businesspeople differ “significantly” in

experimental research. Shanteau [1988] said that the experimental evidence for expert

decision making is weak and mixed; that experts were equally prone to certain errors, but

also often used better decision processes.

The notion that different groups tend to exhibit different behaviors is not necessarily

surprising. However, it does present a complicating factor in attempting to evaluate decision

making in complex or novel environments. Tasks that require domain-specific knowledge

or expert reasoning, for example, can be difficult to examine both because general

populations may not have such knowledge and because of the difficulty or cost in accessing

statistically-significant groups possessing such knowledge or experience. It is, I believe,

equally difficult to draw meaningful inferences from overly-simplified tasks given to more

readily-available populations that are intended to represent some complex or novel “real-

world” task.

One such environment is the combination of choice under uncertainty and choice

over time: risky intertemporal choice. Although the normative approach is essentially settled

with the recursive utility framework of Kreps and Porteus [1978], as extended by Epstein

and Zin [1989], the descriptive theory of risky intertemporal choice is “not settled” [Albrecht

and Weber, 1997], is “complex and not easily understood” [Weber and Chapman, 2005], is

“relatively limited” [Anderson and Stafford, 2009], and is “quite heterogeneous in methods

and findings” [Hardisty and Pfeffer, 2017].

There are four general types of anomalies in risky intertemporal choice that have

been identified:

1. Certainty-Risk Asymmetry (discount rates are higher for certain outcomes than for risky outcomes)

2. Short-Long Asymmetry (violations of stationarity, preference reversals induced by shifting risky choices forward in time)

3. Gain-Loss Asymmetry (discount rates are smaller for gains than for losses) 4. Magnitude Asymmetry (discount rates are higher for larger payoffs)

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The experimental work examining their findings, however, is limited and often

contradictory. Albrecht and Weber [1997] find support for short-long asymmetry in

matching tasks, but not choice tasks. Öncüler and Onay [2009] support violations of

stationarity, but find the evidence on direction of the effect mixed. Keren and Roelofsma

[1995] find support for certainty-risk asymmetry. Anderson and Stafford [2009] find no

support for certainty-risk asymmetry. Shelley [1994] supports gain-loss asymmetry;

Blackburn and El-Deredy [2013] do not. Disagreements involving the interactions between

risk and time emerge from whether subjects evaluate risk first or time first [Weber and

Chapman, 2005] and whether there is a single underlying mechanism [Keren and Roelofsma,

1995] or many mechanisms [Read, 2003]. Albrecht and Weber [1997] note that the empirical

results are sensitive to the elicitation procedure used.

Mindful of these challenges, the objective, then, is to adapt the knowledge and insight

already developed to such an environment. One means by which to do so is to develop a

computational model of a population of decision makers and perform “virtual experiments”

on that population. The role of computational simulation in the social sciences is now well-

accepted (see Epstein and Axtell [1996] and Gaylord and D’Andria [1998] for early

examples). Applying computational simulation methods to behavioral decision-making

questions, however, has been relatively unexplored, but may provide a platform for more

extensive exploration of this complex area.

2.3.4 Presentation Compression and Complexity Reduction

The use of heuristic rules as a means of complexity reduction has been widely studied

for decades [Simon, 1955; Simon, 1956; Polya, 1957; Gigerenzer and Todd, 1999]. Apart

from the problem of insufficient information, decision makers can also suffer from having

to process too much information or too many choices [Camerer, Loewenstein, and Weber,

1989; Kleinmuntz and Schkade, 1993; Iyengar and Lepper, 1999], useless or irrelevant

information [Kroll, Levi, and Rapoport, 1988; Redelmeier, Shafir, and Aujla, 2001], or

useful information absent a context (even a normatively irrelevant context) [Dawes, 1999].

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One objective, in such situations, is to seek to focus the decision maker on the most

relevant information, and then present that information in a format that allows for clear

interpretation. But presentation itself can be a confounding factor. Funtowicz and Ravetz

[1987] write at length about the importance of how quantitative information is presented, if

one wishes the recipient to have a useful appreciation of its strengths and weaknesses and

context, and propose a paradigm for presenting such information.

The degree to which decision tasks can be simplified has been studied in a variety of

contexts. Axtell [1992] wrote extensively about model aggregation as a means of simplifying

complex models. The literature in reduced-form modeling has encompassed numerous areas

including climate modeling [Mendelsohn, Nordhaus, and Shaw, 1994], population dynamics

[Lutz et al., 2002], environmental planning [Webster et al., 2002], and credit risk modeling

[Duffie and Singleton, 2003]. One form of simplifying presentation may be considered

“compression.” Compression refers to the collapsing of information about a decision task

into a single number. For example, in finance many decision problems use compression in

the form of metrics (such as NPV and LCOE) that collapse future cash flows into present

values and uncertainties into expected values. Such compressed presentations are deemed to

be extensionally equivalent to the full presentations in theory.

However, in many settings, such actions are shown to exhibit violations of

extensionality in practice. The non-linear weighting of probabilities, for example, has been

shown to result in preference reversals not present in normative theory [Kahneman and

Tversky, 1979]. Likewise, the time-inconsistent discounting of outcomes, such that one’s

future self would not make the same choice that one would make in the future today, has

also been shown to result in preference reversals [Thaler, 1981]. As a result, financial

metrics—which are forms of decision problem presentation—that collapse across these

dimensions (risk and time) may either (or both) bias or aid decision making.

With regard to practical application, decision makers that succumb to biases related

to risk and time may be benefitted from using a metric that in effect “bypasses” such biases

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by employing a simpler presentation. That is, by focusing the decision maker on the most

relevant information, “less” (information) may actually be “more” (useful). As a result, use

of the LCOE presentation could play an important role as a debiasing technique for

cognitively-constrained decision makers. However, users of the LCOE presentation must

also understand where the opposite effect may occur and biases are introduced by the process

of compression. Joskow [2011] has shown that LCOE is “not a useful way to compare

generating technologies [that have] different production profiles” (e.g., baseload vs.

intermittent) and thus is normatively flawed.

A consequent line of inquiry here asks whether LCOE’s flaws in a normative setting

are more than offset by its benefits in mitigating the impact of biases in a descriptive setting.

Compression, for example, obscures the presence of risk. Certainty-risk asymmetry results

in decision makers applying higher discount rates to certain outcomes. Likewise,

compression explicitly “levelizes” cash flows over time, and short-long asymmetry results

in discount rates declining as events are pushed into the future. Although Joskow’s [2011]

recommendation was to “abandon” levelized cost comparisons, a less drastic response may

be warranted if classes of problem characteristics and decision maker characteristics where

the use of LCOE leads heuristics to become unreliable can be identified, so that its use can

be limited to those larger areas where its reliability is preserved. In the end: how reliable are

heuristics based on compression?

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3 Catastrophic Risk and Securities Design

3.1 Introduction†

Insuring catastrophic risks represents a significant challenge not only for insurance

companies, but also for government agencies, banks, financial institutions, and individuals.

Traditionally, risk management has been handled by a network of insurance companies, with

some government oversight. A policy holder purchases coverage for some event from a

property and casualty (PC) insurer. The PC insurer then typically divests much of that risk

by obtaining coverage from reinsurers. The reinsurers transact with one another in order to

diversify their own exposures.

When the risk of loss from any individual event is both well-known and small, this

system works quite well (e.g., automobile and health risks). Historically, default rates among

insurers have been like those for corporations in general.8 However, with catastrophic losses,

the consequences are more concentrated and the probability of occurrence harder to assess.

These problems have drawn increasing attention as catastrophic losses have increased in

their number and scope. In some cases, like riverine floods, human activities (e.g., land-use

changes) have increased the number of severe events. In other cases, like earthquakes and

hurricanes, more people and insured property are in harm’s way, even if the number of events

has remained the same. Despite advances in hazard prediction, the models are still quite

† A version of this paper appears as Rode, D., B. Fischhoff, and P. Fischbeck. Catastrophic Risk and Securities Design. Journal of Psychology and Financial Markets 1:2 (2000): 111-126. Thanks go to John Miller, Carter Butts, and an anonymous reviewer for their thoughtful comments on earlier drafts, and to Hadi Dowlatabadi and James Risbey for their assistance in providing background information on climate modeling. The authors also appreciate the valuable comments and suggestions of Steven Goldberg and other participants at the NBER Insurance Project. Partial support was provided by the NSF-sponsored Center for Integrated Assessment of Human Dimensions of Global Change. All errors remain our own. 8 Matthews et al. [1999] report that failure frequency in the property and casualty insurance industry has averaged roughly less than 1% per year since 1969 and never exceeded 2.5%. Over the entire period that they studied, only 8% of insolvencies were attributed to catastrophic losses. At the same time, they report that in the period from 1989 to 1993, the percentage of defaults attributable to catastrophic losses increases from 8% to 56% of all defaults.

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imperfect, particularly for limited time periods and geographic areas.9 Helbling, Fallegger,

and Hill [1996] also note increasing tendencies towards litigation, decreasing burdens of

proof in determining liability, and new regulations regarding old, pre-existing risks as

additional reasons for the increasing costs of catastrophic losses. All of these trends

complicate predicting insurance exposures.

Other uncertainties arise from the structure of the insurance industry itself. Cummins

and Doherty [1997] assess the ability of insurers to pay for the “Big One” and find that,

while recent losses of $10 billion to $15 billion may seem manageable compared to the

industry’s total capital of over $300 billion, there is a mismatch in the distribution of that

capital (across firms) and the distribution of claims following a catastrophic loss. In this

context, the capacity of individual insurers is actually quite limited. According to Haag

[1995], it is “unusual” for any insurer to obtain more than $100 million in catastrophe

reinsurance per policy. If insurers wanted more, they would find that worldwide reinsurance

capacity (circa 1994) is approximately $7.2 billion, much smaller than the possible demand.

Claims resulting from some single major catastrophes could reach $70 billion to $100 billion

[Palm, 1995; Wharton Alumni Magazine, 1998]. A repeat of the earthquake that destroyed

Tokyo in 1923 could result in damages of between $900 billion and $1.4 trillion [Valery,

1995].

The gap between the catastrophic coverage that the industry could and does provide

might be traced to failures in the market for coverage. One familiar problem is the cyclical

nature of the insurance business, reflecting its profit incentives. Some analysts have

attributed the laggard performance of insurance and reinsurance firms, relative to other

financial companies and the market as a whole, to “excess capital” and “underleveraging”

9 As Jenkins [1998] notes, there are problems combining the forecasts of global and regional climate models. Global climate models lack the resolution of the regional models in predicting changes to specific areas (such as coastlines and mountain ranges). Although regional models can accommodate such predictions, they depend on global models for input. Jenkins [1998] writes that “problems arise when interpolating to increase the number of data points [to move from one scale to another]. . . . [C]oupled global and regional models can not [sic] give the best results yet because coupled atmosphere-ocean models which provide boundary conditions for the regional climate model are still early in their development.” In essence, the “grave concerns” arise from the newness and extraordinary complexity of most climate models built on a scale useful (to insurers or insurance investors) for hazard prediction.

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[Moody’s, 1997; Standard & Poor’s, 1997; Wehrly and Friedheim, 1998]. However, in fact,

the net written premium-to-surplus ratio declined from 1.82:1 in 1984 to 1.13:1 in 1995 to

0.90:1 at year-end 1997 [Wehrly and Friedheim, 1998]. Regulators allow insurers to

leverage their capital twice (2:1), in terms of which, the industry had “excess” capital of over

$120 billion. Although the premium-to-surplus ratio is only one measure of capitalization

efficiency, its decline suggests that surplus is accumulating at a greater rate than premiums

are increasing. That is, firms are generating more cash than they can efficiently manage.10

The resultant pressure on policy prices has diminished profits. In 1997, industry surplus

stood at $308.1 billion, up 20.1% from the previous year.

The definition of “excess” capital depends on the time frame used. Given the

certainty of eventual catastrophic losses, the capital may not be excessive. Rather, it may

eventually be required to cover losses. However, those losses may be decades into the future.

Only from a short-term perspective is such retained capital excess. Accounting conventions

and the U.S. tax code limit reserves to actual losses or to those losses that may reasonably

be expected within a year [USAA, 1998]. Any additional premium capital set-aside (e.g., for

longer term, less frequent losses) must be transferred to the insurer’s balance sheet, hence is

subject to tax (and possible distribution to shareholders). Liquid capital on an insurer’s

balance sheet reduces the firm’s return on equity. In the long run, this reduced return is

“fair,” in the sense of covering shareholders against expected future losses. However,

myopic [Mossin, 1968] or self-serving [Babcock and Loewenstein, 1997] managers may see

short-term advantage in reallocating that capital to more profitable short-term projects, such

as writing additional insurance coverage in non-catastrophic lines or returning it to

shareholders. By reducing provisions for losses, they will thereby increase future financial

risk. Shareholders should then expect increased returns as compensation for bearing more

risk (even if that risk is overlooked by current shareholders and managers).

Some smaller firms are underreserved, especially those with asbestos and

environmental liabilities [Standard & Poor’s, 1997]. However, the industry as a whole

10 Of course, this situation could be transiently justifiable after a disaster when firms raise premiums to address a decline in surplus. A fuller account would look at multiple measures of financial health.

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appears to face a capitalization paradox: it is over-capitalized from a short-term profit

perspective, while lacking the long-term ability to cover catastrophic losses when they occur.

The paradox could be resolved if the industry made better use of its short-term capacity. As

mentioned, the infrequent nature of catastrophic claims means that insurers who prepare

adequately will suffer long periods of perceived excess capital (in the eyes of myopic

stakeholders) as well as diminished profits (from taxation of capital held against future

liabilities, but not treated as official reserves). Conversely, those who do not prepare

adequately have higher short-term profits, along with higher likelihoods of failure

(bankruptcy). Large catastrophic losses have periodically prompted reorganizations and the

tightening of capital. Then, for some (usually brief) period, perceived excess capital

disappears, prices increase, and profits remain stable. However, as capital flows back to the

industry, firms compete for profits, prices drop, competition intensifies, profits disappear,

and the industry finds itself awash in capital (which it cannot invest in projects profitable

enough to satisfy shareholders and managers) [Standard & Poor’s, 1997; Wehrly and

Friedheim, 1998].

Several recent initiatives have attempted to increase the industry’s capacity by

providing insurers access to capital markets [Lewis and Davis, 1998; Osterland, 1998].

Losses of even catastrophic proportion remain almost negligible, compared to the size of

global capital markets [Cummins and Doherty, 1997; Jaffee and Russell, 1997]. For

example, a $100 billion catastrophe would consume nearly one third of the PC industry’s

total capital and surplus, perhaps pushing some firms into insolvency. Yet, that amount is

less than the average daily variation in global equity wealth.

Catastrophe bonds (“cat” bonds) are one possible way to access capital markets,

building on the wild popularity of securitization for other asset classes and exposures (e.g.,

mortgages, credit card receivables, real estate, David Bowie11). However, although

11 In 1997, rock star David Bowie issued $55 million worth of bonds backed by future royalties from 25 of his albums. The bonds, which were rated AAA by Moody’s, were purchased by the Prudential Insurance Company of America and provide a return of 7.9% over 10 years. Although experts were quick to dismiss the issue as “a glamour investment” and claim that they would only be “attractive to people who want to associate themselves with show-business personalities,” the entire issue was in fact, purchased by a major insurance company [Wall Street Journal, 1998]. However, recent reports [Financial Times, 1999] suggest that the success of the “Bowie

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insurance companies have created a variety of offerings (summarized in Exhibit A), they

have generally experienced but modest success in raising the desired capital at a cost

commensurate with the portfolio risk of the security [Lewis and Davis, 1998].

Reinsurer Instrument Amount (in millions) Status Date

Nationwide CSN $400.0 Closed August 1995

Hannover Re CSN $100.0 Closed 1995

Arkwright CSN $100.0 Closed May 1996

AIG Cat Bond $25.0 Closed May 1996

CAT, Ltd. Cat Bond $50.0 Withdrawn 1996

ACE, Ltd. Cat Bond $35.0 Withdrawn 1996

USAA Cat Bond $500.0 Withdrawn August 1996

Calif. Earthq. Auth. Cat Bond $1,500.0 Withdrawn 1996

RLI CatEPut $50.0 Closed October 1996

Hannover Re Cat Bond $100.0 Closed December 1996

St. Paul Re Pro Rata Bond $68.5 Closed December 1996

Winterthur Cat Bond $282.0 Closed January 1997

Reliance Cat Bond $40.0 Closed April 1997

Horace Mann CatEPut $100.0 Closed April 1997

USAA Cat Bond $477.0 Closed June 1997

Swiss Re Cat Bond $137.0 Closed July 1997

LaSalle Re CatEPut $100.0 Closed August 1997

Tokio-Marine Cat Bond $100.0 Closed November 1997

Exhibit A: Catastrophe-Risk Financial Instruments as of 1997 Source: Lewis and Davis [1998]

A frequently voiced objection by insurance companies is that such structured finance

costs too much for them to use it [Penalva-Zuasti, 1997]. For example, catastrophe bonds

have typically carried premiums of 300 to 500 (or more) basis points over the LIBOR for

medium-term securities with investment-grade ratings (see Exhibit B below). Even with

Bonds” may have been unique. Apart from various structural impediments in the music business (few recording artists own their own master tapes), the illiquid aftermarket for such securities raises many of the same questions discussed here in the context of catastrophe bonds [Silverman, Sparks, and Osterland, 1998].

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these added inducements, buyers have sometimes been scarce. As a result, the critical

question facing the creators of this market is whether potential investors are reluctant to

purchase any security backed by catastrophic risk insurance or just the current offerings. In

an excellent overview, Froot [1997] advances eight possible reasons for the appearance of

insufficient risk sharing:

(1) Actuarially insufficient reinsurance capital12 (2) Undue reinsurer market power (3) Inefficient corporate form for reinsurance13 (4) High frictional costs of reinsurance (5) Moral hazard and adverse selection at the insurer level14 (6) Regulatory interference15 (7) ex post third-party financing16 (8) Behavioral factors

12 By nearly any measure, reinsurance appears very expensive. One problem in measuring the cost of insurance, however, is that measurement requires some estimate of the actuarial value of the insurance. Given the limited historical data available on catastrophic losses, such estimates are automatically suspect. However, capital-market reactions to announcements of reinsurance contracts are often positive (viz. Berkshire Hathaway’s obtaining the reinsurance contract for earthquake losses in California), indicating that the market as a whole believes that the premiums collected substantially exceed what the market believes the actuarially expected loss to be [Froot, 1997]. Indeed, Berkshire uses its financial capacity to tremendous competitive advantage by emphasizing that it can guarantee access to reinsurance capital where other firms cannot. This may explain Berkshire’s strategic response (q.v.), which precluded the issuance of catastrophe bonds in California for earthquake risks, an event that would rob them of what they see as a very lucrative business. 13 Two reasons are possible: (1) Managers of reinsurance firms regard their capital as equity-based and thus require returns in excess of the riskless rate. Writing reinsurance policies for catastrophic risks at actuarially fair rates is seen as being against the shareholders’ interests. However, given the uncorrelated nature of those risks with most other financial assets (although Dong, Shah, and Wong [1996] question this claim, it is generally supported [Guy Carpenter & Co., 1997]), shareholders’ required returns on catastrophic risks should be low. Agency costs may be one factor forcing up required returns - a factor that would not be present in some other (non-corporate) organizational form. (2) Many reinsurers’ shares strongly covary with the general stock market. This would indicate that there exists some systematic risk that would demand compensation. 14 That would occur, for example, if insurers only ceded coverage of risks that they had reason to believe would be bad investments. If the original insurer didn’t want the risk, why would anyone else want it? 15 This does not explain the high prices for catastrophic reinsurance, but it does explain why so little of it is purchased. Froot [1997] uses the analogy of rent control: the only way for insurance companies to increase their profits is to cut expenses - such as reinsurance. Policyholders get what they pay for, because the cheaper insurance is also worth less (given that the firm has an increased likelihood of default). This shifts more of the burden to government insurance pools, financed by taxpayers. 16 This refers to the government compensating losses after the occurrence of some catastrophe, without receiving a premium in advance [Kunreuther, 1996].

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ACE Limited USAA CAT Limited

Principal $25 million $500 million $50 million

Coupon 6-Month T-bill + 550bp 1-Month LIBOR + 300bp 6.72%

Risk Period Last 5 months of 1996 8/96 to 7/97 Last 5 months of 1996

Trigger Level $25 billion industry loss $1 billion of firm losses $55 million of firm losses

Region Covered US US East Coast US Northeast

Risk Index PCS Company’s loss experience Company’s loss experience

Exhibit B: Three Examples of Early Catastrophe Bond Offerings Source: Lewis and Davis [1998]

The remainder of this paper examines catastrophic risk insurance financing through

the lens of behavioral factors, expanding on Froot’s eighth point and related accounts [e.g.,

Lewis and Davis, 1998] by drawing on general processes identified in the psychology of

investment and decision-making behavior. Section 3.2 further describes the insurance and

investment environment for securitization. Section 3.3 proposes that catastrophe bond

offerings cannot be sold at prices that insurance companies find acceptable unless they

address important behavior patterns. Section 3.4 proposes a market-level equilibration

hypothesis, namely that the current problems with catastrophe bond offerings are a function

of the novelty of the product and the psychology of market participants. Section 3.5

addresses tests of these hypotheses and concludes.

3.2 The PC Industry and the Nature of Catastrophic Risks

Although we assert in this paper that investor psychology plays a crucial role in the

market for catastrophic insurance risk, we certainly recognize that it is not the only factor.

There are several institutional and regulatory factors that also influence the development of

the market for securitized insurance risk and risk transfer products. In addition, because there

is likely to be interplay between investor psychology and institutional and regulatory factors,

it is important to comment briefly on the role such factors play in the overall problem.

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3.2.1 The Insurance Market

A. M. Best, an insurance industry research firm, tracks 2,430 property and casualty

insurers [Standard & Poor’s, 1997]. Together, they wrote $259.8 billion in premiums for

1995.17 Although several large players dominate the industry, particularly for catastrophic

risk policies, the industry is still so fragmented that they lack pricing power. In fact, price

pressure, the fragmented distribution of capital across firms, and the increasing needs for a

multinational presence are spurring consolidation in the industry [Standard & Poor’s, 1997].

In 1997, 91 PC mergers were announced [Wehrly and Friedheim, 1998]. However, Wehrly

and Friedheim [1998] predict that competition will continue to escalate, increasing the gap

between weak and strong companies.

One measure of the strength of an insurance company is its surplus or reserves,

relative to its exposures. As mentioned, maintaining sufficiently high reserves is

prohibitively expensive, from both an accounting and strategic standpoint [Helbling,

Fallegger, and Hill, 1996].18 Additionally, firms that write more catastrophic risk insurance

are also more likely to have insufficient capital and surplus [Cummins and Doherty, 1997].

Thus, although the industry as a whole appears to have sufficient capital for even very large

catastrophic losses, that capital cannot actually be “pooled” across firms. Securitization

could offer contingent access to capital, with firms paying for the option value of that capital,

rather than maintaining their own standing reserves.

17 Financial results for PC insurers are reported one year in arrears (hence, a 1997 publication reports the accounting results for fiscal year 1996, which rely, in turn, on 1995 earned premium data). Premiums collected in a given accounting period are not recognized as revenue until the following year. Until then, they are considered “unearned premium income” and are held in reserve against losses that might accrue during the interim period. The length of this “vesting” period varies around the world. 18 Standard accounting practice (U.S. GAAP, namely FASB 5) prohibits companies from keeping “hidden” reserves. As a result, firms must leave large amounts of capital uninvested in the core business. Despite the fact that such assets are “reserved” for (possibly distant) future losses, any earnings from this “non-investment capital” are fully taxable. From a strategic perspective, maintaining large amounts of cash or marketable securities on a balance sheet not only provokes the ire of shareholders (who want their funds invested more profitably), but also can attract the eye of other firms or corporate raiders interested in putting such capital to “better” use. Also, Jaffee and Russell [1997] note that the only potential tax benefits of setting aside reserves (tax-loss carryforwards and backward tax-code provisions) are worthless in the event the firm goes bankrupt under a catastrophic loss, which is precisely when they would be used.

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3.2.2 Regulation

As Klein [1997] notes, “insurance is perceived to be ‘vested with the public

interest.’” As a result, the PC insurance industry is subject to heavy government

involvement. Every state has an insurance commissioner (elected in thirteen), charged with

regulating the nature and premium level of coverage for firms operating in the state. State

and federal government institutions enforce entry and exit restrictions on firms (e.g.,

preventing non-insurance firms from indirectly restricting capital sources). They also limit

firms’ hedging behavior [Klein, 1997].

Such government intervention can impose costs on insurers and policyholders.

Penalva-Zuasti [1997] analyzed a simulated market for catastrophe bonds and earthquake

insurance in California and found that catastrophe bonds carried a 3.7% excess premium (in

1997) relative to estimated competitive prices. The implied efficient market prices were one

order of magnitude lower ($0.29 versus $3.29 per thousand dollars of coverage) than those

proposed by the California Earthquake Authority (CEA, a quasigovernmental agency).19 Not

only was CEA-sponsored insurance highly noncompetitive, but also catastrophe bonds

designed to improve market efficiency traded at a premium to competitive prices. Penalva-

Zuasti [1997] attributed this premium to the novelty of the product and to the “impact of the

highly regulated environment surrounding current insurance markets.”

3.2.3 Intra-Industry Competition

Santomero [quoted in Wharton Alumni Magazine, 1998] notes that insurers are

divided over such non-traditional methods of insurance coverage. For strong firms, with

sufficient capital to endure industry cycles, structured products such as cat bonds put

downward pressure on prices for catastrophic risk coverage, thereby reducing their profits.

For firms chronically short of capital, however, structured finance can strengthen their

19 Penalva-Zuasti [1997] estimated, for example, that for households living in earthquake risk-prone areas (mostly the Los Angeles and San Francisco basins), the average cost of full coverage (no deductible) was $0.29 per thousand dollars. The cost of the proposed CEA coverage (with a 15% deductible) was $3.29 per thousand dollars. Note also that the efficient rate ($0.29 per $1,000) is itself an overestimation of the cost of coverage, because it includes only households in risk-prone areas - not in the whole of California.

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balance sheets at a reasonable price. This is summarized by the view that “the strong thrive,

the weak issue cat bonds.”20 Access to capital is frequently used to competitive advantage

by strong, well-capitalized insurers.

Several firms, in fact, have attempted to thwart the issuance of catastrophe bonds.

For example, the California Earthquake Authority (CEA) decided to issue bonds after

concluding that catastrophe insurance offered by Berkshire Hathaway (through its National

Indemnity subsidiary) would be too costly. However, at the last minute, Berkshire

underwrote the entire issue for approximately $650 million [Osterland, 1998].21 In Berkshire

Hathaway’s 1997 Annual Report, Chairman Warren Buffett [1997] spelled out his dislike of

catastrophe bonds in terms of his perception of their exploitation of investor psychology:

“The second word in this term [catastrophe bonds], though, is an Orwellian misnomer: A true bond obliges the issuer to pay; these bonds, in effect, are contracts that lay a provisional promise to pay on the purchaser. . . . This convoluted agreement came into being because the promoters of the contracts wished to circumvent laws that prohibit the writing of insurance by entities that haven’t been licensed by the state. . . . A side benefit is that calling the insurance contract a ‘bond’ may also cause unsophisticated buyers to assume that these instruments involve far less risk than is actually the case. . . . The influx of ‘investor’ money into catastrophe bonds -- which may well live up to their name -- has caused super-cat prices to deteriorate materially. Therefore, we will write less business in 1998.” [emphasis added]

Although the premium for catastrophe bonds estimated by Penalva-Zuasti’s [1997]

model runs contrary to Buffett’s assertion, his opinions and actions carry considerable

weight. It is unclear whether his public disdain reflects a desire to preserve the market as is

or is, instead, the sort of strategic behavior described by Borch [1962] and others. The

20 In fact, the real value of securities such as these comes from the increase in debt capacity that they provide (allowing firms a larger tax benefit without proportionately larger expected bankruptcy costs). If firms had decided instead to issue conventional debt securities, the expected bankruptcy costs may have prevented them from borrowing at all. Thus, even with a higher interest rate, from a traditional corporate finance perspective, catastrophe bonds may be less expensive than equity. 21 The actual contract provides a fourth layer of coverage to the CEA. Berkshire Hathaway agreed to provide $1.5 billion in coverage at a cost of $161 million per year for four years. The CEA’s financing was structured such that, in addition to working capital, the first layer ($3 billion) was provided by assessments on insurers, the second layer ($2 billion) was provided by reinsurance contracts at a cost of $148 million per year under a two-year contract, the third layer ($1 billion) was provided by possible assessments on policyholders, and the fifth layer again by insurer assessments. It is noteworthy that the fourth layer (Berkshire’s coverage) is more costly than the second, even though it is less likely to be used [California Legislative Analyst’s Office, 1997].

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possibility of such behavior further complicates life for investors and issuers of such

securities, struggling to understand what they are buying or selling.

3.2.4 Definitions

Adam Smith [1776] noted that the insurance premium must compensate for the

expected losses, the expenses of insurer operation, and an appropriate profit on invested

capital. Most insured events happen with sufficient frequency to allow accurate estimates of

expected losses [e.g., Borch, 1969; 1990]. However, catastrophic losses come from

infrequent and unfamiliar events. As such, any model for predicting losses from them is

bound to be critically sensitive to the downside tail of the distributions of dollar losses. It is

precisely in those areas, however, that estimation is most difficult. Moreover, it encounters

the sorts of ambiguities that threaten the usefulness of forecasts [Fischhoff, 1994].

Estimating a probability distribution for “catastrophic events” requires a definition

of that term. Unfortunately, there is little standardization. Standard & Poor’s [1997] defines

a catastrophe as “an event or series of related events that causes insured losses of $5 million

or more.” Swiss Re [1996; 1997; 1998] defines a natural “catastrophe” as, “event caused by

natural forces. The following categories are used: flood, storm, earthquake (including

seaquake/tsunami), drought/bushfire/heat wave, cold/frost, and other (including hail and

avalanche).”

The Guy Carpenter Catastrophe Index (GCCI), used in many insurance-related

contracts (such as catastrophe derivatives), measures “atmospheric damage,” defined as

“hurricanes, tornadoes, windstorms, hail, and freezing temperatures.” It specifically

excludes all other perils, including fire, flood, lightning, earthquake, and riot. There is an

Event GCCI, for a single catastrophe, and an Aggregate GCCI, for a time period. This

method is used for all states except Texas [IndexCo, 1997]. The other major catastrophe

monitoring firm, PCS, defines a catastrophe as an “event resulting in excess of $5 million in

insured property damages and having an effect upon a large number of insurers and insured”

[Ray, 1993].

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Epstein [1996] describes the difficulty of defining “catastrophe” in a contractually

meaningful way. He notes that it must consider the risk relative to the pool of potential

insured individuals. It must determine whether to consider small, but highly correlated losses

(such as asbestos damage) as catastrophes. If it is specific enough to be contractually

satisfying, a definition may be too idiosyncratic to allow generalization. Epstein concludes

by defining a catastrophic event as one “capable of laying devastation to vast numbers of

individuals at a single blow.” However, even he leaves “devastation,” “vast numbers,” and

“single blow” undefined (see also Zeckhauser [1996]).

A workable definition of catastrophic losses must also treat “collateral” or

“collocation” damage, such as debris from a collapsed building damaging neighboring

buildings or fires in structures next to those hit by lightning [Dong, Shah, and Wong, 1996].

If a hurricane (considered a catastrophic event) caused damage that led to a fire (not

considered a catastrophic event), how would the composite event be classified? Whether

these losses are included may determine whether the total insurable loss passes the threshold

for qualifying as a catastrophic loss. A clear definition is essential to investors in catastrophe

bonds.

3.2.5 Estimating the Risks of Catastrophic Events

However defined, the expected losses from catastrophes must be estimated, even if

they do not happen often enough to establish a track record in the actuarial sense [Dong et

al., 1996]. To illustrate this difficulty, Exhibit C shows three years of catastrophic losses as

reflected in Swiss Re’s annual sigma research reports. They show the variability over even

this short period, including the impact of an unusual event, the January 17, 1995, earthquake

in Kobe, Japan. Swiss Re [1996] estimated insured losses at $2.5 billion, but total damage

at $82.4 billion. In contrast, EQE [1995], a catastrophe monitoring firm, estimated total Kobe

losses at $95–$147 billion, not including building contents (such as equipment and

inventory), and insured losses at $6 billion. By either estimate, a much smaller fraction of

losses was insured in Kobe than for equivalent American events. In the 1994 Northridge

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earthquake, $12.5 billion out of the total of approximately $20 billion in damage was insured

[EQE, 1994; U.S. Geological Survey, 1996]. Palm and Hodgson [1992] note similar

coverage rates for the 1989 Loma Prieta earthquake in California. Thus, uncertainty about

current coverage rates further complicate evaluating cat bonds, not to mention possible

future changes.

Exhibit C: Natural Catastrophes in 1995, 1996, and 1997

The dollar figures of these loss estimates are reported in the dollars of the year of the loss, unadjusted for inflation, and converted to U.S. dollars at the time of the loss (using the appropriate market or official exchange rate).

Although it has improved significantly over the past twenty years, the reporting

method for catastrophes still creates uncertainty for investors. Changes in the dollar value or

number of losses may reflect changes in reporting practices (e.g., pressure to reduce

fraudulent claims) as well as changes in the world. Furthermore, Property Claims Services

(PCS), the organization which estimates catastrophe losses, “does not release exact figures

in order to prevent their use by unauthorized third parties.” As a result, even Swiss Re obtains

the insured loss figures from PCS only within relatively wide ranges: the 1998 sigma report

includes the ranges $25 to $100 million and $101 to $300 million. These uncertainties

compound the inherent problems of estimating the probabilities and consequences of

catastrophic events causing catastrophes.

The frequency distributions of past catastrophic natural events are often well-

documented, with future estimates being further refined using basic science. For example,

1995 1996 1997 Total 1995 1996 1997 Total 1995 1996 1997 Total

Floods 45 44 478 567 5,835 6,853 4,950 17,638 $367 $233 $1,420 $2,021Storms 47 50 42 139 3,826 5,385 5,315 14,526 $7,452 $5,252 $2,460 $15,165

Earthquakes 13 8 16 37 8,406 544 2,878 11,828 $2,472 $0 $12 $2,484Drought, bushfires

8 7 5 20 1,452 97 667 2,216 $0 $0 $0 $0

Cold, frost 7 10 7 24 421 779 417 1,617 $536 $2,360 $168 $3,064Other 7 10 1 18 305 292 157 754 $1,602 $61 $80 $1,742

Total 127 129 549 805 20,245 13,950 14,384 48,579 $12,429 $7,906 $4,141 $24,475

Number of Events VictimsInsured Losses

(in millions)

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there is a great deal of (physical) understanding22 of the ENSO (El Niño/Southern

Oscillation) phenomenon which has been described (Zebiak and Cane, 1998) as “second

only to the seasons themselves in driving worldwide weather patterns.” The U.S. Geological

Survey [Michael et al., 1996] notes that “[a]lthough quake forecasting is still maturing, it is

now reliable enough to make official earthquake warnings possible.” Nonetheless,

catastrophic events fall in the tails of these distributions, hence are the least predictable.

Furthermore, predictions often lack the spatial resolution needed by insurers of specific

properties. For example, Gray et al. [1998] caution readers of their hurricane forecasts that

“landfall probability estimates at any one location along the coast are very low . . . no matter

how active an individual season is.” Michael et al. [1996] voice similar warnings concerning

earthquake forecasts.

Estimating the consequences of these events requires understanding a complex web

of related events. Flooding causes landslides, earthquakes cause fires, winter storms often

lead to flooding, and so on [Swiss Re, 1996]. As mentioned, the available information is

disproportionately in the hands of the insurers. That imbalance is a barrier to investors, even

if they realize that the insurers themselves lack confidence in what they know.

Paradoxically, insurers may also avoid situations where their information is

sufficiently good that they could be held legally responsible for model errors. For example,

the State of Florida spent $1 million on certifying models of catastrophic exposure as

scientifically valid. Nonetheless, Florida’s Insurance Commissioner refused to use the

certified models and filed legal action to block state adoption of them [Florida Department

of Insurance, 1997]. Although other models (such as EQECAT’s USWINDTM and E. W.

Blanch’s Catalyst 3.0) have been certified by Florida [e.g., EQECAT, 1998; Property and

Casualty Online, 1998], regulators are still reluctant to use catastrophe models [Kibbee,

1997]. Katten [1997] writes “to a great extent, catastrophe modeling, while a useful tool, has

caused an unnecessary paranoia that adversely affects the market.”

22 For example, Gray et al. [1998] reported correlations of predictions of number of named storms of between r = 0.65 and r = 0.85 over the past 25 years.

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3.3 Structure of Catastrophe Bonds

A cat bond is typically structured as a conventional corporate bond with an embedded

option. Other securities share this basic structure (e.g., convertible bonds, mortgage-backed

bonds, and even U.S. Savings Bonds).23 Lewis and Davis [1998] describe the 18 securities

offerings incorporating catastrophic risk exposure issued to that date. These 18 securities

have three common structures (see Exhibit A): (a) contingent surplus notes (CSNs), (b)

CatEPuts, and (c) catastrophe bonds. In addition to these structures, there was also the unique

St. Paul Re Pro Rata bond which will be described in detail in Section 3.4. CSNs are fully-

collateralized securities. The issuing insurance firm invests the proceeds of the offering in

Treasury securities. If a catastrophic event occurs, the insurance firm can substitute its own

corporate bonds for the Treasury bonds (effectively issuing debt at a prearranged price).

Investors receive the interest from the Treasury securities plus the premium (paid as yield)

for selling to the issuers the option to substitute its own debt. Exhibit D (adapted from Lewis

and Davis [1998]) illustrates the structure of CSN cash flows.

Exhibit D: Contingent Surplus Note (CSN) Cash Flow Structure

23 Convertible bonds obviously have the option (which belongs to either the issuer or the investor) of converting (into equity). Mortgages and mortgage-backed bonds typically have the option of prepayment. Savings bonds have the embedded option to extend the maturity of the bond or cash out early at a predetermined rate.

Treasury Security Collateral Pool

Principal

P&I

P&I, Option Premium

Principal

Trust

Investor

Insurer

Option Premium

"Substitutability" Put Option

3-16

CatEPuts, a contraction of Catastrophic Equity Puts, allow insurance firms to “put”

or sell new equity (in contrast to the new debt provided by CSNs) to investors at a

prearranged price, if a catastrophe occurs [Jewett, 1997]. This new equity typically takes the

form of newly issued shares (thereby diluting earnings for pre-existing shares). These

CatEPuts are a basic option transaction: the insurer pays a premium to investors in return for

the right to put its own shares to them should a catastrophic loss occur.

Cat bonds typically involve a standard corporate bond with a provision for reducing

its principal or interest (or both) in the event of a catastrophic loss. Thus, they provide capital

(or reduced debt) to the issuer when it is needed most. There are two classes of cat bonds:

indemnity cat bonds and index (or recapitalization) cat bonds. Indemnity bonds base contract

threshold payouts on the issuer’s own loss experience. Index-based catastrophe bonds use

indices such as PCS and GCCI (see Exhibits E and F). Using indices encourages a liquid

market in the bonds, but increases basis risk (insofar as the indices deviate from the issuer’s

actual loss exposure). Cat bonds were not issued until 1996, despite years of intense interest.

Even then, they have been hampered by lack of standardization in both the structure of the

bonds and the reference indices [Lewis and Davis, 1998]. (Exhibit B illustrated differences

in three early catastrophe bond offerings.) As a result, securities based on one index can only

be imperfectly substituted for securities based on the other, introducing additional basis risk.

Catastrophe derivatives address some of these liquidity problems. Although they can

be used for risk management in isolation, they are more frequently embedded in other

securities and contracts. The Chicago Board of Trade (CBOT) now makes a market in both

futures and options for which the underlying asset is catastrophic insurance risk in various

regions of the United States [CBOT, 1998].

These securities can be classified in terms of their relative exposure to moral hazard,

credit risk, and basis risk. For example, although reinsurance has a low risk of moral-hazard

problems, it carries a high credit risk. Index-based cat bonds have a low credit risk, but carry

substantial basis risk. Moral hazard refers to the possibility that purchasing an insurance

contract may change firms’ behavior. Reinsurance has greater moral hazard than CBOT

3-17

derivatives because the losses are more exactly matched to the exposure (compared to the

index-based derivatives). Issuers left with residual risk (as a result of the imperfect hedge)

have a greater incentive to reduce such risks.

Features PCS sigma RMS GCCI

Geographic Area

State Country ZIP code ZIP code

Insured Property

All major lines All lines All major lines Homeowners

Perils All significant perils

All perils Earthquakes and hurricanes

Hurricanes, hailstorms, tornadoes, thunderstorms, winter storms, and freezing conditions

Index Value Dollars of loss Dollars of loss Dollars of loss Paid loss-to-insured value ratio

Source of Estimate

Insurer survey, computer model, and ground survey

News and other sources

Computer model 39 companies’ insurance and paid loss records

Other Information Provided

None Number of casualties

None Premiums, deductibles, amounts of insurance, claim counts, paid losses, and construction types

Published 3 to 5 days after event, updated as necessary

Annually 7 days after event, with final value after 28 days

Quarterly

Exhibit E: Catastrophe Insurance Index Basis Comparisons

Source: Thomas [1997]

3-18

GCCI Regions PCS Regions Differences

National 50 States and DC National 50 States and DC -

Northeast CT, DE, DC, ME, MD, MA, NH, NJ, NY, PA, RI, VT, WV

Northeastern ME, NH, VT, MA, CT, RI, NY, NJ, PA, DE, MD (and DC)

WV

Southeast FL, GA, NC, SC, VA Southeastern VA, WV, NC, SC, GA, FL, AL, MS, LA

WV, AL, MS, LA

Gulf AL, AR, FL, LA, MS Eastern ME, NH, VT, MA, CT, RI, NY, NJ, PA, DE, MD (and DC), VA, WV, NC, SC, GA, FL, AL, MS, LA

Not comparable

Midwest /West

AZ, CA, CO, ID, IL, IN, IA, KS, KY, MI, MN, MO, MT, NE, NV, NM, ND, OH, OK, OR, SD, TN, UT, WA, WI, WY

Midwestern OK, AR, TN, KY, OH, MI, IN, IL, WI, MN, ND, SD, IA, NE, KS, MO

AR, AK, and HI are not included by GCCI

Western HI, AK, WA, OR, CA, NV, AZ, NM, UT, CO, WY, MT, ID

Florida FL Florida FL -

Texas TX Texas TX -

California CA GCCI does not offer isolated CA coverage

Exhibit F: GCCI versus PCS Coverage in Index-based Contracts

Source: IndexCo [1997]; Chicago Board of Trade [1998]

If the components of a structured product have liquid markets, then the composite

should trade at parity with the market value of those components. If not, then arbitrage is

possible. The conventional approach to pricing complex or “exotic” securities is to replicate

their cash flow streams with simpler securities that are easier to price [Black and Scholes,

1973]. Thus, the value of a cat bond equals the sum of the values of its constituent

components: a corporate bond and an option. The theories for evaluating both corporate

bonds [e.g., Fabozzi and Fabozzi, 1995] and options [e.g., Hull, 1993] are widely known.

Such arbitrage-supported replication presupposes: (1) that investors approach the valuation

of all securities identically (e.g., in estimating volatility) and (2) that the building blocks

needed to construct the replicating portfolio exist. Should the true value of a security, such

as a cat bond, not be preserved through such arbitrage bounds, investors’ perceptions of that

true value become a relevant factor in the pricing of such securities.

3-19

3.4 Human Behavior and Catastrophe Bonds

Following Olsen [1998] and Froot [1997], we consider how individuals might

perform the cognitively complex task of evaluating such investment products. Depending

on the circumstances, these processes could lead investors to overvalue, undervalue, or

refuse to value these offerings. Exhibit G briefly summarized eight phenomena and their

predicted impact on the market for catastrophe bonds.

Our analyses extrapolate from the research literature of behavioral decision making

to a domain in which no direct studies have been conducted. One constraint on such

extrapolation is that most behavioral decision-making studies have been conducted on

individuals without the financial experience of potential cat-security investors. Currently,

individual investors have no (direct) access to the market for these securities, which, for

regulatory reasons, is limited to institutional investors. Moreover, even these institutional

investors must be licensed to sell insurance by state insurance regulators before they can

transact in the catastrophe bond market [Klein, 1997]. However, the absence of arbitrage-

based pricing models means that these experts must rely on their own judgment. One would

like to believe that (1) experts can avoid mistakes on tasks central to their expertise and (2)

the stakes would motivate them to do so. Unfortunately, there is enough evidence of

imperfect expert judgment to allow the possibility for suboptimal choices in these novel,

difficult, and consequential tasks [e.g., Dawes, 1988; Dawes, Faust, and Meehl, 1989;

Mowen, 1994; Thaler, 1994; Kammen and Hassenzahl, 1999].

3-20

Stylized Facts About Human Decision Making

Features of Catastrophe Bonds

Implications for the Catastrophe-Bond Market

Understanding Facts of Transaction

Cognitively-constrained individuals tend to resort to sub-optimal heuristic decision rules in new and complex environments

Past catastrophe bond offerings have often exhibited very complex structures making hedging and comprehension difficult

May limit market depth if investors are “overwhelmed.” Those who stay may require higher returns as compensation for learning costs

Exaggerated comprehensiveness; individuals tend to overestimate the completeness of their pictures of complex problems

Catastrophe bonds are linked to insurance portfolios of the issuing firms that involve very complicated risk structures and events which are difficult to forecast

Investors (and issuers) may inaccurately estimate risks and thus costs, leading to different expectations of what an appropriate return would be

Illusion of control; the perception of risk varies inversely with the perception of control

Catastrophic events are frequently viewed as “acts of God”

Investors (and issuers) may inaccurately estimate risks and thus costs

Reliance on availability; the likelihood of highly available or vivid events tends to be overestimated

Catastrophic events are infrequent and dramatic

Investors (and issuers) may overestimate risks, and thus costs

Understanding Relevant Values

Small probabilities are overweighted Catastrophic events are, by their nature, very infrequent

Investors (and issuers) may overestimate risks, and thus costs

Violations of extensionality; the structure of a decision problem often influences individuals’ judgments.

Catastrophe bonds have features of both debt and equity, as well as the contingent exposure of options

Inability to think about cat investments with a pre-existing schema raises the cost of entering the market, inhibiting liquidity and increasing required returns

Dimensions of Risk

Individuals often perceive and react to differences between psychological and actuarial perceptions of risk

Events that have an actuarial nature to the firm have a visceral impact on individuals

Investors may be pricing (attaching value to) features of risks that are ignored by traditional financial theory

Asymmetric Information

Individuals tend to improperly weight different pieces of information; aversion to the risks of asymmetric information

Vast resources and the ability to collect primary data provide a substantial informational advantage to insurers

Liquidity of market is substantially constrained

Exhibit G: Behavioral Anomalies and Implications for Catastrophe Bonds

3-21

3.4.1 Cognitive Complexity

There are cognitive limits to individuals’ ability to function effectively in complex

decision-making environments [Simon et al., 1987]. Even where financial theory can distill

a problem to cash-flow streams, people often cannot. Instead, they rely on heuristic

reasoning and “automated” rule-based responses [Newell and Simon, 1972; Cross, 1983;

Albers and Laing, 1991; Becker, 1993]. In financial thinking, Neftci [1991] has

characterized reliance on technical analysis (essentially a collection of heuristic decision

rules) among experienced market participants as showing the pervasiveness of rule-based

decision processes.24

As a result, it would not be surprising to find, as observed by Lewis and Davis [1998],

that “investors sent a clear message to the insurance industry - complexity is a liability,”

after St. Paul Re placed only $68.5 million of $204 million in pro rata capital notes. The St.

Paul Re security, as depicted in Exhibit H, was remarkably complicated. It involved not only

St. Paul Re, but also two special purpose reinsurers (SPRs) created specifically for the deal,

a swap transaction, and two distinct collateral accounts. The pro rata capital notes combined

debt issuance with participation in returns on the reinsurance provided to St. Paul Re, which

was also to cede reinsurance business from five excess-of-loss classes, on a proportional

basis, in two pre-specified layers that adjust over time to reflect claims experience [Lewis

and Davis, 1998]. The bonds also offered options on two Class B St. Paul Re common shares

per $1 million in invested principal. This structure was actually intended to offer additional

protection for investors and, thus, make the bonds more desirable. However, the complexity

and attendant uncertainty over hidden risks overwhelmed investors.

24 Schwager [1992] contains the transcripts of interviews with several professional traders and investment managers. These interviews frequently include long discussions about the value of technical analysis, ex post rationalization of trading strategies, and descriptions of the use of visceral factors or “gut” instincts in making investment decisions—decisions frequently involving tens and hundreds of millions of dollars. It is important to note that even those traders who claimed not to “believe” in technical analysis personally still paid attention to technical trading statistics “because other traders use them.” One trader said the following of his trading system: “There was no system to it. It was nothing more than, ‘I think the market is going up, so I’m going to buy.’ ‘It’s gone up enough, so I’m going to sell.’ It was completely impulsive. I didn’t sit down and formulate any trading plan. I don’t know where the intuition comes from, and there are times when it goes away.”

3-22

Exhibit H: The St. Paul Re Pro Rata Capital Note Cash-Flow Structure Source: Lewis and Davis [1998]

In addition to prompting rule-based rejection, complexity can increase rational

rejection by accentuating investors’ informational disadvantage [Duffie and Rahi, 1995].

Investors must understand the relations in Exhibit H, track the various cash-flow streams,

and then evaluate the probabilities of different outcomes. They must do this well enough to

identify and hedge all sources of risk in the security. Here, that includes not only the risk of

catastrophic loss, but also (1) the counterparty risk of the swap, (2) the tax, accounting, legal,

and regulatory risks of the SPRs, including their offshore (UK) foreign-exchange risks, (3)

the interest rate risk of the zero-coupon securities held in the collateral account, (4) the basis

risk and moral hazard attached to the insurance contract itself, the correlations among these

risks, and possibly many others. At each stage, St. Paul Re is ahead of the investors. It may

just not be worth the transaction costs of catching up.

SwapCounterparty

Investor

Fixed Rate

Floating Rate

$204 millionAvailable Net Income

$204 - $304 million

$204 millionat maturity

$104 million

Reinsurance

Net Income

$100 millionSecurityInterest

Available NetIncome andCompanyExpense

Coverage LimitLimited to Value ofCollateral Account

St. Paul ReUK, plc

Collateral Account

Georgetown Re, Ltd.

10-Year Zero CouponAgency Securities

3-23

3.4.2 Exaggerated Comprehensiveness

Scholes [1996] criticized stock market and accounting regulators for failing to see

the “big picture” of corporate risk-management needs. He pointed specifically at regulators

limiting the use of derivatives in hedging, even when two highly volatile instruments should

hedge one another, thereby reducing overall risk. If his claim is correct, then such behavior

would be a special case of the general tendency to overestimate the completeness of one’s

picture of complex problems [Fischhoff, Slovic, and Lichtenstein, 1978], one source of the

overconfidence that has been found with many difficult tasks [Yates and Stone, 1992].

Such exaggeration could also cause those who do invest in catastrophe bonds to

overlook the risks involved. If their investments fare surprisingly poorly, then they may be

dissuaded from such investments, not understanding just what went wrong. For example,

they might not realize the full implications of a catastrophic event on the issuing firm, such

as the interconnectedness of losses when a hurricane causes landslides, strikes two insured

locations, or triggers associated health and life insurance-related claims. Such possibilities

can reduce a catastrophe bond’s value both by increasing the chances of triggering the

embedded option and by diminishing the issuing firm’s financial capacity.

3.4.3 Illusion of Control

Olsen [1998] summarizes financial evidence of the general phenomenon of people

exaggerating their control over uncertain events, leading, in turn, to underestimating risks.

In a classic study, subjects playing a game of pure chance were more aggressive with an

opponent who appeared naive than with one who appeared sophisticated [Langer, 1975].

The novelty of these securities, highlighted by the term “Act of God” bonds (used by USAA)

may have allowed little room for illusions of control. Inexperienced investors have had little

chance to develop heuristics or confidence needed to convince themselves that they could

beat the averages. If so, then, ironically, the success of these securities may have been limited

by their inability to take advantages of natural biases.

3-24

3.4.4 Reliance on Availability

Tversky and Kahneman [1973] proposed that, when individuals do not know the

frequency or probability of an event, they judge its frequency by its availability to memory.

Although often helpful, this heuristic can exaggerate the likelihood of disproportionately

salient events. For example, Lichtenstein et al. [1978] and also Combs and Slovic [1979]

found that subjects overestimated the frequency of deaths from relatively publicized causes

(e.g., tornadoes and floods), while underestimating the frequency of deaths from less visible

ones (e.g., cancer or heart disease). Potential investors in catastrophe bonds must assess the

probability of adverse events. Unless they accept the modelers’ claims, they must rely on

their own judgments. If catastrophes are disproportionately available, then investors will

overestimate their probability. If so, then investors would demand greater compensation for

bearing these risks than insurers, relying on model estimates, see reason to pay.

3.4.5 Overweighting Small Probabilities

According to prospect theory’s decision weighting function, people pay undue

attention to small probabilities, above and beyond any errors in their estimation (e.g., due to

availability). As statistically rare events, catastrophes might receive such weighting (above

and beyond any tendency to misjudge their probabilities). For example, Kahneman and

Tversky [1979] had subjects choose between a sure loss of $5 and a 0.001 chance at losing

$5,000. Of 72 respondents, 83% preferred the sure loss, even though the two options had the

same expected value. One in a thousand (0.001) is a plausible probability for catastrophe

bonds to exceed the preset threshold and trigger the embedded option payout leading to loss

of principal.25 In a normative pricing model, this small probability would imply a

comparably small premium. A prospect theory weighting function would lead investors to

overweight that admittedly small probability of loss and, thus, demand a higher return.

25 No catastrophe bond (including all securities in Exhibit A) had ever (as of 1999) had its loss threshold triggered yet. Even events the magnitude of the recent Hurricane Floyd have failed to generate losses for cat-bond investors. One analyst noted “everyone’s been wondering what will the capital markets do when there is a real loss” [Wall Street Journal, September 15, 1999].

3-25

Prospect theory’s probability weighting function is discontinuous at the endpoints,

with very small or large probabilities rounded to certainty. Thus, investors who saw the

probability fall below a certain threshold might treat cat bonds as risk free. However, that

would mean ignoring the whole point of the bonds. Rather, it seems likely that some small

overweighted probability would remain.

3.4.6 Violations of Extensionality

Psychologists have long known how formally equivalent ways of describing the

same tasks can affect people’s choices [Turner and Martin, 1984; Poulton, 1989; Fischhoff,

1991; Schwarz, 1999]. Tversky and Kahneman’s [1981] prospect theory provided an

integrated account of such effects, cast in terms of rational actor models. For example, they

showed that patients are less likely to choose surgery framed in terms of the probability of

death rather than the complementary probability of surviving.

In an ideal world, investors would analyze securities on their own merits, in terms of

first principles of finance. However, in fact, they are often trained to analyze types of

investments: bonds, stocks, options, etc. Thus, standard textbooks [e.g., Bodie, Kane, and

Marcus, 1993; Sears and Trennepohl, 1993] discuss the pricing and trading of fixed income

securities, corporate equities, and derivatives in distinct sections, with little overlap. Only

advanced books, directed toward more mathematically-sophisticated audiences [e.g., Park

and Sharp-Bette, 1990; Luenberger, 1998], focus on evaluating pure risky cash-flow

streams.

Although called catastrophe bonds, these securities’ exposure to the equity of the

insurance firm (as subordinated, unsecured debt) means that they also can behave like equity.

However, they are not really equity because they have no ownership interest in the firm.

Exhibit I summarizes ways in which cat bonds exhibit both bond and stock behavior. An

investor using heuristic rules for either bonds or stocks would miss vital features unique to

this hybrid asset class, or erroneously assume features not actually found in catastrophe

bonds. An investor who realized that neither frame of reference worked entirely might shy

3-26

away from the investment, not knowing how to think about it. Consider, for example, an

investor who thought of catastrophe bonds as traditional fixed-income securities. Redeeming

a traditional bond below par means that the issuer was in such poor financial health that it

cannot make full repayment. However, with catastrophe bonds, below-par redemption

reflects the occurrence of a catastrophe. The firm might actually be stronger financially

because the cat bond reduced its exposure.

Characteristic Traditional Corporate Bonds

Common Equity Catastrophe Bonds

Type of Return Fixed, known return “Random” return Partially fixed, partially random, contingent on catastrophe

Ability to Hedge Payoff

Certain, hedgable payoff; liquid markets

Hedgable payoff; liquid markets

Contingent payoff; illiquid markets for hedging; imperfect ability to hedge (basis risk)

Performance Model

Known distribution (lognormal)

Generally known distribution (normal, lognormal)

Discrete, low-frequency data; distribution not precisely known and subject to change

Certainty of Payoff

Unequivocal payoff determination

Unequivocal payoff determination

“Event” definition varies widely between indices and issuers

Default Claims Hierarchy, Managerial Interests

Secured/Guaranteed; Top-tier; No managerial interest

Lowest priority, but managerial discretion

Top-tier structure and appearance, but most are subordinated; no managerial discretion

Risk in the Context of the Firm

Moderate correlated risk

Moderate correlated risk

High correlation risk: ability to repay weakest precisely when catastrophe depresses the bond price (because of the embedded option)

Exhibit I: Comparing and Contrasting Catastrophe Bonds with Conventional Securities

When cat bonds trade below par, it indicates high expected losses that will be paid by the

bondholders. Without paying significant transaction costs, investors may be unable to

decode the unique nature of these securities, adding to their cost, confusion, and chance of

poor choices [Allen and Gale, 1994].

3-27

3.4.7 Dimensions of Risk

The Capital Asset Pricing Models (CAPMs) of Sharpe [1964], Lintner [1965], and

Mossin [1966] state that investors should only be compensated for bearing systematic (or

undiversifiable, market) risk. The psychological literature indicates, however, that

individuals often have rather different notions of risk. In early work, Slovic [1964] found

that perceived risk could not be measured by a single index, noting that a “large amount of

evidence bearing on the convergent validity of [methods assessing risk-taking propensity] is

negative.” As complicating factors, he pointed to emotional arousal and cognitive concerns

outside of classical financial theory.

One common approach to studying the multidimensional character of perceived risk

is to have subjects judge the riskiness of activities along dimensions like those in Fischhoff

et al. [1978]. Factor analyses of these judgments typically find that two factors explain much

of the variance in subjects’ judgments: Unknown risk measures the extent to which potential

effects are delayed, unobservable, new, and unknown to science. Dread risk measures the

extent to which the activity is seen as uncontrollable, inequitable, involuntary, catastrophic,

or potentially fatal [Slovic, 1987; Jenni, 1997]. Slovic et al. [1984] found that, other things

being equal, people are more inclined to accept chronic risks (e.g., auto accidents) than

catastrophic ones (e.g., accidents involving nuclear power), and are particularly averse to

ones evoking a feeling of dread.

Although cat bonds (and the like) have not been studied in these terms, some

speculation seems possible. The dramatic, unpredictable nature of catastrophes may create a

visceral response among investors afraid of losing much (or all) of their investments, perhaps

akin to the feeling of dread in these studies of life-threatening risks. Investors might want

compensation for such feelings, even if they officially subscribe to normative asset pricing

models.

Within those models, expected return might be related to dread risk while variance

captures some of unknown risk. Higher moments might play a role as well, with skewness

3-28

capturing some of dread risk and kurtosis related to unknown risk, in the sense of the

prevalence of extreme (tail) events. However, Payne [1973] found that the moments were

“unacceptable as variables for the theory of risky decision making” because the interactions

terms could not be independently estimated in real-life choices. Coombs and Lehner [1981]

reached the same conclusion for experiments. Preferences over higher-order and partial

moments have been extensively studied in finance [Hogan and Warren, 1974; Kraus and

Litzenberger, 1976; Bawa and Lindenberg, 1977; Fishburn, 1977; Holthausen, 1984; Sortino

and van der Meer, 1991], with mostly disappointing results. Sharpe [1964] found that partial

moments (semivariance) seemed to provide a better fit to the observed data, but rejected

them because of computational complexity that continues to make them impractical for real-

time use. Thus, formal financial models ignore these features, so central to the experience of

risk.

3.4.8 Asymmetric Information

Asymmetric information (as illustrated by Akerlof [1970]) is particularly important

in insurance and risk transfer [Nachman and Noe, 1994]. “Given the potential for adverse

selection […] we might expect markets to collapse if the issuer’s information is sufficiently

large relative to that of potential investors” [Duffie and Rahi, 1995, p. 2]. As mentioned,

such asymmetry exists with catastrophic information, which the insurers both collect and

disseminate. As a result, insurers hoping to create a market should provide as much

information as possible to potential investors, at minimal cost.

Credible communication is particularly important when there seem to be incentives

for strategic reporting. For example, the loss threshold for many early catastrophe bonds

(e.g., the USAA and CAT Limited issues) depended on the issuing firm’s own loss estimates.

Such informational disadvantages could further discourage investors and increase demands

for risk premiums.

3-29

3.5 Market Equilibration

Securities linked to catastrophic risks challenge investors to perform tasks that

research has shown to seem and be difficult, as well as creating mismatches between the

perspectives of investors and issuers. As a result, individuals may shun the market altogether

or perform poorly in it, thereby discouraging future investments. Such discomfort

characterizes many new markets, until investors become more familiar with them. Then,

trading volume and liquidity increase, and prices move towards an equilibrium. Whether this

happens depends on whether investors merely need time and information to understand a

market, or if they need fundamental help with comprehension and debiasing. The issues

raised here suggest there exist barriers to the learning process for cat securities capable of

preventing them from ever leading to a stable and optimal equilibrium. In a situation too

novel to allow immediate comprehension and too complex to allow trial-and-error learning,

the “invisible hand” may be stilled.

3.5.1 Immature Market Structure

Pricing inefficiencies are eliminated most reliably in liquid markets with many active

traders and prompt delivery of detailed, accurate information. Even though neither element

is present in the current market for catastrophe reinsurance-based products, Chichilnisky and

Heal [1998] state confidently that because the “underlying pressure [from insurers to tap

new capital] is relentless,” securitized offerings will eventually predominate.

Swiss Re [1996] makes similar claims, citing parallels to the securitization process

in the banking sector. When the worldwide debt crisis of the early 1980s constrained

commercial lending capacity, direct issuance of securities increasingly complemented and

partly substituted for traditional corporate financing. Trading in U.S. Treasury futures, often

considered the most successful financial innovation in recent memory, began in 1977, but

took 15 years to reach its current volume. Swiss Re’s [1996] projections (Exhibit J) assume

similar market growth for cat bonds.26

26 Although volume in the Treasury futures market continues to grow over time, recent growth levels are much lower than in earlier periods. In fact, the logistic curve tends to provide a good model of development, as

3-30

Exhibit J: Development Scenario for ART Products Source: Swiss Re [1996]

One potential flaw in this analogy is that most investors had investment experience

with Treasury bonds long before Treasury futures were introduced. The same cannot be said

for cat bonds, which were specifically created to access a new capital market. Thus, rather

than “repackaging” an existing product, cat bonds are entirely new for most investors.

Resolving pricing inefficiencies in the cat-bond market and increasing liquidity could take

more time, perhaps even longer than issuers will be willing to tolerate

3.5.2 A Dual Equilibrium

One obstacle to acceptance is a liquidity “Catch-22”: the risk characteristics of

insurance-related securities should be attractive to many investors, but only if they can sell

them, should the need arise. However, the limited liquidity of the cat-bond market

growth rates eventually slow once a market becomes saturated. At this point, further growth is limited by the growth rate of the market itself. Swiss Re developed its projections for cat-bond market development by modeling catastrophic insurance risk as an asset class and determining its weight in an optimally diversified portfolio. This figure determined the maximum possible market share and it was then assumed that market penetration would proceed according to a standard logistic-shaped development cycle.

$0

$5

$10

$15

$20

$25

$30

$35

$40

1992 1995 1998 2001 2004 2007 2010

Bill

ions

of D

olla

rs

Year

New Cat Capacity via Derivative ExchangesNew Cat Capacity via SecuritizationTotal Alternative Cat Capacity

3-31

invalidates standard no-arbitrage arguments and models. At the extreme, the market value

of a security with no liquidity is zero, regardless of what some pricing model claims.

Silverman, Sparks, and Osterland [1998] point to an “illusion of liquidity” in the

securitization market: “[j]ust because an asset is tradable today doesn’t mean it will be

tradable tomorrow.” Without liquidity, traders lack the prices needed to use their models.

Without traders, there is, in turn, no liquidity.

Embrechts [1996] identifies an unfortunate “dual equilibrium”: investors are either

all in or all out of the market.27 Given the abundance of other investments, it is easy enough

simply to go elsewhere with one’s money. One barrier that the issuers are trying to reduce is

the lack of hedging instruments needed by investors pursuing analytical strategies. Indeed,

some progress is being made in developing securities usable for hedging cat bonds (e.g.,

exchange-traded catastrophe options). However, there is still too much variability in the

structure of these different options and too little volume in those markets to cover any sizable

risks. The idiosyncratic structure of most cat-bond offerings makes general hedging

instruments hard to create.

Economides [1995] notes that in financial exchange markets, high liquidity is a

positive externality: it increases the willingness of all participants to trade and is provided to

traders without cost. Economides [1992; 1993; 1995] has demonstrated that any degree of

participation in a market can be sustained as an equilibrium, including none at all. Of course,

equilibria involving greater participation are more beneficial to those trying to create a model

(e.g., insurers and, ultimately, those purchasing insurance).

Embrechts [1995] proposes an institutional approach to inducing participation,

whose details depend on the design of the security in question. According to his analysis,

investor behavior will affect prices (and participation) as long as strict arbitrage bounds are

unavailable. Unless investors can understand securities appropriately, there will be no

externalities, and markets will remain at a low-liquidity equilibrium. Federal Reserve

27 This would explain the “logistic” shape of the product development/market saturation curves: slow initial acceptance → sudden, broad acceptance → sustained tapering off as saturation occurs.

3-32

Chairman Greenspan was quoted as saying “market discipline appears far more draconian

and less forgiving than 20 or 30 years ago. Capital, in times of stress . . . flees more readily

to securities and markets of unquestioned [emphasis added] quality” [Wall Street Journal,

1998]. Thus, while securitization can provide new sources of capital, it can also make the

availability of that capital more volatile.

3.6 Conclusions and Implications for Securities Design

Insurers have an enormous interest in tapping capital markets by securitizing

catastrophic insurance risk. Additional capital could help to cover future losses that

potentially run in the hundreds of billions of dollars. Creating a market for catastrophic risk

would repeat the successes securitization has enjoyed with other cash flows.

In other markets, the required equilibration process involves merely allowing

investors to adjust to new information. However, with significantly novel products like

catastrophic risk, that may never happen because investors are often constrained in their

ability to understand and process the necessary information as it is commonly found. With

vast, complex, and interconnected sources of uncertainty, new schemata might not be created

and existing ones may be misused.

We outlined eight well-known behavioral decision-making results, suggesting how

they might affect investor behavior in this arena. When investors cannot muster proper

information use, they generally resort to heuristic decision making, attempting to use

“similar” schemata to tackle new problems. Unfortunately, such decision making can result

in errors of sufficient magnitude to prevent widespread participation in such new markets.

For example, Bantwal and Kunreuther [2000], building, in part, on an earlier version of this

paper, illustrate how suboptimal decision-making processes could lead to an excessive risk

premium for cat bonds. These processes are likely to play a role in the securitization of any

significantly new (to investors) cash-flow stream, not just cat bonds.

3-33

This analysis is but the beginning of the research process. The next step is to evaluate

these hypotheses in the actual market for catastrophic insurance risk (or analogous novel

securities). Once the contours of these problems are better understood, methods of solving

them must be developed. Our account suggests that widespread acceptance will require

limiting new offerings to relatively simple and standardized products. These will provide

investors with a common and cognitively tractable schema for thinking about the nature of

their investments. That way, they can focus their attentions on the still challenging task of

understanding the world of catastrophes. The design of new securities merits consideration

of human behavior equivalent to that devoted to the design and marketing of consumer

products.

3.7 Epilogue

In the time that has elapsed since this paper was published, the cat bond market has

undergone significant change. Issuance remained largely flat for years after the paper was

published, before beginning to increase in 2006, and again in 2010 (see Exhibit K). Among

the notable events impacting the market subsequent to our paper was the first loss event

experienced by investors. A $190 million issue by KAMP Re 2005 Ltd suffered a total loss

of principal in 2005 due to Hurricane Katrina. The resulting resolution of the issue proceeded

smoothly, giving confidence to potential investors as to the handling of loss events

[Cummins, 2008]. (By 2014, cumulative losses across $51 billion in cat bonds issued totaled

only $682 million (1.3%)—a figure much lower than the average premium paid on the bonds

[Yoon and Scism, 2014].)

Writing in 2005, Hommel and Ritter [2005] acknowledged these high premiums at

the time, noting that the excess premiums paid on early cat bond issues were slowly

declining, but that a lack of understanding persisted in the market. Citing our paper, they

acknowledged that many of the issues we identified were still barriers for investors. Then,

three years later, Cummins [2008] wrote that the market began to experience steady growth

and falling premiums, with (then) recent data suggesting “broad market interest […] among

institutional investors.”

3-34

Exhibit K: Actual vs. Projected Issuance of Cat Bonds Source: Projected issuance is from SwissRe [1996]; actual issuance is from the Artemis Catastrophe Bond &

Insurance-Linked Securities Deal Directory as of February 2017

Exhibit L: Contemporary Standardized Cat Bond Structure

$0

$2,000

$4,000

$6,000

$8,000

$10,000

$12,000

$14,000

$16,000

$18,000

0

10

20

30

40

50

60

1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

Mill

ions

of D

olla

rs

Number of Issues (left axis) Total Size (right axis)

Projected Cat Securitization (right axis)

Hurricane CharleyHurricane Ivan

Hurricane KatrinaHurricane Wilma Hurricane Sandy

Hurricane Ike Hurricane Matthew

Special Purpose Vehicle

InvestorInsurer

Trust Account

Interest Rate Hedge

Fixed Rate

Floating Rate

Principal

Floating Rate+ Premium

PrincipalPrincipal +

Floating Rate

Premium

Proceeds if loss

triggered

Proceeds if loss not triggered

3-35

It was during this period that the cat bond market underwent fundamental change.

Carayannopoulos and Perez [2015] note that the new structures used beginning in 2009 were

positively received by the market. A new “standardized” structure emerged (Exhibit L) that

addressed many of the issues raised in my original paper: (i) the structure was simplified and

standardized to reduce complexity and mitigate concerns about it being a “black box,” (ii)

the treatment of collateral was made more rigorous and third parties were brought in to hold

collateral in trust, allowing the securities to be seen as a “pure play” on catastrophe risk and

diminishing the tendency toward exaggerated comprehensiveness, and (iii) the loss triggers

were simplified and externalized to mitigate concerns about asymmetric information. As a

result, the new structure (Exhibit L) resembled more closely Exhibit D than Exhibit H.

Today, the cat bond market is viewed largely as successful [Scism and Das, 2016].

Nevertheless, the current market for cat bonds is significantly smaller than the projections

made in 1996 for its market share (illustrated in Exhibit K). The industry continues to push

forward though, and has attempted to securitize a broad range of new catastrophic risks, such

as rogue traders, cyber hacking, and accounting fraud [Scism and Das, 2016]. Richards

[2016] summarizes this experience as a market heading toward greater standardization, but

unable to shake an attachment to complexity. In the process, market participants have revised

their beliefs about what is and is not an attractive feature. For example, one of the primary

advantages touted of cat bonds was their lack of correlation to other assets classes. Ironically,

as Richards [2016] notes, some market participants now see the lack of correlation as an

added risk in the form of unpredictability (here, as a type of ambiguity aversion).

Overall, the market has learned a number of important lessons both with regard to

securitizing catastrophic risk in particular and in regard to behavioral factors related to

securities design more generally. This learning process notwithstanding, issuers have been

persistently unable to shake a tendency toward complexity in design. On one hand, this is

not a new observation. Scitovsky [1950] noted that complexity (or consumer ignorance) was

a source of oligopoly power for firms. More specifically, Carlin [2009] noted that firms add

complexity, rather than transparency, as a means of increasing market power and

3-36

maintaining supernormal profits. Henderson and Pearson [2011] make this same case

specifically in regard to innovation in securities design. Insurers, then, may want to improve

transparency (and reduce complexity) in order to attract new investors in cat bonds, but not

by so much that it cedes their pricing power. Maintaining his longstanding opposition to cat

bonds, Berkshire Hathaway’s Warren Buffet lamented that reinsurance had become a

“fashionable asset class” [Scism and Das, 2016], and that the resulting lower prices were

leading Berkshire’s reinsurance subsidiaries to enter into fewer deals.

Some firms, it seems, were all too happy to maintain their arcane aura, and therefore

their profit margins. As a result, encouraging less complex, and more “palatable” design of

securities may not only increase capital to the insurance industry, but may also mitigate

market power and improve insurance pricing to consumers.

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4 Regulated Equity Returns: A Puzzle

4.1 Introduction†

In economics, the equity-premium puzzle refers to the empirical phenomenon that

some equity returns have exceeded the riskless rate of return by more than can be explained

by traditional models of compensation for bearing risk. Since Mehra and Prescott’s [1985]

initial paper on the subject, a large body of research has attempted to explain away the

puzzle, but without much success [Mehra and Prescott, 2003]. The most likely explanation

for the premium appears to be the presence of certain frictions not reflected in classical

equilibrium models (always a less-then-fully-satisfying answer).

It is not our intent, however, to rehash the general equity-premium puzzle discussion.

Rather, we call the reader’s attention to it as a means of introducing our instant problem,

which may be considered a special case of the Mehra-Prescott puzzle. Simply put: why are

the equity returns authorized by electric utility regulators so high, given that riskless rates

are so low? Our “puzzle” involves the large and growing spread, or risk premium, observed

between the rates of return on equity authorized by utility regulators and the riskless rate of

return. In addition to questioning the magnitude of the spread, we also question why it has

grown over time.

This regulated equity return puzzle is important not just from a theoretical asset-

pricing perspective, but also for very practical reasons. The database of more than 1,400 rate

cases since 1980 used in this paper reflects approximately $2 trillion in cumulative rate base

exposure.28 An error or bias of merely one percentage point in the allowed return would

† The author gratefully acknowledges the thoughtful comments received from Tony Páez and from participants at the Carnegie Mellon Electricity Industry Center’s weekly seminar. All responsibility for any errors remains with the author. 28 This figure reflects the simple cumulative sum of authorized rate bases across all cases. Because rate-base decisions may remain in place for several years, this sum most likely underestimates the actual figure, which should be the authorized rate base in each year examined, whether or not a new case was decided. We cite this figure merely as evidence of the substantial magnitude of the costs at stake.

4-2

involve tens of billions of dollars in additional cost for ratepayers in the form of higher retail

power prices and could play a profound role in the allocation of investment capital. Coupled

with utilities’ tendency toward excessive capital accumulation or “gold plating” under rate

regulation [Averch and Johnson, 1962; Spann, 1974; Courville, 1974; Hayashi and Trapani,

1976; Tapon and van der Weide, 1979], the magnitude of the problem makes it incumbent

on the industry to get it right.

There are also policy implications for market design and regulation. A recent PJM

Interconnection [2016] study compared and contrasted entry and exit decisions in

competitive and regulated markets in an attempt to evaluate the efficiency of competitive

markets for power. One finding that emerged from the study was that regulated utilities

appeared to be “overearning” and had generated positive alpha, but competitive firms had

not generated positive alpha.29 Although the study used a limited time window of rate case

data, its findings are consistent with those we explore in more detail here.

As an old joke goes, an economist is someone who sees something work in practice

and asks whether it can work in theory. Undoubtedly, the utility sector has been successful

in attracting capital over the past three decades. We cannot necessarily say, however, that

had returns been consistent with theoretical models (and thus lower), this would still have

been the case. Accordingly, this paper also raises the question of whether our theoretical

models of required return and asset pricing must be refined. Or, at the very least, whether

there are important considerations that must be accounted for in the application of those

models to the regulated electric utility industry.

In this paper, therefore, we examine the historical data on authorized rates of return

on equity in electric utility rate cases. We compare these rates of return to a number of

conventional benchmarks and a theoretical asset-pricing model. We demonstrate that the

spread between authorized equity returns (and also actual “earned” equity returns) and the

riskless rate has grown steadily over time. We investigate whether this growing spread can

29 In asset pricing models, positive alpha is evidence of non-equilibrium returns, meaning that investors are receiving compensation in excess of what would be required for bearing the risks they have assumed.

4-3

be explained by conventional asset pricing parameters and conclude that it cannot. Finally,

we conclude by suggesting alternative reasons for the growing spread and provide some

suggestions for future research and policy-making in the area.

4.2 Regulated Equity Returns and the CAPM

At the outset, let us make clear that we are addressing only regulated rates of return

on equity in this paper. We draw no conclusions or inferences about the behavior of returns

on non-regulated assets. Such returns may be considered a priori appropriate in that they are

subject to the discipline of competitive markets for investment. Our focus is limited to

regulated returns because in such cases it is regulators who are tasked with standing in for

the discipline of a competitive market and ensuring that returns are just and reasonable. For

more than a century, courts have ruled consistently in support of this objective, while

recognizing that achieving it requires consideration of numerous factors that are subject to

change over time.30 The task set to regulators, then, is to approximate what a competitive

market would provide, if one existed.

Mindful of this mandate, two U.S. Supreme Court decisions are commonly thought

to provide the conceptual foundation for utility rate-of-return regulation. In Bluefield Water

Works & Improvement Co. v. Public Service Commission of West Virginia, the Court ruled

that:

“The return should be reasonable, sufficient to assure confidence in the financial soundness of the utility, and should be adequate, under efficient and economic management, to maintain and support its credit and enable it to raise money necessary for the proper discharge of its public duties.”31

30 In Bluefield Water Works & Improvement Co. v. Public Service Commission of West Virginia (262 U.S. 679 (1923)), the Court identified eight factors that were to be considered in determining a fair rate of return. In United Railways & Electric Company of Baltimore v. West (280 U.S. 234 (1930)), the Court concluded: “What is a fair return […] cannot be settled by invoking decisions of this Court made years ago […]. The problem is one to be tested primarily by present day conditions.” 31 Bluefield Water Works & Improvement Co. v. Public Service Commission of West Virginia (262 U.S. 679 (1923)).

4-4

Then, in Federal Power Commission v. Hope Natural Gas Company, the Court ruled:

“…return to the equity owner should be commensurate with returns on investments in other enterprises having corresponding risks.”32

In both Bluefield and Hope, the Court sought to balance the need for utilities to attract capital

sufficient to discharge their duties with the need for regulators to protect ratepayers from

what would otherwise be rent-seeking monopolists.

These efforts in determining “just and reasonable” returns received significant

assistance in the 1960s when groundbreaking advances in asset pricing theory were made in

finance. Specifically, the development of the Capital Asset Pricing Model (“CAPM”)

[Sharpe, 1964; Lintner, 1965; Mossin, 1966] provided a rigorous framework within which

the question of the “appropriate” rate of return could be addressed in an objective fashion.

The security market line representation of the CAPM set out the equilibrium rate of return

on equity, , as the sum of the rate of return on a riskless asset, , and a premium related

to the level of risk being assumed, : .

It is outside of the scope of this paper to delve too deeply into the foundations of

asset pricing. We note, also, that the CAPM methodology is not the sole candidate for rate-

of-return determination in utility rate cases. Morin [2006, p. 13] identifies four main

approaches used in the determination of the “fair return to the equity holder of a public

utility’s common stock,” of which the CAPM is but one.33 Nevertheless, the concept of the

appropriate rate of return on equity being a combination of a riskless rate of return and a

premium for risk-bearing has since become widely accepted as a means of determining the

appropriate authorized return on equity in utility rate cases [Phillips, 1993] and the CAPM

32 Federal Power Commission v. Hope Natural Gas Company, 320 U.S. 591 (1944). 33 The other three approaches identified by Morin are: Risk Premium (which is an attempt to derive empirically what the CAPM derives theoretically), Discounted Cash Flows (or “DCF,” which is a Gordon-type dividend capitalization model), and Comparable Earnings (which is an empirical approach to deriving cost of capital from market comparables based on the Hope ruling cited above). A typical example of these approaches’ use in practice is found with the Pennsylvania Public Utility Commission [2016]: “The Commission determines the ROE […] based on the range of reasonableness from the DCF barometer group data, CAPM data, recent ROEs adjudicated by the Commission, and informed judgment.”

4-5

in particular has been seen as the “preferred methodology” in regulatory proceedings [Roll

and Ross, 1983].

Further, in Hope, the Court advocated the “end results doctrine.” By that, the Court

acknowledged that regulatory methods were immaterial so long as the end result was

reasonable to the consumer and investor. In other words, there is no single formula for

determining rates. Although we will generally be content in this paper to follow the Hope

doctrine and examine returns at a very general level as riskless rate plus risk premium, we

will call upon the CAPM approach in order to make quantitative assessments of the data

examined.

To the extent that the spread, – , has grown under any of the theoretical models,

it must be because compensation for risk-bearing has increased. Although the CAPM is but

one model of compensation for risk-bearing, it will be useful in this paper as a means of

categorizing our various investigations into the growth of that compensation. In the CAPM,

spread growth is related directly to two types of factors: (i) , the measure of the market-

relative riskiness of an asset, and (ii) the market risk premium ( ), which is the market

price of risk (and thus the competition for capital).

Before we turn to the data, however, let us dispense with an alternate formulation of

the underlying question. In questioning the size of the spread and why equity returns are so

high, one might also ask instead why the riskless rate is so low. Indeed, Mehra and Prescott

[1985] ask this very question, before dismissing it on theoretical grounds. We may revisit

this question in light of recent data and ask whether the observed spread growth is more a

function of riskless rates being forced down by the Federal Reserve’s intervention, than of

equity returns increasing (since the manifest intent of quantitative easing is to lower riskless

rates).34 Our historical data, as the next section indicates, does not support that hypothesis.

34 This has been an ongoing issue of contention in recent regulatory proceedings. In Opinion 531-B (issued March 3, 2015), FERC found that “anomalous capital market conditions” caused the traditional discount rate determination methods not to satisfy the Hope and Bluefield requirements (150 FERC ¶ 61,165 at 7). But in a related decision only eighteen months later (Order on Complaint, Establishing Hearing and Settlement Judge Procedures, issued September 20, 2016), FERC acknowledged that expert witnesses disagreed as to whether any market conditions were “anomalous” (156 FERC ¶ 61,198 at 10).

4-6

The spread growth has persisted since the beginning of our data series in 1980 and has

persisted across a variety of monetary and fiscal policy regimes.

4.3 Regulated Electric Utility Returns on Equity Since 1980

4.3.1 Historical Authorized Return on Equity Data

The data used in this paper reflect the collective experience of 1,421 electric utility

rate cases from almost every state in the country from January 1980 through December 2015.

We examine the returns on equity authorized by the regulatory agencies, not the returns

requested by the utilities.35 Out of all rate cases filed in the United States, the data only

include rate cases in which the utility has requested a rate change of at least $5 million or a

regulator has authorized a rate change of at least $3 million. We further exclude cases in

which no decision was made with regard to the return on equity and capital structure. Lastly,

only cases that have been fully litigated or settled are included; cases pending decision or

under appeal at the time of our analysis are not considered.

Nearly all fifty states and Washington D.C. are represented in the data set.36 Twenty-

eight electric utility rate cases satisfying the qualifications listed above were filed in the

average state over the past thirty-five years, with the most being filed in Wisconsin (115)

and the fewest being filed in Alaska, Alabama, and Tennessee with one each (as shown in

Exhibit M). Although Wisconsin is the most common state in the data, the frequency of

filing in a state does not appear to have any relationship to spread growth. The premium has

grown in both the ten states that completed the most rate cases and the ten states that

completed the fewest rate cases, and has grown at very similar rates (see Exhibit N). In fact,

as Exhibit O illustrates, the general trend across all states is similar.

35 To be clear, we refer to the rates set by regulators as the “authorized” rates. These may be contrasted with the utilities’ “requested” rates and also with the actual “earned” rates of return realized by utilities. Regulatory authorization of a rate is not a guarantee that a utility will actually earn such a rate. We address this issue in further detail in a later section. 36 Only Nebraska did not have a reported rate case meeting the parameters of the data set.

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Exhibit M: Qualifying Rate Cases Filed per State for the Ten Most Frequently- and Least Frequently-Filing States, 1980-2015

Exhibit N: Risk Premium Growth by Frequency of Case Filing. Gaps in the series reflect years in which no rate cases were filed for the subject group

In the early 1980s there were over 100 rate cases filed each year. By the late 1990s,

in the midst of widespread deregulation of the electric power industry, the number of filings

reached its lowest point (with five in 1999). Since then, filing frequency has increased to an

average of more than thirty-five per year over the last three years (see Exhibit P). The decline

in rate case activity in many instances was the direct result of rate moratoria related to the

transition to competitive markets in the late 1990s, as well as to moratorium-like concessions

0

100

200

300

400

500

600

700

800

900

1,000

1980 1985 1990 1995 2000 2005 2010 2015

Spr

ead

of R

ate

of R

etur

n ov

er U

.S.

Trea

sury

Rat

es (

in b

asis

poi

nts)

Average of 10 Least Frequently-Filing StatesAverage of 10 Most Frequently-Filing States

4-8

made to regulators related to merger approvals over the last decade. Many of these moratoria

will expire over the next several years, suggesting a new increase in rate case activity is

likely.37 Finally, no individual utility had an outsized influence on the sample. One hundred

forty-five different companies filed rate cases, but many have since merged or otherwise

stopped filing.38 The average firm filed ten rate cases in our sample. Within our sample the

most frequently-filing entity was PacifiCorp, which filed seventy-one rate cases, or 5% of

the sample.

Exhibit O: Range of Risk Premium Growth Across States. States with highest (VA) and lowest (SD) rates of growth (among states with at least 5 rate cases) are

highlighted

37 Although these new rate cases may tend to be dominated by transmission and distribution utilities as opposed to generation utilities, given the structural shifts that have occurred within the industry. 38 The level of analysis is at the regulated utility level. We recognize that many holding companies have multiple ring-fenced regulated utility subsidiaries.

4-9

Exhibit P: Filing Frequency by Year

4.3.2 The Regulated Equity Premium

Generally speaking, regulated equity returns are equal to the sum of the riskless rate

of return and a premium for risk-bearing. In the CAPM, the premium for risk-bearing is

given by . Rearranging the security market line equation, we define the regulated

equity premium as – . Presented thus, we first note that the existence of

a (positive) regulated equity premium is not, by itself, evidence of irrational investor

behavior or model failure. Neither is the existence of a growing regulated equity premium.

We take no position here on what the “correct” premium should be in any particular instance.

Rather, we shall be content in this paper simply to determine whether or not the behavior of

the risk premium in practice is consistent with existing financial theory.

Of the 1,421 rate cases used in the analysis, all but nineteen (1.3%) had approved

rates of return greater than the riskless rate at the time.39 On average, the authorized return

on equity is 4.8% higher than the riskless rate. The standard deviation on the spread is 2.1%.

Exhibit Q illustrates the average authorized return on equity over the period against the

average annual riskless rate and investment-grade corporate bond rate.40 For avoidance of

39 The small number of exceptions is exclusively from the early 1980s when a rapid increase in interest rates made the problem of regulatory lag particularly acute. 40 We used the 10-year constant maturity U.S. Treasury note yield as a proxy for the riskless rate and the yield on the Moody’s Seasoned Baa Corporate Bond Index as a proxy for investment-grade corporate bond rates. Board of Governors of the Federal Reserve System (US), 10-Year Treasury Constant Maturity Rate [DGS10], retrieved from FRED, Federal Reserve Bank of St. Louis https://research.stlouisfed.org/fred2/series/DGS10,

4-10

doubt, we note that only the U.S. Treasury note rate should be considered the riskless rate.

We include corporate bond rates solely to assess whether the trend in riskless rates is

materially different from the trend in risky debt. Exhibit R shows the distribution of the

premium for all of the rate cases in our sample.

Exhibit Q: Authorized Return on Equity vs U.S. Treasury and Investment Grade Corporate Bond Rates

Exhibit R: Distribution of Premium Across All Years

March 7, 2016; Board of Governors of the Federal Reserve System (US), Moody’s Seasoned Baa Corporate Bond Yield© [BAA], retrieved from FRED, Federal Reserve Bank of St. Louis https://research.stlouisfed.org/fred2/series/BAA, March 7, 2016.

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

1980 1985 1990 1995 2000 2005 2010 2015

Rat

e of

Ret

urn

Authorized Return on EquityAverage 10-Year U.S. Treasury NoteAverage Moody's Seasoned Baa Corporate Bond

4-11

While the regulated equity premium has averaged 483 basis points across the entire

time period, in 1980 the average premium was only 278 basis points, whereas in 2015 it

averaged 771 basis points. Exhibit S shows the difference between the authorized return on

equity and the riskless rate for each case in the data over the past thirty-five years. Although

the spread is determined against the riskless rate of return (represented here as the yield on

a 10-year U.S. Treasury note), we also present for comparison the spreads determined

against the yield on the Moody’s Seasoned Baa Corporate Bond Index to illustrate that the

effect is not an artifact of recent monetary policy on Treasury rates. The trends of the two

series are quite similar (and both have statistically-significant positive slopes41);

accordingly, we shall present only the Treasury rate-determined spreads throughout the

remainder of this paper.

Exhibit S: Authorized Return on Equity Premium, 1980-2015

Given that a large and growing regulated equity premium exists, our question is

whether or not it can be explained within an equilibrium asset-pricing framework such as

the CAPM. If were to have increased during the time period in question, for example, the

41 With both U.S. Treasury rates and corporate bond rates, the slopes are reliably positive (p < 0.001).

4-12

growth of the regulated equity premium may well be explained by the increasing (relative)

riskiness of utility equity. As the next section demonstrates, however, in fact it cannot.

4.4 Potential Theoretical Explanations for the Premium

Having demonstrated the existence of a large and growing regulated equity premium,

we investigate various potential explanations. As we indicated above, we proceed with our

investigation of explanations for the premium via the Capital Asset Pricing Model. The

CAPM allows three basic mechanisms of action for a change in the risk premium: (i) the

manner in which the underlying assets are financed has changed, (ii) the risk of the

underlying assets themselves has changed, and/or (iii) the rate at which the market in general

prices risk has changed. We explore each in turn.

4.4.1 Capital Structure Effects

As corporate leverage increases, the underlying equity becomes riskier and thus

deserving of higher expected returns. In finance, the Hamada equation decomposes the

CAPM equity beta ( ) into an underlying asset beta ( ) and the impact of capital structure

[Hamada, 1969; 1972]. Specifically, the Hamada equation states that 1 1 ,

where is the tax rate and D and E are the debt and equity in the firm’s capital structure,

respectively.42

One explanation for a growing risk premium would be steadily increasing leverage

among regulated utilities. However, regulators also generally approve of specific capital

structures as part of the rate-making process. As a result, our database also contains the

authorized capital structures for each utility.43 In fact, utilities are less leveraged today than

42 We use the marginal corporate federal income tax rate for the highest bracket, as provided in the SOI Tax Stats, Historical Table 24. Downloaded from https://www.irs.gov/pub/irs-soi/histabb.xls on March 8, 2016. 43 To be clear, the authorized capital structures evaluated here apply to the regulated utility subsidiaries, and not necessarily to any holding companies to which they belong. The holding companies themselves may utilize more or less leverage, but typically the regulated utility subsidiaries are “ring-fenced” so as to isolate them from holding company-level risks. Similarly, rate-of-return regulation would apply only to the regulated subsidiaries, not to the parent holding company. As a result, the capitalization of the regulated entity (studied here) is often different from the capitalization of the publicly-traded entity that owns it.

4-13

they were in 1980. The average debt-to-equity ratio in the first five years of the data set

(1980-1984) was 1.73; in 2011-2015 it was 1.04. More generally, we can observe the impact

of leverage moving in the opposite direction of what one may expect, whether we examine

the debt-to-equity ratio exclusively or the Hamada capital structure parameter (i.e., the

portion of the Hamada equation multiplied by , or 1 1 ) in its entirety. Exhibits

T and U illustrate these results. As a result, it does not appear as if capital structure itself can

explain the behavior of the risk premium.

Exhibit T: Authorized Rate-of-Return Premium vs. Utility Leverage

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Exhibit U: Authorized Rate-of-Return Premium vs. the Hamada Capital Structure

Parameter

4.4.2 Asset-Specific Risk

As noted above, the Hamada equation decomposes returns into compensation for

bearing asset-specific risks and for bearing capital structure-specific risks. Even if a firm’s

capital structure remains unchanged, the riskiness of its underlying assets may change. This

risk is represented by the unlevered asset beta, . An increase in the asset beta applicable

to such investments would, all else held equal, justify an increase in the risk premium.

To examine such a hypothesis, we used the fifteen members of the Dow Jones Utility

Average between 1980 and 2015 as a proxy for “utility asset risk.” We calculated five-year

equity betas for each firm by regressing their monthly total returns against the total return

on the S&P 500 index.44 The equity betas calculated were then converted to asset betas using

Hamada’s equation and corrected for firm cash holdings using firm-specific balance sheet

information. We then averaged the fifteen asset betas calculated in each year as our proxy

44 We evaluated the composition of the Dow Jones Utility Average index at the end of each year and used a rolling five-year window to perform the regressions. For example, the 1980 regression betas were calculated based on monthly returns from 1975-1979, the 1981 regression betas were calculated based on monthly returns from 1976-1980, and so on.

4-15

for utility asset risk.45 The results remain substantively unchanged whether an equal-

weighted or a capitalization-weighted average is used.

Exhibit V: Authorized Rate-of-Return Premium vs. Industry Average Asset Beta

Although there is, of course, variation in the industry average asset beta across the

thirty-five years, the general trend is down. Exhibit V presents the risk premium in

comparison to the industry average asset beta. As a result, the asset beta is moving in the

opposite direction from what one might expect, given a steadily-increasing risk premium,

and therefore does not appear to explain the observed behavior of the risk premium.

4.4.3 The Market Risk Premium

The last CAPM-derived explanation for a changing risk premium relates to the

pricing of risky assets in general. If investors require greater compensation for bearing the

45 The balance sheet and total return data are taken from the Standard & Poor’s COMPUSTAT database. We calculate 1 1⁄ and 1⁄ , where C equals the amount of cash and cash equivalents held by each firm and D and E represent, respectively, the debt and equity of each firm. We measure D as the sum of Current Liabilities, Long-Term Debt, and Liabilities–Other in the COMPUSTAT data.

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systematic risk of the market in general, then the risk premium across all assets would

increase as well (all else held equal) as a result of the average risk aversion coefficient of

investors increasing. The market risk premium reflects this risk-bearing cost in the CAPM.

Although we can observe the ex post market risk premium, investors’ assessment of

the ex ante market risk premium is generally based on assuming that historical experience

provides a meaningful guide to future experience.46 It is customary to examine the actual

market risk premium over some historical time period and base one’s estimate of the

expected future market risk premium on that historical experience (see, for example, Sears

and Trennepohl [1993]).

Exhibit W: Market Risk Premium Trends over Time by Historical Window

Exhibit W illustrates the ex ante market risk premium determined in each year by

examining a historical window of n years and using the average ex post premium calculated

46 We do not dwell here on the issue of the “observability” of the market portfolio as it relates to testability of the CAPM. We shall assume that the S&P 500 index is a reasonable proxy for the market portfolio.

-10%

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within that window.47 It is sufficient for our purposes to observe simply that the slope of the

market risk premium over time has been negative irrespective of the historical window used.

Throughout the remainder of this paper, we use a fifty-year historical window for calculation

purposes. As Exhibit X illustrates, that declining trend in the ex ante market risk premium

appears inconsistent with the increasing risk premium exhibited by the rates of return

authorized by regulators.

Exhibit X: Authorized Rate-of-Return Premium vs. Ex Ante Estimated Market Risk Premium

4.4.4 Testing a Theoretical Model of the Risk Premium

In this section, we examine each component composing the risk premium under the

CAPM and observe that the historical experience of each of these series is at odds with what

the CAPM would imply about the risk premium derived from rates of return authorized by

regulators. We can go further, however, than making these general observations. By

47 The market risk premium data used here are taken from data on the S&P 500 and 10-year U.S. Treasury notes collected from the Federal Reserve and maintained by Prof. Aswath Damodaran. Downloaded from http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html on March 8, 2016.

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combining the security market line representation of the CAPM and the Hamada equation,

we can quantitatively identify the risk premium, .

1 1 [1]

In [1], is the risk premium, or the difference between the authorized rate of return on

equity and the riskless rate, taken as the average of the yield on the 10-year U.S. Treasury

note during the year in which the equity return was authorized. The asset beta, , is

calculated as in Section 4.4.2. The middle component is taken from the Hamada equation

and reflects the marginal corporate income tax rate in effect in the year in which the equity

return was authorized and the authorized debt-to-equity ratio reflected in the regulators’

decisions. Lastly, MRP is the ex ante estimate of the market risk premium based on a fifty-

year historical window as of the year in which each equity return was authorized.

By using a logarithmic transform of [1], we arrive at an equation that can be tested

via linear regression:

ln ln ln 1 1 ln [2]

Finance theory would hypothesize that should be zero (or not significant) and , , and

should be positive and significant. What we find, however, is exactly the opposite of that.

The intercept is negative and significant and the coefficients are negative and strongly

significant (Exhibit Y).48 Further, a comparison of the actual risk premium spreads to the

regression-model spreads reveals a good fit (Exhibit Z).

48 We removed 19 data points (approximately 1.3% of the data set) that had negative spreads from use in the regression analysis.

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ln , Constant -5.638****

(0.151)

, Asset beta,ln -0.184**** (0.027)

, Capital structure,ln 1 1 -0.487**** (0.116)

, Market risk premium,ln -0.957**** (0.039) R-squared 42.6% Adjusted R-squared 42.4% F statistic 345.3**** No. of observations 1,402

Standard errors are reported in parentheses. *, **, ***, and **** indicate significance at the 90%, 95%, 99%, and 99.9% levels, respectively.

Exhibit Y: Regression Results for CAPM-based Risk Premium Model

Exhibit Z: Actual vs. Regression-Model Risk Premium Spreads

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Exhibit Z also reveals a distinct shift in the predicted trend of the risk premium

beginning in 1999. This is notable because for many parts of the U.S., 1999 represented the

year that implementation of deregulation began, with wholesale markets commencing

operation and several divestiture transactions of formerly-regulated generating assets

occurring. To examine this point in time, we divided the data into two sets, 1980-1998 and

1999-2015, and estimated separate regression models for each subset (Exhibit AA).

Although the results in both cases are consistent with our earlier finding that the standard

finance model appears at odds with the empirical data, the two regression models are

noticeably different from one another and appear to better represent the data (Exhibit BB).

We find this result suggestive that deregulatory activity may have an influence even on still-

regulated utilities, although we leave further exploration to future work.

1980-1998 1999-2015 ln ln

, Constant -15.552**** -4.156**** (0.725) (0.101)

, Asset beta,ln -0.894**** -0.084**** (0.133) (0.009)

, Capital structure,ln 1 1 -0.131 -0.333****

(0.153) (0.056)

, Market risk premium,ln -4.585**** -0.497**** (0.263) (0.027) R-squared 27.2% 45.5% Adjusted R-squared 27.0% 45.2% F statistic 113.6**** 134.2**** No. of observations 916 486

Standard errors are reported in parentheses. *, **, ***, and **** indicate significance at the 90%, 95%, 99%, and 99.9% levels, respectively.

Exhibit AA: Regression Results for a Two-Period CAPM-based Risk Premium Model

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Exhibit BB: Actual vs. Two-Period Model-Predicted Risk Premium Spreads

4.5 Possible Implications

The consequences of these findings are significant, both because of the cumulative

amount of capital and ratepayer expense at stake, and also because of what they may imply

for finance theory and public policy. For example, although fuel costs and wholesale power

prices have declined since 2007 (see Exhibit CC), the retail price of power has increased

over the same period (see Exhibit DD). One explanation for this divergence in wholesale

and retail rates may be the presence of a growing premium attached to regulated equity

returns and therefore embedded into rates. To be sure, other forces may also be at work (for

example, recovery of transmission and distribution system investments is consuming a

greater portion of retail bills—a circumstance potentially exacerbated by excessive risk

premiums). Further, even if the growing divergence between wholesale and retail rates is

related to a growing risk premium, it does not necessarily follow that such growth is

inappropriate or inconsistent with economic theory. Nevertheless, the potential for

embedding of such quasi-fixed costs into the cost structure of electricity production may be

significant for end users.

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Two-Period Regression Model

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To the extent that the size and growth of the risk premium over time cannot be

explained by traditional asset pricing models, we examine potential causes and consequences

of this behavior of regulated rates of return in four distinct areas as a guide toward further

study and an indicator of potential policy implications.

Exhibit CC: Wholesale Fuel and Power Price Trends, 2007-2015 Data Source: Intercontinental Exchange; U.S. Department of Energy, Energy Information Administration

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Exhibit DD: Wholesale vs. Retail Power Prices, 2007-2015

Data Source: Intercontinental Exchange; U.S. Department of Energy, Energy Information Administration 4.5.1 Potential Alternative Finance Explanations

In Mehra and Prescott’s [2003] review of the equity premium puzzle literature, the

authors acknowledge that uncertainty about changes in the prevailing tax and regulatory

regimes may explain the premium. Such forces may also be at work with regard to regulated

rates of return. To the extent that investors require higher current rates of return because they

are concerned about future shocks to the tax or regulatory structure of investments in

regulated electric utilities (e.g., EPA’s promulgation of the Clean Power Plan, the U.S.

Supreme Court’s stay of the Clean Power Plan), such concern may be manifest in a higher

degree of risk aversion unique to the electric utility sector than would otherwise be obtained.

A separate line of inquiry concerns a criticism of the Hamada equation in the

presence of risky debt (Hamada [1972] excluded default from consideration). Conine [1980]

extended the Hamada equation to accommodate risky debt by applying a debt beta.

Subsequently, Cohen [2008] sought to extend the Hamada equation by adjusting the debt-

to-equity parameter to incorporate risky debt. We view neither of these proposed solutions

as entirely satisfying, and note that they tend to be material only for high leverage, which is

not common to regulated utilities. Nevertheless, we acknowledge that adjustments to the

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capital structure may influence the risk premium. However, applying the Cohen [2008]

modification49 and using the Moody’s Seasoned Baa Corporate Bond Yield as a proxy for

the cost of risky debt ( ), we note that our regression results are substantively unchanged.

Lastly, some researchers have suggested that the Arbitrage Pricing Theory (“APT”)

[Ross, 1976] is preferable to the CAPM because the CAPM produces a “shortfall” in

estimated returns [Roll and Ross, 1983] and “underestimates” actual returns in utility

settings [Pettway and Jordan, 1987]. While the works of Roll and Ross and of Pettway and

Jordan are suggestively similar to the analysis contained in this paper, we note that those

authors were examining the actual returns on utility common stocks, rather than the rates of

return authorized by regulators for assets held in utility rate bases.

To address a similar point, we also examined the actual earned rates of return on

equity for the 15 utilities in the Dow Jones Utility Average over our historical window. We

used each firm’s actual return on equity, calculated annually as Net Income divided by Total

Equity, as reported in the COMPUSTAT database. This measure of firm profitability

examines how successful the firms were at converting their authorized returns into earned

returns. In general, the earned returns closely tracked the authorized returns, suggesting that

the decisions of regulators are significantly influencing the actual earnings of regulated

utilities. Exhibit EE compares the spread of authorized rates of return over riskless rates to

the spread of earned rates of return over riskless rates and to the median net income of

utilities in constant dollars.50 The steadily increasing risk premium we have identified is

present in both series.51 Further, the “capture rate” (the percentage of authorized rates

actually earned by the utilities) averaged 96% over the entire time period. As a result, we

49 Cohen’s modified Hamada equation is 1 1 . 50 We used the median earned rate of return over the 15 Dow Jones utilities. The results are substantively equivalent if the average earned rate of return is used, but are more volatile due to the impact on earnings of the California energy crisis of 2000-2001 and the collapse of Enron in 2001. 51 These measures of firm performance must be interpreted with caution. The authorized rates of return apply to jurisdictional utilities, while the earned rates of return are calculated based on holding company performance, which in many cases are not strictly equivalent. Further, increasing net income may be due to industry consolidation producing larger firms (with income increasingly only proportionally to size), rather than an increase in profitability itself. Nevertheless, the results are suggestive.

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conclude that the trend of increasing risk premiums is not an abstract anomaly occurring in

a regulatory vacuum, but rather a direct contributor to the earnings of regulated utilities.

Exhibit EE: Comparability of Spreads Measured with Authorized and Earned Rates of Return and Utility Net Income

We have not taken that analysis the final step and examined the relationship between

firm performance and stock performance. However, the findings of Roll and Ross [1983]

and Pettway and Jordan [1987] stated in different terms suggest that regulated utilities have

realized higher stock returns than can be explained by the CAPM—a finding congruent with

our work and suggestive of other factors being priced by the market. This does not entirely

explain, however, why regulators appearing to use a CAPM approach provide utilities with

returns that also appear to be excessive.

4.5.2 Potential Public Policy Explanations

Public policy, or regulation itself, may be a causal factor in the observed behavior of

the risk premium. The U.S. Supreme Court acknowledged, in Duquesne Light Company et

al. v. David M. Barasch et al. (488 U.S. 299 (1989)) that “the risks a utility faces are in large

part defined by the rate methodology, because utilities are virtually always public

$0

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Authorized Rates (left axis) Earned Rates (left axis)

Median Net Income (right axis)

4-26

monopolies dealing in an essential service, and so relatively immune to the usual market

risks.” The recognition that the very act of regulating utilities subjects them to a unique class

of risks may influence its cost of capital determination. And yet, if the purpose (or at least a

purpose) of regulating electric utilities is to prevent these quasi-monopolists from charging

excessive prices, but the practice of regulating them results in a higher cost of equity capital

than might otherwise apply, it calls into question the role of such regulation in the first place.

Similarly, regulators may also question whether the hybrid regulated and non-

regulated nature of the electric power sector plays a role as well. Has deregulation caused

risk to “leak” into the regulated world because both regulated and non-regulated firms must

compete for the same capital? Has the presence of non-regulated market participants raised

the marginal price of capital to all firms? We note that the trajectory of public policy during

the entire time period studied has been toward deregulation (beginning before 1980 with

Public Utility Regulatory Policy Act, through the Natural Gas Policy Act in the 1980s, and

electric industry deregulation in the 1990s) and that “today’s investments face market,

political and regulatory risks, many of which have no historical antecedent that might serve

as a starting point for modeling risk.” [PJM Interconnection, 2016] Has the progressive

deregulation of the industry caused a convergence in regulated and non-regulated returns

over that time period? The data do not suggest that utilities in states that have never

undertaken deregulation have meaningfully different risk premiums, but there are many

ways to evaluate the “degree” of deregulatory activity that could be explored.

Another public policy-related factor could be a change in the nature of the rate base

or of rate-making itself. Toward the beginning of our study period, most of the electric

utilities were “vertically integrated” (i.e., in the business of both generation and transmission

of power). Over time, generation became progressively exposed to deregulation, while

transmission and distribution of power has tended to remain regulated. To the extent that the

portion of the rate base comprised of transmission and distribution assets has increased at

the expense of generation assets, it may suggest a shift in the underlying risk profile of the

assets being recognized by regulators. We note, for example, that public policy has tended

to favor transmission investments with “incentive rates” in recent years in order to address

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a perceived relative lack of investment in transmission within the electric power sector.

Although we do not present the results here, there does not appear to be a meaningful

difference between the average annual risk premiums for vertically integrated utilities and

non-vertically integrated utilities.

As for a change in the nature of rate-making itself, we note that the industry has

tended to move from cost-of-service rate-making to performance-based ratemaking. Has this

shift, in an attempt to increase utility operating efficiency, inadvertently raised the cost of

equity capital through the use of incentive rates, and has the net cost-benefit balance been

positive if so?

4.5.3 Potential Behavioral Economics Explanations

One curious observation in the empirical data is that the average rate of return on

regulated equity appears to have “converged” to 10% over time. Although the underlying

riskless rate has continued to drop, authorized equity returns have generally remained fixed

in the neighborhood of 10% recently. Anecdotally, we have observed a reluctance among

potential investors to accept equity returns on power investments of less than 10%—even

though those same investors readily acknowledge that debt costs have fallen. To that extent,

then, a behavioral bias may be at work.

In economics, “money illusion” refers to the misperception of nominal price changes

as real price changes [Fisher, 1928]. Shafir, Diamond, and Tversky [1997] proposed that this

type of choice anomaly arises from framing effects, in that individuals give improper

influence to the nominal representation of a choice due to the convenience and salience of

the nominal representation. The experimental results have been upheld in several subsequent

studies in the behavioral economics literature [Fehr and Tyran, 2001; Svedsäter, Gamble,

and Gärling, 2007].

The effect here may be similar: investors and regulators may conflate “nominal” rates

of return (the authorized rates) with the risk premium underlying the authorized rate. The

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apparent “stickiness” of rates of return on equity around 10% is similar to the “price

stickiness” common in the money illusion (and, indeed, the rate of return is the price of

capital). If there was in fact a tendency (intentional or otherwise) to respect a 10% “floor,”

one might expect that the distribution of authorized returns within each year may “bunch

up” in the left tail at 10%, where absent such a floor one may expect them to be distributed

symmetrically around a mean. As Exhibit FF illustrates, we see precisely such behavior. As

average authorized returns decline to 10%, the skewness of the within-year distributions of

returns becomes persistently and statistically significantly positive, suggesting a longer

right-hand tail to the distributions, consistent with a lack of symmetry below the 10%

threshold.52

Exhibit FF: Authorized Rates of Return on Equity and Skewness

A related finding has been reported by Fernandez, Ortiz, and Acín [2015], where

respondents to a large survey of finance and economics professors, analysts, and corporate

managers tended, on average, to overestimate the riskless rate of return. In addition, their

estimates exhibited substantial positive skew, in that overestimates of the riskless rate far

52 Our test statistic for skewness is equal to the skewness divided by its standard error

6 1 2 1 3⁄ , where n is the sample size. The test statistic has an approximately normal distribution [Cramer and Howitt, 2004].

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exceed underestimates.53 The authors found similar results not just in the U.S., but also in

Germany, Spain, and the U.K. In the U.S., the average response exceeded the

contemporaneous 10-year U.S. Treasury rate by 30 to 40 basis points. It may be that

overestimating the riskless rate is simply one way for participants in regulatory proceedings

to “rationalize” maintaining the authorized return in excess of 10%. Alternatively, it may be

an additional bias in the determination of authorized rates of return.

If such biases exist, there are clear implications for the regulatory function itself. For

example, this apparent 10% “floor” was even recognized recently in a FERC proceeding: “if

[return on equity] is set substantially below 10% for long periods […], it could negatively

impact future investment in the [New England Transmission Owners].”54 One notable

jurisdictional difference in regulatory practice is between formulaic and judgment-based

approaches to setting the cost of capital. In Canada, for example, formulaic approaches are

more prevalent than in the United States [Villadsen and Brown, 2012]. By pre-committing

to a set formula (e.g., government bond rates plus n basis points) in lieu of holding

adversarial hearings, regulators could minimize the potential for deviation from outcomes

consistent with finance theory. Villadsen and Brown [2012] note, for example, that recent

rates set by Canadian regulators have tended to be lower than those set by U.S. regulators

despite nearly equivalent riskless rates of return.

4.5.4 Potential Public Choice Explanations

The last category of potential explanations emerges from the public choice literature.

Regulators may be deliberately or inadvertently providing a “windfall” of sorts to electric

utilities. Stigler [1971], among others in the literature on regulatory capture, noted that firms

may seek out regulation as a means of protection and self-benefit. Close relationships

between regulators and the industries that they regulate have been observed repeatedly, and

one explanation for the size and growth of the risk premium is the electric utility industry’s

53 At the time of the survey, the 10-year U.S. Treasury rate was 2.0%. The average riskless rate reported by the 1,983 U.S. survey respondents was 2.4% (median 2.3%), but responses ranged from 0.0% to 8.0%. 54 Martha Coakley, et al. v. Bangor Hydro-Electric Co., et al., Initial Decision, 144 FERC ¶ 63,012 at 576 (2013).

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increasing “capture” of regulatory power. For example, Hagerman and Ratchford [1978]

find that utility commissioners facing very long terms tend to be more generous to firms. In

contrast, states with elected utility commissioners [Kwoka, 2002] or commissioners whose

appointment by the executive requires approval by the legislature [Boyes and McDowell,

1989] tend to have lower electricity prices. We also note the similarities here to an Olson-

type collective action problem of concentrated benefits (excess profits to utilities may be

significant) and diffuse costs (the impact of those excess profits on each individual ratepayer

may be small) [Olson, 1965].

We are somewhat skeptical of this explanation, however, both because of the degree

of intervention in most utility rate cases by non-utility parties, and because the data do not

suggest that regulators have become progressively laxer over time. Exhibit GG compares

the rates of return on equity requested by utilities in our data set against the rates of return

ultimately authorized. As the trend line illustrates, this ratio has remained remarkably stable

over the thirty-five years of data, even as the risk premium itself has steadily increased. As

a result, the data do not suggest an obvious, growing permissiveness on the part of regulators

(although the last six years are suggestive of an increased level of accommodation among

regulators).

Exhibit GG: Rate of Return Authorized as a Percent of Rate of Return Requested

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4.6 Conclusion

In this paper, we have examined a large database of electric utility rates of return

authorized by regulatory agencies over the past thirty-five years. These rates have

demonstrated a growing spread over the riskless rate of return across the time horizon

studied. The size and growth of this spread—the risk premium—does not appear to be

consistent with finance theory, as expressed by the CAPM. In fact, regression analysis of the

data suggests the opposite of what would be predicted if the CAPM holds.

The apparent persistence of large and growing risk premiums authorized by

regulators has broad implications across the electric power sector and beyond. In particular,

if rate case activity increases over the next several years as rate moratoria expire, the public

policy implications may be significant. Although our work suggests that the empirical

behavior of the risk premium is not explained by traditional asset-pricing models,

specifically the CAPM, we have identified a diverse collection of possible alternative

explanations that draws on work in finance, public policy, behavioral economics, and public

choice economics. We also suspect that these findings are not unique to electric utilities, and

therefore exploration of other regulated industries—both within and outside of the United

States—may be fruitful.

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5 A Computational Framework for Risky Intertemporal Choice

5.1 Introduction

Computational simulation models have been used broadly within the social sciences

for decades. From the early efforts of Schelling [1978], more comprehensive work

blossomed in the general treatments of Epstein and Axtell [1996] and Gaylord and D’Andria

[1998], and has been complemented by more recent efforts such as Miller and Page [2007].

In many specific fields in the social sciences, computational simulation has made targeted

contributions, including to economics (e.g., Arthur et al. [1997] on the behavior of markets),

to organizational theory (e.g., Carley and Prietula [1994] on social networks and group

dynamics), to sociology (e.g., Butts [1998] on the emergence of collective beliefs), and to

political science (e.g., Kollman, Miller, and Page [1992] on the evolution of spatial voting

models). As a result of this now-vast literature, the use of computational simulation has

become widely accepted in virtually all of the social sciences.

Psychology, however, has proved more resistant to this innovation. Despite early

enthusiasm from Abelson [1968], twenty years later, it was still not widely adopted as a

methodology [Stasser, 1988]. In an effort to reverse this trend, Ostrom [1988] asserted the

advantages of computational simulation not only in testing, but also in formal theory

development and hypothesis generation. Yet again, now another thirty years later, it remains

underutilized, especially in the behavioral decision-making literature. Behavioral decision

making has remained almost exclusively dependent on experimental work. While such

efforts absolutely have a central role to play, I would propose that computational simulation

can also contribute to deepening our understanding of behavior, especially in novel and

complex environments.

For example, despite having models of decision making that address risky

intertemporal choice, the experimental results of tests of those models have been limited and

5-2

inconsistent. This essay develops a computational approach, in the spirit of Ostrom [1988],

to the generation of hypotheses on which future experimental work can be conducted. The

advantage of using a computational approach is the ability to identify quickly areas of the

problem space where further experimental exploration would be most fruitful. In addition,

computational simulation can allow for hypothesis testing in applications where

experimentation with human subjects is difficult or costly. The significant advances made to

date in developing descriptive theories of choice have enabled a computational methodology

to extend previous findings and assist with statistical inference from the results.

In this chapter, I develop a probabilistic computational simulation of risky

intertemporal choice and address two topics made possible with its use: (i) the inclusion of

probabilistic information about the population of decision makers that constitutes the

“decision demographics” of the population, and (ii) the use of computational methods to

facilitate experimental exploration in novel or complex decision environments.

In Section 5.2, I review the literatures on choice under risk and choice over time, as

well as the comparatively limited literature on risky intertemporal choice, and introduce the

building blocks of the decision models used. Section 5.3 develops a model of the decision

problem faced by a population of heuristic decision makers, as well as the measures used to

evaluate decision performance. Section 5.4 describes the simulation analysis performed and

communicates the results. Finally, Section 5.5 concludes by discussing the implications of

the methodology and their practical applications.

5.2 Literature Review

Historically, the theories of choice under risk and uncertainty and choice over time

have evolved separately. Most real-world decision-making applications, however, involve

resolving questions of both uncertainty and time. These include personal decision making

(such as retirement planning and health-related decision making), as well as business

decision making (such as capital investment and policy-related decision making), among

many others. The remainder of this section reviews the separate literatures on uncertainty

5-3

and time, before reviewing the comparatively limited literature on risky intertemporal

choice.

5.2.1 Choice Under Risk and Uncertainty

The normative literature on risky choice has existed for more than half a century and

is vast and well-settled. From the pioneering efforts of von Neumann and Morgenstern

[1947] in the axiomatic derivation of expected utility theory, to Savage’s [1954]

axiomatization of subjectively-expected utility and probability, to Arrow’s [1953]

development of the state-preference approach to uncertainty used in general equilibrium

theory, to Pratt’s [1964] work on risk aversion, the normative theory of choice under risk

and uncertainty has remained virtually unchanged. Summarized in simple terms: lotteries

can be compressed into expected utility. For outcomes x, probabilities p, and concave utility

function u, the expected utility across i states of the world is ∑ .

Notwithstanding this work on normative choice, an extensive literature subsequently

developed questioning the descriptive accuracy of the normative approach. The literature on

non-expected utility theories is vast (see the review in Starmer [2000]), but the general result

has been to transform payoffs by emphasizing losses and to transform probabilities from a

linear to an S-shaped function. These approaches were formalized by Kahneman and

Tversky [1979] into prospect theory, and subsequently into cumulative prospect theory

[Tversky and Kahneman, 1992]. Quiggin [1982] and Lattimore, Baker, and Witte [1992],

among others, have also developed alternative probability-weighting functions, but the vast

majority of this research has resulted in the general characteristics of reference points

(characterization of gains and losses as relative to a salient reference point), loss aversion,

and S-shaped probability-weighting functions.

In the prospect theory formulation, the prospect value V of a lottery is a function of

transformed values of p and x, where is a probability-weighting function and is a value

function. Accordingly, ∑ . Tversky and Kahneman [1992] later

proposed specific functional forms for and and a large literature developed to

5-4

parameterize those functions based on experimental data or to infer them from real-world

choice examples. The approaches in this section—both normative and descriptive—

however, deal solely with choice under risk and uncertainty at a single point in time.

5.2.2 Choice Over Time

For choices over time, a similar foundational scenario emerged. The normative

theory of intertemporal choice emerged from Samuelson’s [1937] introduction of the

exponential discounting of utility and Koopman’s [1960] demonstration that certain basic

assumptions lead to impatience over infinite consumption programs (i.e., preference for

immediate values over delayed values). From these models, which involved only payoffs

with certainty, a general model emerged such that the expected utility of a sequence of

certain payoffs over time periods t could be calculated as ∑ , where

1 and r is the discount rate (or rate of time preference). In other words, multi-period

payoffs could be compressed into a single discounted utility. This normative formulation has

the important characteristic of time-invariant discount rates.55

And once again, a large series of empirical results demonstrated the descriptive

inadequacy of the normative model. Thaler [1981] found evidence of both dynamic

inconsistency and gain-loss asymmetry relative to the normative exponential discounting

model in intertemporal choice. Loewenstein [1988] found that incorporation of a reference

point (as in prospect theory) led to what he referred to as delay-speed-up asymmetry, where

subjects would require more compensation for postponing consumption than they would be

willing to pay for accelerating consumption. Ainslie [1991] and Kirby and Maraković [1995]

proposed that the hyperbolic discounting model provided a better fit to the experimental data

on intertemporal choice. Read [2001] asserted that a subadditive discounting model provided

a better fit than the hyperbolic model, although both explained the experimental results. The

primary conceptual difference between the hyperbolic and subadditive models is the

55 For any discount function , f is time-invariant if ⁄ is a constant with regard to t. For example, for the exponential discount function ⁄ . However, for the Lowenstein-Prelec hyperbolic discount function 1 ⁄ 1 ⁄⁄ 1 , and therefore it remains a function of t.

5-5

motivation for the present bias as being either impulsiveness (for the hyperbolic model) or

the perception of time (for the subadditive model).

In general, the hyperbolic model became commonly accepted as the preferred

descriptive model of intertemporal choice under certainty. I use the hyperbolic model

specified in Prelec [1989] and Loewenstein and Prelec [1992]: 1 / , where

r is the traditional (exponential) discount rate and adjusts the rate at which near and distant

outcomes are compared. As → 0, converges to the exponential discounting function.

The hyperbolic formulation does not display time invariance. Rather, the discount rates

determined under hyperbolic discount functions are all functions of t. Other functional forms

are compared and contrasted in Section 5.3.1 in the context of experimental work using the

different forms.

5.2.3 Risky Intertemporal Choice

Despite significant advancements in choice under risk and choice over time, what

has been left relatively unexplored is their combination: risky intertemporal choice.

Although the normative approach is essentially settled with the recursive utility framework

of Kreps and Porteus [1978], as extended by Epstein and Zin [1989], the descriptive theory

of risky intertemporal choice is “not settled” [Albrecht and Weber, 1997], is “complex and

not easily understood” [Weber and Chapman, 2005], is “relatively limited” [Anderson and

Stafford, 2009], and is “quite heterogeneous in methods and findings” [Hardisty and Pfeffer,

2017].

Four general types of anomalies in risky intertemporal choice have been identified:

1. Certainty-Risk Asymmetry (discount rates are higher for certain outcomes than for risky outcomes)

2. Short-Long Asymmetry (violations of stationarity, preference reversals induced by shifting risky choices forward in time)

3. Gain-Loss Asymmetry (discount rates are smaller for gains than for losses) 4. Magnitude Asymmetry (discount rates are higher for larger payoffs)

5-6

The experimental work examining these findings, however, is limited and often

contradictory. Albrecht and Weber [1997] find support for short-long asymmetry in

matching tasks, but not choice tasks. Öncüler and Onay [2009] support violations of

stationarity, but find the evidence on direction of the effect mixed. Keren and Roelofsma

[1995] find support for certainty-risk asymmetry. Anderson and Stafford [2009] find no

support for certainty-risk asymmetry. Shelley [1994] supports gain-loss asymmetry;

Blackburn and El-Deredy [2013] do not. Disagreements involving the interactions between

risk and time emerge from whether subjects evaluate risk first or time first [Weber and

Chapman, 2005] and whether there is a single underlying mechanism [Keren and Roelofsma,

1995] or many mechanisms [Read, 2003]. Albrecht and Weber [1997] note that the empirical

results are sensitive to the elicitation procedure used. Wang et al. [2016] report global

experimental results that show significant correlations in time preference with cultural

variables, particularly in regard to cultural traits that are related to high levels of uncertainty

avoidance.

In short, comparatively little clarity has emerged from the experimental literature on

compression and risky intertemporal choice other than a general recognition that hyperbolic

discounting is well-supported and that resolution of uncertainty involves an S-shaped

decision-weighting function and differential treatment of gains and losses. I proceed,

therefore, with models based on those generally-accepted characterizations.

In general, the normative approach is characterized by the discounted expected utility

framework and uses the value function provided in [1]. For the descriptive approach, the

prospect theory value function is combined with the hyperbolic discounting model, which

produces the value function in [2] [Prelec and Loewenstein, 1991; Öncüler, 1999].

[1]

5-7

[2]

To parameterize the prospect theory value function, the probability-weighting function [3]

and value function [4] proposed by Tversky and Kahneman [1992] are maintained. In those

formulations, , , and represent, respectively, the curvature of the gain and loss functions

(i.e., the degree of reference point-dependent risk aversion) and the loss aversion parameter.

The in the probability-weighting function controls the degree to which the function is S-

shaped and is contingent on whether the outcome x is characterized as a gain or a loss.

1 / [3]

00

[4]

5.3 Simulating the Population of Decision Makers

5.3.1 Parameterization and Decision Demographics

Numerous experiments have been performed in the literature to estimate the

parameters required by cumulative prospect theory. In Tversky and Kahneman’s [1992]

original work, the parameters for [3] and [4] were estimated as 0.88, 2.25,

0.61, and 0.69, where and indicate, respectively, the probability

weighting function coefficients for gains and losses. However, there is certainly no

theoretical reason to believe that only a single set of parameters exists for all decision

makers. Rather, each decision maker in a population would be expected to have parameter

values drawn from a distribution of such values. Much like describing the population

demographics of a group (e.g., percent of each ethnicity, percent of age group), I am

interested in characterizing the decision demographics of the population (e.g., percent loss

averse, percent risk seeking for losses). I examined the literature to estimate the distribution

5-8

of parameter values. Exhibit HH summarizes the parameter value estimates from a variety

of such studies (recognizing that not every study estimated all parameter values). Exhibit II

provides the results of a single group of identical studies performed on populations of

decision makers worldwide [Rieger, Wang, and Hens, 2017]. The resulting distributional

information in Exhibit JJ incorporates the estimates in both Exhibits HH and II.56 Summary

statistics are provided in Exhibit KK for the combined data, with and without the country-

level detail in Rieger, Wang, and Hens [2017] (noted as “ex RWH”).57

Exhibit HH: Summary of Studies Estimating Cumulative Prospect Theory Parameters

56 To be precise, the dispersion common to the experimental results cited is such that by convention the median coefficients are typically reported. This is true for the Rieger, Wang, and Hens [2017] data, for example. Accordingly, the distributions presented in Exhibit JJ are actually the distributions of the median coefficients, not the population distribution or the distribution of mean coefficients. While the Central Limit Theorem would ensure normality if the mean coefficients were reported, additional (but not overly onerous) regularity conditions must be imposed in order to adapt the Central Limit Theorem to order statistics such as the median. That being said, for a sample of size 2 1 drawn from an infinite population with density function

, the sampling distribution of the median is nevertheless approximately normal with mean and variance 1 8⁄ [David and Nagaraja, 2003; Genton, Ma, and Parzen, 2006]. I proceed as if these distributions are normally distributed. 57 Correlations are calculated only for the Rieger, Wang, and Hens [2017] data because they are complete and consistent.

Year Study4.80 1979 Fishburn and Kochenberger [1979]

0.88 0.88 2.25 0.61 0.69 1992 Tversky and Kahneman [1992]0.22 0.56 1994 Camerer and Ho [1994]0.50 0.71 1996 Wu and Gonzalez [1996]0.39 0.84 1998 Fennema and van Assen [1998]0.49 1999 Gonzalez and Wu [1999]0.89 0.92 0.60 0.70 2000 Abdellaoui [2000]

0.67 2000 Bleichrodt and Pinto [2000]0.61 0.61 2001 Donkers et al. [2001]

2.17 2001 Bleichrodt et al. [2001]1.43 2002 Schmidt and T raub [2002]1.81 2003 Pennings and Smidts [2003]

0.97 2004 Etchart-Vincent [2004]0.94 0.96 2005 Abdellaoui et al. [2005]0.68 0.74 3.20 2005 Tu [2005]1.01 1.05 2006 Fehr-Duda et al. [2006]0.81 0.80 1.07 0.76 0.76 2006 Andersen et al. [2006]0.72 0.73 2.04 2007 Abdellaoui et al. [2007]0.86 1.06 2.61 2008 Abdellaoui et al. [2008]0.24 0.26 2008 Pitcher [2008]0.71 0.72 1.38 0.91 0.91 2009 Harrison and Rutström [2009]0.88 -0.26 1.87 2009 Booij and van de Kuilen [2009]0.86 0.83 1.58 0.62 0.59 2010 Booij et al. [2010]0.80 0.78 2.39 0.01 5.48 2010 Chow et al. [2010]0.82 0.88 1.83 0.58 0.73 2011 Nilsson et al. [2011]0.73 1.52 0.74 1.24 2012 Glöckner and Pachur [2012] (values are midpoint)0.21 0.06 1.34 2016 Harrison and Swarthout [2016]0.73 0.73 1.11 2017 Murphy and ten Brincke [2017]

5-9

Exhibit II: Parameter Estimates by Country from Rieger, Wang, and Hens [2017]

Year Country0.60 0.60 1.25 0.35 0.88 2016 Angola0.48 0.68 1.11 0.45 0.71 2016 Argentina0.41 0.45 1.08 0.62 1.00 2016 Australia0.37 0.37 1.28 0.54 0.78 2016 Austria0.56 0.59 1.08 0.41 0.98 2016 Azerbaijan0.44 0.55 1.42 0.64 0.94 2016 Belgium0.54 0.37 0.99 0.39 0.90 2016 Bosnia-Herzegovina0.42 0.83 1.62 0.44 0.60 2016 Canada0.54 0.90 1.72 0.52 0.73 2016 Chile0.54 0.55 1.43 0.52 0.94 2016 China0.42 0.37 1.26 0.40 0.78 2016 Colombia0.53 0.33 1.36 0.34 0.90 2016 Croatia0.56 0.45 1.49 0.46 1.00 2016 Czech Republic0.51 0.90 1.71 0.57 0.73 2016 Denmark0.35 0.37 1.52 0.40 0.78 2016 Estonia0.50 0.61 1.49 0.52 0.82 2016 Finland0.41 0.49 1.38 0.48 0.98 2016 France0.80 0.90 3.80 0.30 0.73 2016 Georgia0.42 0.49 1.38 0.44 0.71 2016 Germany0.50 0.30 1.29 0.44 0.82 2016 Greece0.35 0.34 1.27 0.39 0.78 2016 Hong Kong0.39 0.49 1.37 0.45 0.71 2016 Hungary0.41 0.49 1.38 0.52 0.71 2016 India0.42 0.49 1.32 0.40 0.71 2016 Ireland0.42 0.37 1.31 0.44 0.78 2016 Israel0.42 0.55 1.43 0.44 0.94 2016 Italy

0.26 0.55 1.37 0.71 0.94 2016 Japan0.30 0.21 1.10 0.38 0.81 2016 Lebanon0.48 0.31 1.29 0.36 1.00 2016 Lithuania0.46 0.46 0.94 0.55 0.75 2016 Luxembourg0.32 0.31 1.06 0.62 0.70 2016 Malaysia0.31 0.37 1.14 0.39 0.68 2016 Mexico0.71 0.60 1.95 0.52 0.88 2016 Moldova0.47 0.90 1.47 0.82 0.73 2016 Netherlands0.44 0.33 0.99 0.47 0.76 2016 New Zealand

0.71 0.37 1.05 0.30 0.78 2016 Nigeria0.39 0.45 1.27 0.55 1.00 2016 Norway0.47 0.55 1.59 0.45 0.94 2016 Poland0.48 1.72 2.31 0.50 0.34 2016 Portugal0.48 1.72 3.19 0.50 0.34 2016 Romania0.39 0.30 1.41 0.41 0.82 2016 Russia0.32 0.42 1.31 0.54 1.00 2016 Slovenia0.44 0.68 1.28 0.70 0.71 2016 South Korea0.44 0.74 1.63 0.47 0.88 2016 Spain0.48 0.82 1.60 0.58 0.80 2016 Sweden0.37 0.49 1.37 0.54 0.98 2016 Switzerland0.26 0.49 1.33 0.71 0.71 2016 Taiwan0.87 0.90 1.01 0.84 0.73 2016 Tanzania0.44 0.49 1.61 0.64 0.71 2016 Thailand0.55 1.06 1.51 0.55 0.94 2016 Turkey0.44 0.49 1.06 0.47 0.98 2016 UK0.42 0.49 1.36 0.44 0.71 2016 USA0.56 0.55 1.29 0.41 0.94 2016 Vietnam

5-10

Exhibit JJ: Empirical Distributions of Cumulative Prospect Theory Parameters

0%

20%

40%

60%

80%

100%

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10

Freq

uenc

y

Alpha Parameter (risk aversion for gains)

10th percentile 90th percentile

Tversky & Kahneman [1992]

0%

20%

40%

60%

80%

100%

0%

5%

10%

15%

20%

25%

30%

35%

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Freq

uenc

y

Gamma (Gains) Parameter

10th percentile

90th percentile

Tversky & Kahneman

[1992]

0%

20%

40%

60%

80%

100%

0%

5%

10%

15%

20%

25%

0.00 0.30 0.60 0.90 1.20 1.50 1.80

Freq

uenc

y

Beta Parameter (risk aversion for losses)

10thpercentile

90th percentile

Tversky & Kahneman

[1992]

0%

20%

40%

60%

80%

100%

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Freq

uenc

y

Gamma (Losses) Parameter

10th percentile

90th percentile

Tversky & Kahneman [1992]

0%

20%

40%

60%

80%

100%

0%

5%

10%

15%

20%

25%

0.80 1.30 1.80 2.30 2.80

Freq

uenc

y

Lambda Parameter (loss aversion)

10th percentile

90th percentile Tversky & Kahneman [1992]

5-11

Exhibit KK: Descriptive Statistics and Correlations for the Cumulative Prospect Theory Parameters

It is worth noting that the results, generally, differ materially with the initial estimates

of Tversky and Kahneman [1992], suggesting that incorporating distributional information

is important in terms of characterizing the population of decision makers. For calculation

purposes to eliminate numerical outliers, ranges explored for each of the parameters are

truncated to the 10th and 90th percentiles of the distributions in Exhibit JJ (and indicated in

the blue-shaded rows in Exhibit KK). Based on this assumption, the space of decision makers

can be described in cumulative prospect theory terms as being contained within the gray-

shaded spaces in Exhibit LL (for the value function58), Exhibit MM (for the probability

weighting function for gains), and Exhibit NN (for the probability weighting function for

losses), although not every point in those spaces is equally likely to be represented by a

decision maker.

58 The graph presents results for the interval ∈ [-$100, $100], but obviously could be extended arbitrarily.

Count 76 72 71 66 62Count (ex RWH) 22 18 17 12 8Average 0.53 0.62 1.58 0.51 0.88Average (ex RWH) 0.68 0.74 2.02 0.59 1.39Median 0.48 0.55 1.38 0.50 0.78Median (ex RWH) 0.73 0.81 1.83 0.61 0.75Minimum 0.21 -0.26 0.94 0.01 0.34Maximum 1.01 1.72 4.80 0.91 5.4810th Percentile 0.32 0.33 1.07 0.37 0.7010th Percentile (ex RWH) 0.25 0.45 1.25 0.29 0.6690th Percentile 0.84 0.92 2.25 0.71 1.0090th Percentile (ex RWH) 0.89 0.99 2.85 0.76 2.51

RWH = Rieger, Wang, and Hens [2017]

1.00

0.32* 1.00

0.31* 0.66*** 1.00 -0.09 0.26 -0.12 1.00

0.01 -0.57*** -0.42** -0.07 1.00

*, **, and *** indicate significance at the 95%, 99%, and 99.9% levels

5-12

Exhibit LL: Parameter Space for the Value Function

Exhibit MM: Parameter Space for the Probability Weighting Function (Gains)

-200

-150

-100

-50

0

50

100

-100 -80 -60 -40 -20 0 20 40 60 80 100

Val

ue F

unct

ion

Payoff

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Dec

isio

n W

eigh

t (G

ains

)

Probability

5-13

Exhibit NN: Parameter Space for the Probability Weighting Function (Losses)

A similar analysis can, conceptually, be performed with hyperbolic discounting.

However, estimation of the degree of “present bias” found in experimental results is

significantly complicated by the variety of functional forms assumed by researchers.59 There

are also issues with separating time discounting from the payoff amounts (or “amount-

dependent discounting” [Frederick, Loewenstein, and O’Donoghue, 2002]) in experimental

work, evaluating the relative credibility of promised future payoffs between experimental

designs, and specifying subject utility functions. Takeuchi [2011] even notes that

“correction” of these factors can induce future bias instead of present bias, although both

may coexist in subjects.

Notwithstanding these issues, an attempt must be made to compare the diverse

experimental results on a common footing in order to estimate the distribution of present

bias parameters across the population. I begin by employing the most general functional

form for time discounting in the literature: the generalized Weibull with fixed costs

[Benhabib, Bisin, and Schotter, 2010]. The generalized Weibull form for the discount factor

59 To be clear, by “present bias” we mean the empirical finding underlying hyperbolic discounting that decision makers have higher short-term discount rates (or lower short-term discount factors) and lower long-term discount rates (or higher long-term discount factors) than would be expected under an exponential discounting model.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Dec

isio

n W

eigh

t (Lo

sses

)

Probability

5-14

D [5] is useful because it allows for both present bias and future bias and nests the

exponential, hyperbolic, and quasi-hyperbolic models within it.

, ; , , , , 1 1 [5]

In [5], y is the payoff in question, t indexes time, is the curvature parameter of the discount

function ( 1 implies exponential discounting, 2 implies hyperbolic discounting), r

is the time discount rate, b is the fixed cost present bias parameter (for 0), and and q

are present bias parameters ( 1 and 1 indicate present bias).

Exhibit OO is a sort of “Rosetta Stone” that presents the functional forms employed

by previous experimental work and shows how each of the forms emerges from the

generalized Weibull model in [5]. In order to make appropriate comparison of the hyperbolic

bias parameters, each study’s functional form must be converted into the same shared form.

As a balance between modeling detail and parsimony, I use the Loewenstein and Prelec

[1992] model as a common ground for this study (the shaded row in Exhibit OO). When I

introduced this model in Section 5.2.2, I retained the notation common to the literature,

1 / , however, as the prospect theory functions already employ in the

value function (as the risk aversion parameter for gains), I will henceforth use instead to

indicate the hyperbolic bias parameter (or what is sometimes referred to as the degree of

hyperbolicity) in order to avoid confusion. The hyperbolic discounting function used,

therefore, is given in [6], where r is the time discount rate and is the hyperbolic bias

parameter (as → 0, [6] becomes exponential).

; , 1 / [6]

Each study in Exhibit OO was modeled according to its own parameters and

formulation. Then, the resulting data for each experiment was fit to [6] by minimizing the

sum of the resulting squared differences between the original functional form and [6]. The

5-15

result of this procedure was a distribution of hyperbolic bias parameters all common to a

single functional form. This distribution is illustrated in Exhibit PP.60

Common Name

Generalized Weibull with Fixed Costs parameters Discount Factor Formula Used by

y t q r b Generalized

Weibull with Fixed

Costs

y t q r b 1 1 Benhabib, Bisin, and

Schotter [2010]

Generalized Weibull y t q 1 r 1 0 1 /

Tanaka, Camerer, and Nguyen [2010]; Takeuchi

[2011]

Loewenstein and Prelec y t 1 1 r 1 0 1 /

Loewenstein and Prelec [1992]; Cairns and van

der Pol [2000]

Myerson and Green y t 1 1 s k 1 0 1

Myerson and Green [1995]; McKercher et al.

[2009]

Rachlin y 1 2 1 0 1 McKercher et al. [2009]

Harvey y t 1 1 b 1 0 1 Cairns and van der Pol [2000]; van der Pol and

Cairns [2002]

Mazur y t 1 2 k 1 0 1

Kirby and Maracović [1995]; Myerson and

Green [1995]; Kirby and Maracović [1996]; Cairns and van der Pol [2000];

Johnson and Brickel [2002]; van der Pol and

Cairns [2002]; Madden et al. [2003]; Anderson et al. [2008]; McKercher et al. [2009]; Tanaka, Camerer,

and Nguyen [2010]

Phelps-Pollak, or

the ( ) model

y t 1 → 1 ln

0

Paserman [2008]; Andreoni and Sprenger [2012]; Fang and Wang [2014]; Wang, Rieger,

and Hens [2016]; Laibson [2017]; Laibson et al.

[2017]

Exponential y t 1 → 1 r 1 0

Exhibit OO: Time Discounting Model Hierarchy

60 The data categorized under “No Fit” in Exhibit PP indicates the small portion of the sample (approximately 7%) for which the Loewenstein and Prelec [1992] model did not provide a reasonable fit. Those data points are excluded from the following analysis. The of all of the fits ranged from 87.6% to 100.0%, with an average of 97.7%.

5-16

Exhibit PP: Distribution of Hyperbolic Present Bias Parameters

Based on these results from the experimental work listed in Exhibit OO, for

calculation purposes in my study, the range explored for the hyperbolic parameter given

by the interval [0.1, 0.5]. → 0 is specifically excluded from the interval because I consider

the exponential discounting model separately. The population of decision makers, therefore,

is characterized as having the set of parameters , , , , , for the equations [2], [3],

[4], and [6] as defined in Exhibit QQ. In the next section, I turn to the assumptions made

about the “logistical” characteristics of their decision-making processes.

Parameter Purpose Lower Bound Upper Bound Risk aversion – gains 0.32 0.84 Risk seekingness – losses 0.33 0.92 Loss aversion 1.07 2.25 Probability weight – gains 0.37 0.71 Probability weight – losses 0.70 1.00 Hyperbolic bias 0.10 0.50

Exhibit QQ: Summary of Decision Maker Parameter Bounds

0%

20%

40%

60%

80%

100%

0%

10%

20%

30%

40%

50%

60%

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 NoFit

Cum

ulat

ive

Freq

uenc

y

Hyperbolic Bias Parameter usingthe Loewenstein and Prelec [1992] Functional Form

5-17

5.3.2 Decision Processes and Sequencing

Whereas the previous section characterized the population of decision makers

according to their preferences (as represented by the parameters of their objective functions),

in this section I turn to the functional representation of their decision processes and

sequencing. The conventional partition of decision makers has been that normative decision

makers follow both exponential discounting and expected utility theory. Likewise, the

descriptive model assumes that heuristic decision makers follow hyperbolic discounting and

prospect theory.

Exponential Discounting Hyperbolic Discounting

Expected Utility Theory Normative Normative Risk / Descriptive Time

Prospect Theory Descriptive Risk / Normative Time

Descriptive

Exhibit RR: Basic Taxonomy of Decision Processes

The off-diagonal entries in Exhibit RR, however, are also possible. Decision makers

might discount time in normative fashion (a hyperbolic function where → 0), but not

uncertainty. Similarly, decision makers might exhibit hyperbolic bias for time ( ≫ 0), but

respond normatively to uncertain choice tasks (a prospect theory formulation for which →

1, → 1, etc.). Accordingly, I allow for “quasi-normative” decision makers by adding [7]

and [8] to complement [1] and [2], thereby allowing for decision makers’ decision processes

to be affected by task presentation in such a way as to “resolve” one form of bias but not the

other (e.g., levelizing may suppress biases involving uncertainty, but not the perception of

time).

hyp [7]

exp [8]

5-18

Likewise, the sequencing of the decision process itself may be influenced by task

presentation to the extent that it raises the prominence of one dimension over another. Do

decision makers resolve time first or uncertainty? Conventionally, it is assumed that

uncertainty is resolved first, and then time second [9].

Uncertainty1st

Time2nd

[9]

But suppose that task presentation alters the decision maker’s perception of time such that

time is resolved first, and uncertainty is resolved second [10].

Time1stUncertainty2nd

[10]

Under the descriptive decision model (for example, if decision makers’ perception of time

varies [Read, 2001]), changing the decision sequence can result in different choices. In a

risky intertemporal choice framework, Weber and Chapman [2005] found that adding risk

to a choice task eliminated the immediacy effect (i.e., the violation of stationarity that gives

rise to the hyperbolic discounting model), while adding delay (time) to a choice task

eliminated the certainty effect (i.e., the violation of the independence axiom that gives rise

to the Allais paradox and can be explained by the incorporation of a nonlinear probability-

weighting function). These findings, however, were dependent on the presentation of the

various prospects to their subjects. As a result, I allow for the different sequences of decision

making in [9] and [10] to investigate these findings further.

5.4 Analysis and Findings

Having described the population of decision makers and their decision processes, I

now turn to their analysis. First, as a normative basis for comparison, I consider a utility

5-19

function [11] that exhibits constant absolute risk aversion and for which the Arrow-Pratt

coefficient of absolute risk aversion is ′′ ⁄ .

;

11 [11]

The analysis looks at the population of decision makers and illustrates the usefulness

of computational methods in informing experimental design. Based on the experimental

results in the literature, I create a “population” of decision makers. Each decision maker is a

(1 7)-vector of decision model parameters , , , , , , , where each parameter

is distributed according to the experimental results.61 As noted previously, because studies

have typically reported median parameter values, it is a distribution of medians, although I

assume (at minimal cost) that the distributions are asymptotically normal according to the

limiting distribution for the median order statistic.

The population, therefore, is multivariate normal, and each decision maker

~ , , with the vector of mean parameters and its variance-covariance matrix, both

parameterized and subject to truncation as specified in Section 5.3. If prospect theory and

hyperbolic discounting are accurate descriptive models of choice, then this specification

characterizes the “decision demographics” of the population and Monte Carlo simulation

can be used to conduct “virtual” experiments.

For each such virtual experiment, I generate 100,000 samples of x using a seven-

dimensional Sobol’ sequence of uniform [0,1] random variates transformed into a ,

distribution. A Sobol’ sequence [Sobol’, 1967] is a low-discrepancy or “quasirandom”

sequence that trades off statistical randomness for minimal statistical discrepancy (or equi-

distribution) in order to increase rates of convergence in Monte Carlo simulation.

61 The risk aversion coefficient is assumed to be truncated by 0.0001 and 0.02. The lower bound of 0.0001 is selected because it is approximately risk neutral. The upper bound of the risk aversion coefficient was calculated such that losses carried 7 times the weight of gains, reflecting extreme risk aversion. Given [11], and letting be the maximum level of payoff (or terminal wealth), I solved ; ; 7⁄ for , which is ln 7 ≅ 2 . When $100, ≅ 0.02.

5-20

To be sure, individual decision makers are likely to have a unique set of parameters.

The researcher undertaking an experiment with human subjects is drawing a sample of

from an “unknown” distribution. Thus, they must contend with not knowing whether the

effect they seek does not exist or whether the individuals subject to such an effect are simply

infrequently found within the population. By modeling decision makers at the population

level, this difficulty can be avoided.

I see two primary benefits of these virtual experiments. First, the incorporation of

probabilistic information (i.e., the decision demographics) can highlight areas where results

are “significant, but insignificant.” In other words, indicating where an experimental result

can be confirmed, but is only likely to affect a small portion of the population of decision

makers and is therefore of limited practical significance. Second, the virtual experiments

help to identify what should be expected from applying existing theory to novel problems.

In particular, the ability to evaluate the role of variable interactions on choice problem

outcomes is useful.

5.4.1 Incorporating Probabilistic Information into Decision Problems

First, consider the probabilistic information contained in the simulated population

results. Prior to examining the distribution of the population of decision makers, there was

no means by which to determine whether positive (or negative) findings were of practical

significance. That is, it is less interesting whether or not an experiment can be constructed

to elicit some outcome; rather, the result of interest should be how large the percentage of

the population (or what sub-population) produces a given result. By incorporating the

distribution of parameters throughout the population, one can observe both the distribution

of the prospect theory components themselves (Exhibits SS, TT, and UU), but also the

resulting distribution of population behavior for any given choice problem. For example,

consider the choice problem eliciting a preference for either a fixed immediate payment F

or a lottery at time t (the per period discount rate is 10%) of a 90% chance of receiving $200

and a 10% chance of owing (or losing) $1,000. The expected value of the lottery is $72.4 at

5-21

t = 1. The percentage of the population preferring the lottery measured relative to both F and

t is illustrated in Exhibit VV.

Exhibit SS: Probabilistic Representation of the Probability Weighting Function for Gains for the Simulated Population of Decision Makers

Exhibit TT: Probabilistic Representation of the Probability Weighting Function for Losses for the Simulated Population of Decision Makers

5-22

Exhibit UU: Probabilistic Representation of the Value Function for the Simulated Population of Decision Makers

Exhibit VV: Population Decision Demographics for a Choice Problem

5-23

Among the findings from this simulation are: (i) that the decision weighting function

exhibits considerably more dispersion for gains than for losses, (ii) that most of the activity62

in the decision weighting function for gains involves small probabilities, while a sizable

portion of the activity in the decision weighting function for losses involves larger

probabilities, and (iii) that only a relatively small portion of the population exhibits

meaningful loss aversion, although for those that exhibit loss aversion it tends to be severe.

Applying the population of parameters to a decision problem reveals (in this case) that the

percentage of population electing the lottery varies considerably according to the fixed

alternate payment F, but varies only slightly with time delay.

5.4.2 Evaluating Novel and Complex Problems

The second benefit is the ability to generate and test hypotheses with regard to the

outcome of novel choice tasks. I illustrate this ability with the results of two of the main

anomalies noted in the risky intertemporal choice literature. The first is the Certainty-Risk

Asymmetry, which proposes that discount rates are higher for certain outcomes than for risky

outcomes. In other words, a risky gain shifted into the future will become relatively more

attractive than a certain gain (and the opposite occurs for losses). If supported, this anomaly

would turn finance on its head, as discount rates are (normatively) a function of risk and

therefore should increase in risk and decrease in certainty. The experimental evidence for

Certainty-Risk Asymmetry is mixed, however, with Keren and Roelofsma [1995] finding

support for it, but Anderson and Stafford [2009] finding no support for it.

Consider the following two choices adapted from Anderson and Stafford [2009]63:

62 By “activity,” I mean that a plurality of the population is located in the referenced area. For example, in Exhibit SS, the plurality of decision makers is concentrated at overestimating small probabilities, while a smaller number exhibit far more diverse behavior for larger probabilities. 63 I begin the comparisons five periods into the future to avoid issues with the “immediacy effect” found by Karen and Roelofsma [1995].

5-24

Choice #1: 50 at or 50 at Δ Choice #2: 50 at or p chance of at Δ

1 chance of 0 at Δ

The lottery option is constructed to have the same expected present value as the fixed

options, except for the variable , which is used to manipulate the state 1 lottery payoff to

less than, the same, or greater than the expected present value. Certainty-Risk Asymmetry

is present if the discount rate implied by the risky option (Choice #2) is lower than the

discount rate implied by the certainty option (Choice #1), causing a preference reversal. For

example, in Choice #1, a preference for the deferred payoff would imply a discount rate of

less than 10%, while in Choice #2 a preference for the fixed payoff would imply a discount

rate of greater than 10% (at 0), the results together implying an asymmetry.

I performed simulations varying the state 1 probability p (5%, 50%, and 95%), the

adjustment to the state 1 lottery payoff value (-5, 0, +5), and the delay period Δ (1, 2, 3,

4, 5). As output, I captured the percentage of the simulated population switching their

preferences from Choice #1 to Choice #2. Exhibit WW illustrates the percentages of the

population showing preference reversals under each tested condition. An examination of

these results indicates how obtaining mixed results is feasible in a heterogeneous population

of decision makers. Looking primarily at the central column in Exhibit WW (the column

indicating no adjustment to the state 1 lottery payoff), several general findings emerge:

1. Decision makers following the normative rule (EDEU) do not exhibit Certainty-Risk Asymmetry (as expected).

2. Among heuristic decision makers following the traditional “uncertainty first” decision sequence, only between roughly 50% and 90% of decision makers exhibit Certainty-Risk Asymmetry.

3. Among mixed-rule decision makers (i.e., those that exhibit normative choice for either risk or time, but non-normative choice for the other), such as HDEU, the proportion exhibiting Certainty-Risk Asymmetry falls into the single digits.

4. Resolving time-related biases (shifting HD to ED) plays a bigger role in reducing the percentage of the population exhibiting Certainty-Risk Asymmetry than resolving uncertainty-related biases (shifting PT to EU).

5-25

Exhibit WW: Percent of Population Exhibiting Certainty-Risk Asymmetry The State 1 Adjustment reflects the amount added to either the fixed deferred payment or the deferred lottery payment. At zero, the expected values are equal, thus the adjustment amount can reveal risk preference. Simulations were performed based on whether the decision makers were assumed to resolve uncertainty first or time first as described in Section 5.3.2. The abbreviations in the second column refer to the decision models employed: EDEU (exponential discount, expected utility), HDEU (hyperbolic discounting, expected utility), EDPT (exponential discounting, prospect theory), and HDPT (hyperbolic discounting, prospect theory).

Probability of State 1 (p )

State 1 Adjustment (S 1)

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

EDEU 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 100 64.9 42.5 29.2 20.2HDEU 0.1 65.1 79.9 84.5 86.3 91.7 91.3 90.1 90.5 90.1 99.8 98.0 95.8 94.0 92.7EDPT 16.6 14.5 12.6 10.9 9.5 16.8 14.7 12.7 11.0 9.6 29.1 10.0 12.4 11.1 9.7HDPT 20.5 32.6 43.6 47.2 48.5 55.6 55.4 55.0 54.2 53.0 76.0 67.0 62.3 59.1 56.5EDEU 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 100 100 100 100 100HDEU 0.3 79.1 89.9 92.7 93.7 99.7 98.8 98.0 97.2 96.5 99.6 98.8 97.9 97.2 96.5EDPT 19.0 19.0 19.0 19.1 19.1 19.2 19.2 19.2 19.2 19.2 80.6 80.6 80.6 80.1 80.6HDPT 21.6 64.0 67.7 66.6 64.4 78.2 75.3 72.3 69.1 65.9 77.9 75.2 72.1 68.9 65.7

Probability of State 1 (p )

State 1 Adjustment (S 1)

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

EDEU 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 92.0 59.0 38.1 25.9 17.7HDEU 3.1 52.2 57.1 55.0 52.0 80.1 70.4 63.0 57.6 53.3 79.9 71.0 63.8 58.0 53.7EDPT 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 46.1 5.1 0.4 0.0 0.0HDPT 0.0 37.9 58.8 67.5 72.4 71.5 73.8 75.7 77.4 78.8 96.9 89.2 85.6 84.1 83.5EDEU 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 83.3 84.9 86.3 87.6 88.8HDEU 4.4 59.8 54.7 45.5 37.4 82.8 67.0 54.5 44.2 36.0 70.0 58.0 47.8 39.4 32.5EDPT 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 100 100 100 100 100HDPT 0.0 80.1 91.9 95.4 97.0 100 100 100 100 99.8 100 100 100 99.9 99.7

Probability of State 1 (p )

State 1 Adjustment (S 1)

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

EDEU 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 18.9 13.0 7.4 5.2 3.2HDEU 0.0 8.3 4.0 2.7 2.0 9.3 4.1 2.8 2.1 1.8 0.7 1.9 2.0 1.8 1.7EDPT 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 46.1 5.1 0.4 0.0 0.0HDPT 0.0 37.9 58.7 67.0 70.3 71.5 73.8 75.4 75.7 74.2 96.9 88.8 84.0 79.9 75.9EDEU 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 18.9 13.0 7.4 5.2 3.2HDEU 0.0 3.0 0.9 0.4 0.3 2.6 1.1 0.6 0.5 0.3 0.0 0.0 0.0 0.0 0.0EDPT 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 100 100 100 100 100HDPT 0.0 80.1 91.8 94.1 91.2 100 100 99.1 95.5 89.0 100 99.1 96.0 90.4 83.1

Lottery Delay ()

50%

95%

Uncertainty First

T ime First

-5 0 5

-5

Lottery Delay ()

Lottery Delay ()

Uncertainty First

T ime First

Uncertainty First

T ime First

0 5

-5 0 5

5%

5-26

The question, then, is less about whether Certainty-Risk Asymmetry exists, but

rather: (i) for whom does it exist, (ii) under what conditions does it exist, and (iii) how should

debiasing efforts be organized (if at all)? Exhibit WW starts to answer these questions. First,

Certainty-Risk Asymmetry is primarily a function of biased decision making with respect to

time. Succumbing to prospect theory biases alone does relatively little to induce widespread

Certainty-Risk Asymmetry behavior. The behavior exhibits relatively little sensitivity to

either the state 1 adjustment or the delay in receiving the lottery outcome. There is a greater

degree of sensitivity to the probability attached to the lottery payoff, and that sensitivity itself

is a function of the decision process used (see Exhibit XX). This is interesting because, as I

have previously stated, the prospect theory variables play a relatively small role in the

problem, but yet the probabilities (which are transformed by the prospect theory decision-

weighting function) vary significantly with other variables. It appears that the probabilities

become relevant even outside of the decision weighting function, because they control the

amounts subject to hyperbolic discounting.

Exhibit XX: Percent of Population Exhibiting Certainty-Risk Asymmetry with State 1 Adjustment at Zero, Using “Uncertainty First” Decision Sequence, and Varying

Decision Process

5%

50%

95%

5%

50% 95%

5%

50% 95%

0

20

40

60

80

100

Per

cent

age

of P

opul

atio

n E

xhib

iting

C

erta

inty

-Ris

k A

sym

met

ry

Lottery Delay (periods)1 2 3 4 5

EDEU

HDEU

EDPT

HDPT

Probability of State 1 Payoff

5-27

These interrelationships can be confirmed through further analysis of the simulation

data. I performed a logistic regression on the data in order to assess the influence on the

“switching” behavior of each member of the population as a function of their decision

demographics (Exhibit YY). The results of the analysis indicate that, in addition to the

prospect theory risk and loss aversion coefficients, the hyperbolic bias coefficient is also

strongly significant. More importantly, even though the decision-weighting function and

coefficient of risk aversion parameters are not individually significant, they are in

combination with other variables. These results suggest that while resolving hyperbolic bias

appears (as in Exhibit WW) to be most influential in affecting exhibition of Certainty-Risk

Asymmetry, the interaction of that bias with elements of the uncertainty-related parameters

is also influential.

z | | | | Constant -59.458 10.626 -5.595 ****

94.869 13.697 6.926 **** 13.283 1.430 9.290 **** -2.444 0.545 -4.481 **** -7.785 9.925 -0.784 -0.756 10.650 -0.071

-3.745 31.003 -0.121 69.206 22.908 3.021 ***

-29.286 1.992 -14.703 **** 1.002 0.648 1.545 64.985 34.887 1.863 * -17.861 18.059 -0.989 12.502 1.679 7.446 **** 19.753 12.812 1.542 -16.457 21.312 -0.772 -13.938 13.730 -1.015 54.893 22.967 2.390 **

AIC 8,594.4 Cragg-Uhler Pseudo-R2 95.6% Likelihood ratio statistic ( ⋯ 0) 102,347 , 0.0001 No. of observations 100,000

*, **, ***, and **** indicate significance at the 90%, 95%, 99%, and 99.9% levels, respectively.

Exhibit YY: Logistic Regression Results for Certainty-Risk Asymmetry. Case used is p = 0.5, = 3, and = 0 for HDPT, Uncertainty First.

5-28

The second choice task I examine involves Short-Long Asymmetry. In this anomaly,

the discount rate is observed to be higher in the short-term than in the long-term, as shifting

choices into the future makes them more attractive. This behavior is a clear violation of the

stationarity axiom, as shifting the choices across time should not alter subjects’ preferences.

Here, again, the experimental results in the literature are mixed. Albrecht and Weber [1997]

find (some) support for Short-Long Asymmetry. Öncüler and Onay [2009] find support for

the effect, but find the direction of the results mixed. Weber and Chapman [2005] note that

there is disagreement about the effect when subjects resolve risk or time first.

The basic structure of the anomaly is as follows. Subjects choose between two

lotteries in two choices:

Choice #1 50% chance of $100 now or 50% chance of $100+premium at t 50% chance of $0 now 50% chance of $0 at t

Choice #2 50% chance of $100 at Δ or 50% chance of $100+premium at Δ 50% chance of $0 at Δ 50% chance of $0 at Δ

Under normative choice rules, shifting the entire choice into the future by an amount Δ

should have no impact on the selection of lottery within each choice. The choice should,

normatively, remain consistent across time. I performed simulations varying the state 1

probability (5%, 50%, and 95%), the premium attached to the state 1 payoff for deferral of

receipt (-10, 0, 10), and the period of time the lotteries are moved into the future (Δ) and the

time between lotteries within each choice (t):

Short time shifts

Short vs long

Moderate time shifts

Long vs short

Long time shifts

Δ 1 1 5 10 10 t 1 10 5 1 10

5-29

Exhibit ZZ: Percent of Population Exhibiting Short-Long Asymmetry The State 1 payoff adjustment reflects the amount added to the state 1 payoffs in the deferred lotteries. Simulations were performed based on whether the decision makers were assumed to resolve uncertainty first or time first as described in Section 5.3.2. The abbreviations in the second column refer to the decision models employed: EDEU (exponential discount, expected utility), HDEU (hyperbolic discounting, expected utility), EDPT (exponential discounting, prospect theory), and HDPT (hyperbolic discounting, prospect theory).

Probability of State 1

State 1 Payoff Adjustment

11

110

55

101

1010

11

110

55

101

1010

11

110

55

101

1010

EDEU 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0HDEU 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 25.2 0.0 3.1 76.0 1.8EDPT 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0HDPT 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 15.6 0.0 0.3 83.8 0.1EDEU 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0HDEU 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 10.8 0.0 16.9 15.0 10.9EDPT 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0HDPT 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 10.8 0.0 16.9 15.0 10.9

Probability of State 1

State 1 Payoff Adjustment

11

110

55

101

1010

11

110

55

101

1010

11

110

55

101

1010

EDEU 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0HDEU 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 25.2 0.0 3.1 76.0 1.8EDPT 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0HDPT 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 15.6 0.0 0.3 83.8 0.1EDEU 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0HDEU 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 10.8 0.0 16.9 15.0 10.9EDPT 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0HDPT 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 10.8 0.0 16.9 15.0 10.9

Probability of State 1

State 1 Payoff Adjustment

11

110

55

101

1010

11

110

55

101

1010

11

110

55

101

1010

EDEU 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0HDEU 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 25.2 0.0 3.1 76.0 1.8EDPT 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0HDPT 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 15.6 0.0 0.3 83.8 0.1EDEU 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0HDEU 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 10.8 0.0 16.9 15.0 10.9EDPT 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0HDPT 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 10.8 0.0 16.9 15.0 10.9

5%

-10 0 10

Uncertainty First

T ime First

Uncertainty First

T ime First

50%

-10 0 10

Uncertainty First

T ime First

Shift into future ()T ime between lotteries (t )

Shift into future ()T ime between lotteries (t )

Shift into future ()T ime between lotteries (t )

95%

-10 0 10

5-30

As before, the output captured the percentage of the simulated population switching

their preferences from Choice #1 to Choice #2. Exhibit ZZ illustrates the percentages of the

population showing preference reversals under each tested condition. The vast majority of

variations showed no evidence of Short-Long Asymmetry. However, some elements of the

population do exhibit the effect. I consider this particular anomaly to investigate the question

as to whether the order of resolution of the decisions affects the likelihood of observing the

bias.

Keren and Roelofsma [1995], for example, have asserted that uncertainty and (time)

delay share a common dimension, but that uncertainty is the “more fundamental” of the two.

That is, that delay makes an outcome more uncertain, either due to the possibility that the

subject may not be alive (or otherwise available) to receive a deferred payoff, or that the

value of the deferred payoff may be reduced once it is actually received due to some then-

unforeseen event. Similarly, Weber and Chapman [2005] consider whether the presence of

one factor (uncertainty or time) can affect response to the other factor. The authors’

experiments supported answering both questions in the affirmative.

The design of the simulation developed here allows these claims to be investigated

directly. I simulated decision rules that implied resolution of uncertainty first and others than

implied resolution of time first. From this construct, I can evaluate the influence of each part

of the decision demographics on the percentage of the population exhibiting Short-Long

Asymmetry given that population members resolve uncertainty or time first. As the

classification tree in Exhibit AAA illustrates, however, use of the standard logistic regression

model is likely to fall prey to quasi-complete separation, as certain predictors work “too

well” in explaining the dependent variable. This is a common problem with logistic models

[Albert and Anderson, 1984]; here, it is the hyperbolic bias parameter that has an outsized

influence on the result.

Resolving the separation issue typically involves employing some form of bias

reduction in the maximum likelihood estimation process, since separation causes improper

inflation of the maximum likelihood estimates. An early bias reduction method was the

5-31

penalized maximum likelihood method proposed by Firth [1993], which employs what is

essentially a Jeffreys prior to remove first-order bias from the maximum likelihood estimate.

But the use of Jeffreys priors can sometimes cause computational issues of its own. Instead,

I use the Bayesian generalized linear model approach of Gelman et al. [2008], which uses a

Cauchy prior to provide a more stable estimation process in fitting the logistic regression.

Exhibit AAA: Classification Tree Analysis Illustrating Quasi-Complete Separation. Case used is p = 0.05, = 10, t = 1, and Premium = 100 for HDPT, Uncertainty First.

The traditional “Uncertainty First” model is presented in Exhibit BBB. When the

population of decision makers is assumed to resolve uncertainty first, all of the prospect

theory and hyperbolic bias parameters are strongly significant in explaining the occurrence

of Short-Long Asymmetry. That is, the population’s biases influence their judgments, and

83.8% of the population therefore exhibits Short-Long Asymmetry. In contrast, when the

population of decision makers resolves time first (in Exhibit CCC), only the time-related

parameter ( ) is significant ( , the prospect theory risk aversion parameter for losses (or

“risk-seekingness”), is weakly significant, but small). In the “Time First” case, the

population’s uncertainty-related biases do not influence their decision making, and only

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15.0% of the population exhibits Short-Long Asymmetry, which appears to occur primarily

because of time, or hyperbolic bias.64

Std. Error z | | | | Constant -29.626 1.786 -16.753 ****

36.185 2.564 14.111 **** 8.315 0.787 10.572 **** 2.092 0.276 4.580 **** -17.977 1.547 -11.625 **** 22.427 1.645 13.632 ****

-2.543 17.579 -0.145 92.941 5.134 18.104 ****

-12.987 1.067 -12.166 **** -0.860 0.351 -2.448 ** -17.185 19.578 -0.878 8.843 10.062 0.879 -15.149 1.016 -14.913 **** 26.177 2.301 11.374 **** 40.073 4.393 9.121 **** -30.938 2.454 -12.605 **** -57.118 4.619 -12.367 ****

Null deviance 88,604 on 99,999 degrees of freedom Residual deviance 25,509 on 99,983 degrees of freedom AIC 25,543 Cragg-Uhler Pseudo R2 79.6%

*, **, ***, and **** indicate significance at the 90%, 95%, 99%, and 99.9% levels, respectively.

Exhibit BBB: Bayesian Logistic Regression Results for Short-Long Asymmetry. Case used is p = 0.05, = 10, t = 1, and Premium = 100 for HDPT, Uncertainty First.

Using the simulation approach provides a useful addition to the results of Keren and

Roelofsma [1995] and Weber and Chapman [2005]. The results presented here suggest that

directing the decision makers to time first may “fix” biases related to uncertainty in the

Short-Long Asymmetry tasks. Obviously, because the simulation is not a human subject,

this is not a result of the decision makers’ biases being corrected, but rather that changing

64 This can also be confirmed by “turning off” hyperbolic bias in the decision demographics (in effect, making all decision makers exponential discounters) and re-running the simulation. In this case, where the population exhibited all of the uncertainty-related parameters, but not the time-related parameter, no cases of Short-Long Asymmetry occurred.

5-33

the structure of the problem to emphasize resolving time-related decision making first can

“immunize” decision makers in this task against the consequences of uncertainty-related

biases because most of the effect is caused by time-related factors.

Std. Error z | | | | Constant 7.215 1.406 5.133 ****

0.045 2.293 0.020 -1.521 0.902 -1.687 * -0.232 0.348 -0.666 -0.180 1.293 -0.139 0.157 1.205 0.131

-24.098 21.426 -1.125 -66.348 4.970 -13.349 ****

1.382 1.203 1.149 0.346 0.431 0.804 30.058 24.105 1.247 1.598 12.549 0.127 -0.721 1.759 -0.410 -1.768 2.109 -0.838 7.623 6.286 1.213 -0.522 2.184 -0.239 0.402 2.351 0.171

Null deviance 84,680 on 99,999 degrees of freedom Residual deviance 17,126 on 99,983 degrees of freedom AIC 17,160 Cragg-Uhler Pseudo R2 86.0%

*, **, ***, and **** indicate significance at the 90%, 95%, 99%, and 99.9% levels, respectively.

Exhibit CCC: Bayesian Logistic Regression Results for Short-Long Asymmetry. Case used is p = 0.05, = 10, t = 1, and Premium = 100 for HDPT, Time First.

Using simulation to investigate novel and complex decision problems in virtual

experiments is useful not only because of the lower cost of conducting the experiments, but

because a greater variety of treatments and manipulations can be explored, and cross effects

more easily examined. Further, while simulating experiments is not a substitute for the use

of human subjects, it is a useful testing ground for designing such experiments and

generating and evaluating hypotheses. Lastly, the parallel use of simulated experiments

provides a means of investigating the degree to which unintended experimental factors can

influence the results. The simulated populations are not sensitive to the actions of the

experimenter, or the design of the instrument, or the instructions given. Thus, it provides an

5-34

objective means of testing whether the results observed in an experiment are substantive or

superficial.

5.5 Applications and Implications

Relative to many other areas in the social sciences, behavioral decision making has

remaining rather underexplored by the computational social science approach. In this

chapter, I developed a computational framework to simulate experiments in risky

intertemporal choice on a population of decision makers whose demographics have been

estimated from a large body of prior experimental work on human subjects. Two primary

classes of applications were identified.

First, incorporating probabilistic information about the population of decision

makers helps to provide context to experimental results about the practical impact of biases

and the likelihood of observing certain patterns of behavior in large populations. This

information can be used to moderate attention on areas that are “significant, but

insignificant,” or areas where an effect is determined to be present, but lacking in a material

impact for a particular problem or problem environment. Such attention can be redirected to

areas where effects may be weak, but widely prevalent in a population or particularly

material for a problem.

Second, simulation can be used to perform virtual experiments on novel or complex

environments. This can be done both as a prelude and guide to experimentation with human

subjects, as well as a substitute in areas where experimentation with human subjects may be

impractical or impossible. The use of computational methods to facilitate the design of

experiments is a novel application, and may allow a more efficient and structured evaluation

of hypotheses when interactions are present, as well as to provide an experimental default

case where effects can be tested in a virtual “clean room,” stripped of the influence of human

experimenters and experimental instruments.

As a result, I believe the computational approach can provide for a symbiotic

relationship with the experiments on human subjects common to behavioral decision

5-35

making, as each approach informs and provides a check on the other. Behavioral decision

making has tended, necessarily perhaps, to focus on the decision making of individuals. A

different level of insight can be obtained from using computational methods to aggregate the

behavior of these diverse individuals and thus provide an atomistic means of examining the

behavior of large, diverse populations.

6-1

6 Presentation Compression: Investment Metrics & Heuristics

6.1 Introduction

Finance commonly considers decision problems that involve both risk and time.

These problems usually involve choice between “projects,” “investments,” or “policies.”65

Corporate managers must choose between undertaking different projects that have different

lifespans and different risks. Investors must choose among securities that have different

payoff profiles. Policymakers must consider alternative policies that have varying and

uncertain cost-benefit streams. More abstractly, these choice problems may be considered

intertemporal lotteries (combinations of payoffs and probabilities), which I shall call

“prospects” after Kahneman and Tversky [1979].

Finance practitioners are commonly taught to calculate and use certain metrics to

facilitate decision making about prospects [Shapiro, 1988; Brealey and Myers, 2003]. These

metrics include Net Present Value (“NPV”) and Internal Rate of Return (“IRR”) for business

applications, Equivalent Uniform Annual Cost66 (“EUAC”) for engineering applications,

and, for the power industry, the Levelized Cost of Energy (“LCOE”). Certain heuristic rules

are associated with these metrics. For example, the NPV rule states that Project A can be

judged preferred to Project B if the NPV of Project A is greater than the NPV of Project B.

These metrics, therefore, “compress” information about a prospect in that they collapse risk

and time into single figures (“expected present values” or “discounted expected values”) that

can be compared directly.

This compression process is intended to simplify decision making (it is “convenient”

[EIA, 2016]), even though classical finance has not generally discussed the use of metrics in

65 Or, implicitly, choice between the maintaining the status quo and another option. 66 There are a variety of iterations of this concept, which is commonly used in engineering and dates to Fish [1923], including Equivalent Uniform Annual Cost, Equivalent Uniform Annual Benefit, Equivalent Uniform Annual Worth, and Equivalent Uniform Annual Cash Flow, among others.

6-2

such decision-making terms. Normatively, however, the compressed presentation form of a

prospect is extensionally equivalent to the full presentation form of a prospect (see

Hirshleifer [1958], for example, regarding NPV). The information “lost” to compression has

no normative relevance to decision making. Heuristic decision makers, however, may not

see the two forms as extensionally equivalent [Bourgeois-Gironde and Giraud, 2009].

The complexity of transforming prospect presentation without altering preference

has long been demonstrated in the decision-making literature [Rugg, 1941; Schelling, 1981;

Tversky and Kahneman, 1981]. The practical challenges that compression imposes have led

some to assert that, in practice, decision makers should be given less information to make

better decisions, contradicting traditional economic theory [Iyengar and Lepper, 2000;

Schwartz, 2004]. However, this difficulty in maintaining consistent preferences across

presentation forms has done little to diminish the demand for such tools, which is ubiquitous:

“In spite of these manifest inadequacies in the available information, the policy-maker must frequently make some sort of decision without delay. The temptation for her/his advisors is to provide her/him with a single number, perhaps even embellished with precise confidence limits of the classic statistical form. When such numbers are brought into the public arena, debates may combine the ferocity of sectarian politics with the hyper-sophistication of scholastic disputations. The scientific inputs then have the paradoxical property of promising objectivity and certainty by their form, but producing only greater contention by their substance.” [Funtowicz and Ravetz, 1987: page 62]

This clash between presentation form and substance is at the core of this essay.

To the extent that presentation form influences preference over prospects for

heuristic decision makers, it becomes important to know how, and to what extent, such

influence extends. In other words, compression and the metrics created for it can be both

helpful and harmful devices depending on the characteristics of the decision maker and the

nature of the problem in question. For what types of problems do the use of metrics by

cognitively-constrained decision makers improve or worsen decisions as measured by

agreement between the descriptive choice rule employed and their choice made by a

normative choice rule? In this chapter, I apply the computational framework developed in

Chapter 5 to a practical application. I evaluate presentation forms for prospects designed to

be representative of many power-related investments (among other applications) and

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identify not only the types of problems for which compression may be either problematic or

beneficial, but also the types of decision makers for whom compression may be problematic

or beneficial.

In Section 6.2, I introduce LCOE as a metric and discuss its use. Section 6.3 develops

a model of the decision problem faced by heuristic decision makers, as well as the measures

used to evaluate decision performance. Section 6.4 reviews the specific analyses performed

and communicates their findings. Finally, Section 6.5 concludes by discussing the

implications of the findings and their practical applications.

6.2 The Levelized Cost of Energy in Theory and Practice

6.2.1 The Levelized Cost of Energy

Although several metrics are commonly calculated for decision making involving

prospects, I focus on one, the Levelized Cost of Energy, that is of particular relevance to

energy policy analysis. In its most basic form, the LCOE is a means of combining both fixed

and variable costs into a unitized cost. As such, it has three components: (i) recovery of fixed

cash flows, (ii) pass-through of variable cash flows, and (iii) unitization. Although LCOE

has traditionally been utilized to discuss competing energy investments or policies, its

calculation is applicable to any series of cash flows and is closely related to EUAC and to

NPV [Brown, 1994].

Assume a series of n costs or capital requirements , , … , . Given a discount

rate r, the NPV of those costs is ∑ 1 . The per-period “levelized” fixed payment

Γ is determined such that:

Γ1 1

[1]

The left side of [1] has a closed form:

6-4

Γ1

Γ Γ 1

Γ 1 1

[2]

Equating the levelized fixed payment to the costs:

Γ ∙1 1

1 [3]

Rearranging, the levelized fixed payment amount [4] can be determined.

Γ

1

TotalCapitalEmployed

∙1 1FixedChargeFactor

[4]

To arrive at the traditional operational definition of LCOE, the summation on the right side

of [4] can be referred to as the Total Capital Employed, which is multiplied by the Fixed

Charge Factor (which is essentially an annuity factor). The product of these figures, Γ,

reflects the per-period recovery of fixed capital costs. To this figure must be added per-

period non-capital fixed costs and variable costs, and the entire figure expressed on a unitized

basis (e.g., divided by per-period generation in megawatt-hours). The LCOE, which I shall

refer to as L, is then given by [5], which is expressed in dollars per MWh or cents per kWh,

or a similar form.

Γ FixedCostsGeneration

VariableCosts [5]

6-5

Although referred to as the Levelized Cost of Energy (or sometimes Electricity),

Reichelstein and Rohlfing-Bastian [2015] note that it is equivalent to long-run marginal

product cost, or what is called “life-cycle full cost” in cost accounting, and has applications

in manufacturing and service industries. Similarly, Grabowski and Vernon [1990] show that

levelized cost is also used in production of pharmaceutical products. However, it is by far

most commonly used in energy policy analysis worldwide for evaluating responses to

environmental regulation [MacDonald et al., 2016], capacity planning [ATSE, 2011; Nitsch

et al., 2012; Alberici et al., 2014; Danish Energy Agency, 2015; IEA, 2015; JANRE, 2015],

and project investment [Lazard, 2016].

In support of this widespread use are staunch defenders such as Sovacool [2008],

who has noted that within LCOE all decision elements are “reflected and quantified as best

as they can be” [ibid., p. 249]. Notwithstanding his advocacy, a cottage industry has emerged

in generating “fixes” for LCOE. These modifications are intended to address what are

asserted to be shortcomings in the use of LCOE that lead to less-than-optimal choices. They

have included its failure to include residual values and financing effects [Velosa and Aboudi,

2016], its handling of outages and mid-life capital additions and replacements [Kakade,

1989], its failure to recognize differential rates for investing and borrowing [Manzhos,

2013], and its failure to include system integration costs (for intermittent renewable energy

sources) [Ueckerdt et al., 2013; Hirth, Ueckerdt, and Edenhofer, 2015]. In virtually each

case, the solution proposed was the inclusion of additional parameters in the formula. A

single value for each option was still produced, but it was computed with more input data—

that is, significant increases in compression were involved.

Taking a slight step backward, the U.S. Department of Energy’s Energy Information

Administration’s proposed “fix” was the creation of a separate measure called Levelized

Avoided Cost of Energy (“LACE”) [EIA, 2016], that was intended to be used in conjunction

with LCOE in order to better reflect “economic value.” This could be considered a degree

of “decompression.” It is telling, however, that the EIA acknowledged that their long-term

projections of capacity additions “use neither LACE nor LCOE concepts” [ibid.].

6-6

6.2.2 Levelized Cost vs. Levelized Cash Flow

What many of the above “fixes” demonstrate is that LCOE has exclusively been a

measure of costs, or capital outflow. This characteristic is by design, as it emerged from the

regulated utility world in which the costs of an investment approved by regulators were its

revenues. But critiques of LCOE on such matters as differential borrowing and lending rates

or exclusion of residual values target this cost-only foundation.

Perhaps the most forceful critique of this nature has been that of Joskow [2010;

2011]. Joskow [2010] noted that LCOE had emerged from the regulated utility world and

was not generally suitable for the merchant power generation world. Joskow [2011] then

demonstrated that LCOE tends to misrepresent the value of intermittent (renewable) sources

of generation relative to dispatchable sources of generation because it neglects the value of

the electricity generated by each source (recall that LCOE is a cost measure). Because

electricity in deregulated markets is not a homogeneous commodity (it is delivered at

different times in different locations), its value varies widely (by, I would note, time and

uncertainty of delivery). Not only does LCOE then create an improper comparison between

intermittent and dispatchable resources, but also between different intermittent resources

(e.g., wind and solar) themselves.

Rather than “fix” LCOE as so many others have proposed, Joskow’s [2011] advice

was to abandon it in favor of looking at actual market values for the electricity by each

source. Restated in the terms of this essay: Joskow argued that the use of LCOE as a metric

and the heuristics that employ it could lead to preference reversals because the compression

process omitted information that did, in fact, have normative relevance. I don’t take as

extreme a stance. The idea of “levelizing” cash flows (not just costs) appears in many areas

and can have useful applications. Annuities and mortgages, for example, are typically

levelized positive and negative cash flows (at least to the recipient), respectively, that can be

attractive means of intertemporal income and consumption smoothing. Even in electric

power markets, expected capacity revenue is often modeled as a “residual fixed cost,” which

is the levelized revenue requirement of a generator unmet by variable revenue sources and

6-7

thus the result of the classic two-part tariff problem in economics [Hopkinson, 1892; Oren,

Smith, and Wilson; 1985]. In most deregulated electric power markets, for example, capacity

prices are determined (in general terms) as the intersection of the Cost of New Entry

(“CONE”) less earnings from energy market operations (energy and ancillary services

revenue) (“Net CONE”) and the demand curve. Net CONE is expressed as a levelized figure

inclusive of both positive and negative cash flows (depending on the perspective assumed).

For the remainder of this essay, I use LCOE in this general sense to refer to the

“levelized” or compressed presentation of cash flows (both positive and negative). For

convenience of exposition, I ignore the characteristics that make it specific to electric power

(i.e., the per-period fixed costs, variable costs, and unitization), as they are not material to

the discussion of compression. Accordingly, my references to LCOE in the remainder of this

essay are to Γ as defined in [4] above—the levelized portion of (capital) cash flows. It is this

portion of the LCOE that deals directly with compression.

6.3 The Decision Problem

Consider two prospects, A and B. Each decision maker follows either a normative

(N) or descriptive (D) choice rule that indicates their preference over the prospects as

presented.67 For example, ≻ indicates that a decision maker using a normative choice

rule would prefer A to B. A rational decision maker is assumed to act in accordance with N;

a heuristic decision maker in accordance with D. A prospect may be presented in one of two

forms: a full form F or a compressed form C. The full form of a presentation is as a lottery

or decision tree or, in finance terms, a cash flow profile (i.e., it conveys detailed information

about uncertainty and time). The compressed form of a presentation is a metric—here, as

LCOE. To continue the example, ≻ indicates that a decision maker using a

normative choice rule and presented with A and B in full form would prefer A to B.

67 I ignore indifference throughout this description in the interest of clarity.

6-8

The usefulness of a presentation and its associated heuristic (which I refer to as a

“presentation-heuristic pair”68) is measured by the agreement their use induces with a

normative choice rule under the full (or compressed) presentation. The full and compressed

presentations are treated equivalently by the normative rule and therefore I do not distinguish

between them further. Exhibit DDD illustrates the various paths of this decision-problem

construction. The outcome space can be characterized by six basic descriptions. The first

two refer to the sorts of heuristics and biases commonly discussed in the behavioral decision-

making literature. I describe a choice rule D that results in the same choice as a choice rule

N as well-calibrated, in the sense that the heuristic choice rule leads to the normative

selection. In contrast, a choice rule D that results in a choice other than the normative choice

rule N is considered biased, in the sense that its use of simplifying heuristics potentially

subjects the decision maker to biases in judgment.

Exhibit DDD: Diagram of Choice Rule and Presentation Relations

The remaining four descriptions noted in Exhibit DDD refer to the actions of

heuristic decision makers presented with both full and compressed presentations. A heuristic

68 To reiterate, for the sake of clarity, the presentation is, for example, NPV, and the heuristic in that case is “pick the project with the greatest NPV.”

≻ ≺

≻ ≺

≻

BiasedWell-calibrated

Simplifying

Counter-productive

IrrelevantUseful

Areas of the problem space where the use of

C should be encouragedAreas of the problem space where

use of C should be carefully monitored or discouraged

6-9

decision maker presented with a decision problem in compressed form that makes the same

decision as a heuristic decision maker using the full form (i.e., a well-calibrated decision

maker) and a normative decision maker indicates that the compressed form is simplifying.

That is, the correct decision is being made with less information and therefore less cognitive

effort. If, in contrast, the compressed form leads such a well-calibrated decision maker to

indicate a preference in opposition to the descriptive and normative rule, the compressed

form is counter-productive. That is, the compression of information causes a bias in

decision making that was otherwise not present with the full form of the problem.

Discordance between the full and compressed forms, however, may not necessarily be a

negative trait. If a heuristic decision maker is led to make a normatively-incorrect decision

when presented with the full form of a decision problem that could be “corrected” by use of

the compressed form, then the compressed form is useful.69 In this case, it is the reduction

in (rather than the presence of) information presented that triggers a biased decision by the

heuristic decision maker. If, however, such a decision maker continues to make the

normatively-incorrect choice using the compressed form, then the compressed form is

irrelevant. In this case, presentation compression is “transparent” in that it has no bearing

on the original biased decision made by the decision maker.

The simplifying and useful areas of the outcome space, then, demarcate areas where

certain aspects of the decision problem and/or certain characteristics of the decision maker

lead to favorable outcomes that should be encouraged. In short: areas where compression is

a beneficial force. In contrast, the counter-productive and irrelevant areas of the decision

space indicate areas to be avoided. In short: areas where compression is an unhelpful force.

The purpose of this analysis, then, is to identify the areas of the problem space and the

segments of the population of decision makers where and for which the use of metrics and

heuristics are simplifying or useful and where they are counter-productive or irrelevant.

69 For example, if the full presentation form of a problem involved decision problems involving heavy losses or small probabilities, etc., one may expect a heuristic decision maker to succumb to the biases commonly-acknowledged in such circumstances. Such a decision maker’s biases may not be triggered if the compressed form obscures those characteristics through levelizing.

6-10

Any practical advice on the proper use of heuristics must be given cognizant of the

boundaries imposed by the “imperfectness” of the compression they employ. In finance, by

way of example, advocacy for the use of the internal rate of return (“IRR”) as a metric is

always tempered by the caveat that multiple sign changes in cash flows between periods

leads to unstable results (because the solution of the polynomial equation then has multiple

roots). So, too, should use of LCOE—or indeed any metric—be guided by the contours of

the space it traverses.

The response to this space can be estimated by using well-established theories of

heuristic decision making under risky intertemporal choice. A considerable body of evidence

(cited extensively in Chapter 5) supports the prospect theory [Kahneman and Tversky, 1979]

and hyperbolic discounting [Thaler, 1981; Ainslie, 1991] models in such circumstances. If

prospect theory and hyperbolic discounting models are accurate representations of human

behavior with regard to uncertainty and time, then one means by which such insight could

be obtained is the computational exploration of that space. This sort of computational

approach is shared with the “Candle-Lighting Analysis” of Kimbrough and colleagues

[Kimbrough et al., 1992; Kimbrough, Oliver, and Pritchett, 1993], as well as Miller’s [1998]

“Active Nonlinear Tests,” although their approaches generally employ heuristic

optimization methods.

I argue that such exploration should occur prior to experimental exploration of that

space because of the relative efficiency of computational methods in exploring vast search

spaces. Additionally, because knowledge of the problem space can facilitate the generation

of structural hypotheses that can then be supplemented and shaded with the substructural

detail more appropriate for exploration with human subjects. Such a computational approach

has two distinct components: (i) a model of the decision makers and (ii) a model of the

decision problems.

Chapter 5 of this dissertation develops a computational model of heuristic decision

makers and develops a simulation framework for evaluating the decision-making behavior

of a population confronted with various decision problems. I use that model and approach

6-11

here and proceed with a simulated population of decision makers, for which each member

of the population is represented by the 7-tuple , , , , , , , which comprises,

respectively, the risk aversion coefficients for gains and losses, the loss aversion coefficient,

the decision weight parameters for gains and losses, the Arrow-Pratt coefficient of risk

aversion, and the hyperbolic bias parameter particular to that decision maker. Each of these

“virtual” decision makers are then exposed to a set of decision problems. The remainder of

this section details the process by which the decision problems are evaluated. Section 6.4

then develops a model of decision problems and conducts the search over the space of

problems.

6.3.1 Decision Problem Structure

Consider a population of decision problems S.70 In order to set out the evaluation

structure of the compression decision problem, I define a decision function

≻ ; , ∈ that takes a choice rule71 ∈ , (as described in Sections 5.3.1

and 5.3.2) and a prospect presentation form ∈ , (described below) and indicates a

preference for a pair of prospects in S, the set of all prospects (described in more detail in

Section 6.4).72 For example, ≻ ; , indicates that a normative choice rule acting

on the full-form presentation of prospects A and B results in the choice A. Having established

this notation, the following steps are performed:

70 In abstract terms, these decision problems are intertemporal lotteries. In the application discussed in this chapter, they are specific power project investments. 71 By “choice rule,” I mean exponential discounting-expected utility for normative (N) decision makers and hyperbolic discounting-prospect theory for heuristic (D) decision makers. 72 The notion of a “decision function” here may be considered a computational substitute for a human subject in a more traditional experimental setting. They are, in a sense, automata, designed to represent the choices of decision makers acting according with certain rules and presented with certain choices.

6-12

1. Randomly select two prospects from S, 2. Randomly select a representative sample of decision makers from the

simulated population of decision makers (Chapter 5), 3. Apply ≻ ; to the prospects, 4. Apply ≻ ; to the prospects, 5. Apply ≻ ; to the prospects, 6. Measure agreement between the choices indicated by the functions in steps

3-4.

With each of the steps evaluated, an outcome classification can be made in keeping with

Exhibit DDD. This outcome classification (Exhibit EEE) draws a correspondence between

the agreement among presentation-heuristic pairings and their usefulness. The evaluation of

a particular presentation-heuristic pair (as Simplifying, Useful, etc.) is a function of the

consistency pattern of its decision functions.

Two presentation forms are considered: Full and Compressed. The Full

presentation form is an intertemporal lottery of multiple periods, with the per-period time

discount rate equal to r. The Full intertemporal lottery form (for three periods) is illustrated

in Exhibit FFF. The Compressed presentation form (also illustrated in Exhibit FFF) is the

levelized equivalent of the lottery. The levelized amount Γ is defined as in [4] such that the

NPV of the lottery (at r) is equal to the NPV of the levelized payment stream (at r).73 I denote

probabilities as p and the payoff amounts as Π , where s represents the state of the world

and t indexes time. Having defined the structure of the problem and the means of evaluation,

I now turn to the analysis of the prospects.

73 That is, ∑ Π 1 Π Γ∑ in this notation.

6-13

≻ ; , ≻ ; , ≻ ; , Simplifying

≻ ; , ≻ ; , ≻ ; , Counterproductive

≻ ; , ≻ ; , ≻ ; , Irrelevant

≻ ; , ≻ ; , ≻ ; , Useful

Exhibit EEE: Presentation-Heuristic Pairing Agreement Classification

Exhibit FFF: Full and Compressed Presentation Forms

=

=

Simplifying

=

≠

Counterproductive

≠

=

Irrelevant

≠

≠

Useful

1

Π

Π1

Π

Π1

Π

Π

Γ Γ Γ

6-14

6.4 Analysis and Findings

6.4.1 Power Investments as Intertemporal Lotteries

The objective of this study is to investigate decision making involving power projects

in a plausibly realistic, yet tractable setting. The task, then, becomes how to represent power

projects as intertemporal lotteries. Such projects can be characterized generally as consisting

of three phases: (i) a construction phase, (ii) an operating phase, and (iii) a decommissioning

or salvage phase. The total duration of the three phases varies according to project type, and

can involve considerable uncertainty related to technological, economic, and regulatory

factors [Rode, Fischbeck, and Páez, 2017]. Furthermore, there is uncertainty involved in

each phase as to the costs, as well as the operating and financial performance, of the projects.

Most of the common financial metrics are based on the cash available for finance (by

either debt or equity) (“CAFF”).74 Alternatively, in certain settings, such as cost-of-service

regulation, a cost-only measure is more appropriate. In either case, the metrics in question

(such as NPV, IRR, or LCOE) make use of a “bottom line” cash flow number per period

(see Exhibit GGG). Accordingly, each period must comprise a separate lottery reflecting the

cash flow or cost experiences particular to that period. The resolution of that uncertainty in

each period provides the cash flow or cost employed by the financial metric for decision-

making purposes.

74 Cash available for finance is defined as the total cash available for distribution to a firm’s capital structure. It is equal to the free cash flow in an Adjusted Present Value model [Brealey and Myers, 2003] and the free cash flow to equity in a 100% equity-financed model. The CAFF is what is available either for the payment of debt service or distribution to equity holders.

6-15

Exhibit GGG: Typical Power Project Cash Flow Derivation

These lottery representations include many of the characteristics known to influence

decision making (e.g., low probability-high consequence outcomes, periods framed as gains

and losses, payoffs stretched across time, and risk). Accordingly, in the context of the

framework described in Section 6.3.1, each period involves a lottery between a base outcome

(the top branch of the lottery) and an alternate outcome (the bottom branch of the lottery),

each of which occurs with a particular probability. I seek to examine the particular

characteristics of such constructions that pose potential problems or opportunities for

heuristic decision makers.

6.4.2 Basic Prospect Structures and Design Elements

To populate S, the set of prospects, I create power project intertemporal lotteries

defined along nine dimensions and then create a “population” of power projects by exploring

all of the combinations possible along these nine dimensions. The nine dimensions are

Revenues Costs+ Energy Revenue + Fixed Operating & Maintenance Costs ("FOM")+ Capacity Revenue + Variable Operating & Maintenance Costs ("VOM")

+ Fuel Costs= Total Revenues = Total Costs

– Initial Capital Cost & Future Capital Expenditures= Total Expenses ← Expense-only presentation

Total Revenues – Total Costs= Gross Margin – Depreciation= Taxable Income – Income Tax= Net Income+ Depreciation+ Tax Incentives – Initial Capital Cost & Future Capital Expenditures= Cash Available for Finance ("CAFF")

6-16

defined as below, and reflected in a series of binary lotteries over time. All of the “payoff”

values are converted to dollars per kilowatt-year ($/kW-year, or $/kW for short, when the

time period is unambiguous) for comparative purposes and presented in constant dollars.

Exhibit HHH: Four Example Cash Flow Profiles

-$10.0

-$5.0

$0.0

$5.0

$10.0

1 6 11 16 21 26 31 36 41 46 51 56Ln(

$/kW

)(c

onst

ant d

olla

rs)

Nuclear

Base

Alternate

-$10.0

-$5.0

$0.0

$5.0

$10.0

1 6 11 16 21 26 31 36 41 46 51 56Ln(

$/kW

)(c

onst

ant d

olla

rs)

Wind

Base

Alternate

-$10.0

-$5.0

$0.0

$5.0

$10.0

1 6 11 16 21 26 31 36 41 46 51 56Ln(

$/kW

)(c

onst

ant d

olla

rs)

Solar

Base

Alternate

-$10.0

-$5.0

$0.0

$5.0

$10.0

1 6 11 16 21 26 31 36 41 46 51 56Ln(

$/kW

)(c

onst

ant d

olla

rs)

Natural Gas Combined Cycle ("NGCC")

Base

Alternate

6-17

First, I model four general types of project: nuclear, wind, photovoltaic solar, and

natural gas combined cycle (“NGCC”). These four main project types reflect a diverse array

of cash flow profiles due to their operational, economic, and incentive-related characteristics

(illustrated in Exhibit HHH).75 The alternate cases within each lottery are created by

worsening the estimated capital cost and decommissioning costs by 50% and the operating

costs by 10%. Especially in the case of capital costs, these estimates may prove conservative,

as there is a great deal of evidence of significant cost overruns among large infrastructure

projects [Flyvbjerg, Bruzelius, and Rothengatter, 2003]. Each of these project types has a set

of inputs unique to their technology, including capital cost, capacity factor (percent of the

year in operation), and operating costs, as described in Exhibit III.76

Exhibit III: Four Power Plant Classes and Class-Specific Information

Second, I model six different project-lifespan levels based on a sixty-year lifespan

limit, with the model variables reflecting 50%, 60%, 70%, 80%, 90%, or 100% of that limit.

I emphasize that not all technologies are equally likely to realize different parts on this range

of lifespans. For example, while a nuclear power plant may be commonly expected to remain

75 The figures in Exhibit HHH are presented in a log scale, with negative values calculated as ln . 76 The items Capital Cost (the initial construction cost of the plant, expressed as an overnight cost), Fixed Operating & Maintenance (“FOM”) (such as labor and routine maintenance that does not vary with the level of production), Variable Operation & Maintenance (“VOM”) (such as consumables and usage-dependent maintenance), and Fuel are calculated based on figures from the U.S. Department of Energy’s Energy Information Administration’s Assumptions to the AEO and Annual Energy Outlook 2017 document, with the exception of the fuel costs for nuclear plants, which is taken from figures provided by the Nuclear Energy Institute. Estimated nuclear decommissioning costs are based on the actual costs of the nuclear plants that have completed the decommissioning process. All dollar figures provided in $/MWh are converted to $/kW-year based on assumed capacity factors, as discussed below. The Capacity Availability Rating reflects the percentage of plant capacity that is permitted to receive capacity revenue, and is based on the forced outage ratings commonly accepted in many wholesale capacity markets (I assume availability = 1 – eFORd).

Capital Cost (2016$)

FOM(2016$/kW-year)

VOM (2016$/MWh)

Fuel (2016$/MWh)

Capacity Availability

Rating

Decommissioning Expense

(2016$/kW)Nuclear $5,880 $99.65 $2.29 $6.76 95% -$1,200Wind $1,686 $46.71 $0.00 $0.00 5% $0Solar $2,277 $21.66 $0.00 $0.00 0% $0NGCC $1,094 $9.94 $1.99 $30.93 90% $0

6-18

in operation for sixty years, such a period of commercial operation would be rather

unprecedented for a solar project.

Third, I model capacity-factor levels uniquely for each technology based on ranges

commonly experienced. The resulting seven levels for each technology are provided in

Exhibit JJJ below. Capacity factor is important not just as a measure of energy generation,

but also as an indicator of the energy prices realized by generators (as prices vary by time of

day, day of week, and month of year). Only a generator that operates 100% of the year could

be expected to realize the average annual energy price. In contrast, although a solar power

plant may only operate 20% of the year, those hours tend to be the highest-priced peak hours,

and therefore they would be expected to receive revenue more than the average annual

energy price (or the average price, conditional on time of delivery). For the sake of simplicity

in this analysis, I ignore transmission constraints and assume each generator operates under

daily operating discretion as a merchant. I constructed a price-duration curve based on 10-

years of historical energy price data for four regions across the country.77 From that data, a

conditional average energy price can be constructed based on the assumption that each

generator’s operation is scheduled to occur during the highest-price hours.78

Exhibit JJJ: Capacity-Factor Levels for Each Type of Power Plant Included

77 The four regions were selected to reflect a broad cross-section of the country’s electricity markets are comprise prices at the Southern (south), Palo Verde (western), PJM (mid-Atlantic), and ISO-NE (northeast) trading hubs. 78 Except for wind, which operates intermittently across all hours.

Level Nuclear Wind Solar NGCC1 70.0% 25.0% 15.0% 30.0%2 73.3% 26.7% 15.8% 36.7%3 76.7% 28.3% 16.7% 43.3%4 80.0% 30.0% 17.5% 50.0%5 83.3% 31.7% 18.3% 56.7%6 86.7% 33.3% 19.2% 63.3%7 90.0% 35.0% 20.0% 70.0%

6-19

Exhibit KKK: Capacity Factor and Energy Price Multiplier Curves

Fourth, an important part of the economic equation for many generators is the level

of government incentives they receive. These incentives can take several forms from

accelerated depreciation, to production tax credits, to investment tax credits. Each

technology is modeled based on the incentives to which they are entitled. Each power plant

type benefits from MACRS depreciation appropriate to its property class (5 years for

renewable projects, 15 years for nuclear, and 20 years for NGCC).79 Further, wind projects

are eligible for production tax credits amounting to $23/MWh for ten years (less 20% for

projects entering commercial operation in 2017). Lastly, solar projects are eligible for an

investment tax credit, paid at commercial operation, equal to 30% of the eligible cost basis.

These incentives play a significant role in altering the cash-flow profiles for renewable

projects.

Fifth, in order to incorporate uncertainty over future energy prices, I incorporated

five different “trajectories” to energy prices: flat, rising, falling, peak, and trough. The levels

are set in each such scenario to not alter the lifetime average price, but simply to shift that

79 MACRS is the Modified Accelerated Cost Recovery System and is used by the Internal Revenue Service to determine the amount of annual depreciation permitted for a given asset.

0%

50%

100%

150%

200%

250%

0.0x

0.5x

1.0x

1.5x

2.0x

2.5x

0% 20% 40% 60% 80% 100%

Ene

rgy

Pric

e R

eali

zed

Con

ditio

nal o

n C

apac

ity

Fac

tor a

nd R

elat

ive

to A

vera

ge

Prc

ie

Ene

rgy

Pri

ce R

elat

ive

to A

nnua

l Ave

rage

Percent of the Year

Price Duration Curve (left axis) Realized Price Curve (right axis)

6-20

price across time. Given that all energy prices are given in constant dollars, the “rising”

trajectory could indicate real increases in the price of energy. The “peak” trajectory could

indicate a “break-in” period early in a powerplant’s life, followed by performance

degradation as it approaches retirement. The remaining trajectories could be characterized

similarly. Exhibit LLL illustrates the five trajectories incorporated.

Exhibit LLL: Energy-Price Trajectories with Multipliers Relative to Average Price

Sixth, evaluations can be made using the expenses only, or the cash available for

finance calculations. In the expense-only option, all revenues are excluded, but incentive

payments are still allowed to offset expenses.

Lastly, the seventh, eighth, and ninth dimensions comprise the probabilities

associated with the capital cost, operational, and decommissioning phases of project life.

Three levels (5%, 50%, and 90%) are used during each phase and applied to the top branch

of each lottery. The probabilities for the bottom branch are set to be one minus the top branch

probability in each case.

1 Flat

2 Rising

3 Falling

4 Peak

5 Trough

1.0x 1.0x

0.75x

1.25x

0.75x

1.25x

0.75x

1.25x

0.75x

0.75x

1.25x 1.25x

6-21

Collectively, the combinations of these elements allow for 4 6 7 2 5 2

3 3 90,720 different possible prospects covering a wide range of cash flow or expense

profiles. From this set, 60,480 scenarios reflecting infeasible combinations are eliminated.

These include scenarios that include the presence of renewable energy incentives for nuclear

and NGCC and the presence of decommissioning expenses for non-nuclear plants. The

remaining 30,240, because of their construction, are also designed to be representative of the

cash flow profiles of actual projects.80 Therefore, these 30,240 power plant project prospects

are defined as the population of prospects, from which comparisons are drawn for evaluation

purposes in the next section.

6.4.3 Compression and Different Prospect Designs

This paper began by proposing to investigate the extent to which one form of problem

presentation—compression—influences choice, here in a specific application: choice

between power projects. As outlined in Exhibit DDD above, there are two parts to this

question: (i) for what types of problems is compression characterized as Simplifying,

Counterproductive, Irrelevant, or Useful, and (ii) for what types of decision makers is

compression similarly characterized? The intent of asking these questions is to receive a

better understanding of the role of compression, and the usefulness (or lack thereof) of LCOE

as a compressed metric and basis of a heuristic rule within a real-world problem

environment.

In addition to describing the general simulation environment used, this section

addresses the first question. Section 6.3.1 described the modeling process in general terms.

As to specifics, 6,000 random draws of two prospects from the population of 30,240

prospects are performed. Each pair of prospects is evaluated by a population of 500

simulated decision makers using each of three rules to produce a “choice triple.” Each choice

80 Similarly, scenarios that compare expense-only cash flow profiles to full cash flow profiles are eliminated in the sampling process as they represent unfair comparisons. Also, because the order in which prospects A and B are selected is not relevant, results from comparing Prospect i to Prospect j are consolidated with those comparison Prospect j to Prospect i.

6-22

triple is then classified as Simplifying, Counterproductive, Irrelevant, or Useful, as defined

in Section 6.3.1. I then further consolidate the outcomes as either Good (Simplifying or

Useful) or Bad (Counterproductive or Irrelevant) and indicating either Change

(Counterproductive or Useful) or No Change (Simplifying or Irrelevant) for purposes of

describing the results. Outcomes classified as Good represent those for which the use of

compression does no harm. Also of interest is whether or not the use of compression prompts

decision makers to change their decisions. Such changes may or may not have positive

outcomes, but are clearly evidence of a lack of procedural invariance.

I examine whether there are different characteristics of the prospects (described in

Section 6.4.2) that result in different outcomes. For example, does the use of compression

(i.e., levelizing) with prospects of a certain type (e.g., long-lived or accelerated cash flows)

result in “Good” or “Bad” outcomes when applied to choices involving power projects?

There are clear a priori reasons behind such questions that allow for the formulation of

hypotheses. Many of these reasons, however, have been based on largely abstract

experiments. Of interest is whether the findings from such experiments carry over into a

more realistic environment.

For example, the Short-Long Asymmetry studied by Albrecht and Weber [1997].

This finding suggests that the discount rates applied by decision makers decline over time,

in support of the hyperbolic discounting model, but in contrast to most normative theories

of discount rates. If such a finding holds, it might be expected to manifest in decision making

for power plant investments by biasing decisions made for investments with different time

horizons or that are subject to incentives that alter the temporal cash flow profile of an

investment. Accelerated depreciation, for example, shifts project values toward the present,

increasing returns from a normative perspective, but also shifting them toward a period

where decision makers tend to apply higher perceived discount rates, perhaps reducing the

perceived return of the investment.81

81 Accelerated depreciation is common to many renewable power investments. By accelerating the realization of depreciation over time, the project’s taxable income in early years is reduced (because depreciation is a tax-deductible expense), lowering cash taxes paid and allowing more cash to flow earlier to investors.

6-23

The question, then, is not simply whether or not two different projects would result

in different choices being made by normative versus heuristic decision makers, but to what

extent does the process of levelizing influence that choice? Just as accelerating depreciation

moves cash flow emphasis toward the present, levelizing “undoes” such an emphasis by

equalizing cash flows over time. Accordingly, it may be a “useful” metric in those instances.

Similarly, comparing projects with different expected lives may also create issues for

decision makers that exhibit Short-Long Asymmetry.

Consider, for the sake of example, two projects, A and B. Project A’s lifespan is 3

years; Project B’s lifespan is 5 years. In comparing the two projects, the discounted cash

flows of each project can be compared (as illustrated in Exhibit MMM). For a decision maker

using exponential discounting, Project A is preferred to Project B. However, for a heuristic

decision maker using hyperbolic discounting, Project B is preferred to Project A. If the

projects’ cash flows are levelized prior to being given to the heuristic decision maker to

compare, however, that decision maker would revert to the normative choice, with Project

A being preferred to Project B. This pattern, as described in Section 6.3, is considered

“Useful,” as the use of compression for this problem allows the heuristic decision maker to

align his choice with the normative decision maker.

The example below illustrates, for a single set of projects and a single decision

maker, the particular characterization (“Useful”) of compression as a heuristic. With the

simulation approach described previously, a far greater diversity of project types and

decision makers can be explored to identify the portions of the population likely to exhibit

each possible outcome and compare those results to hypotheses suggested by the existing

literature on risky intertemporal choice. In each case, a set of hypotheses is presented using

a common format (illustrated in Exhibit NNN) that illustrates the difference in decision-

maker population demographics (i.e., the percentage of the population resulting in the

Simplifying/Counterproductive/Irrelevant/Useful/Bad/Change outcome) under two project

trait conditions (e.g., does project trait “X” or “Y” result in a larger percentage of

Simplifying outcomes?).

6-24

Project A is indicated in blue. Project B is indicated in orange. The columns represent the per-period (undiscounted) cash flows for each project. The lines represent the cumulative present value of the cash flows, as measured by each type of decision maker. The discount rate is 15% and 0.5.

Normative

Exponential Discounting Heuristic with Full Profile

Hyperbolic Discounting Heuristic with Compression

Hyperbolic Discounting

Exhibit MMM: Comparison of Two Stylized Projects with Different Lifespans for which Compression is a Useful Heuristic

Exhibit NNN: Interpretation of Hypothesis Tables

I begin with Short-Long Asymmetry and projects with different lifespans as

described in Exhibit OOO. The results of this analysis are presented in Exhibit PPP (in this

exhibit and those that follow, hypotheses that are not supported are indicated in red text). In

this case, the only hypothesis that was not supported was the “Irrelevant” one. Otherwise, I

$0

$50

$100

$150

1 2 3 4 5

A≻B

$0

$50

$100

$150

1 2 3 4 5

A≺B

$0

$50

$100

$150

1 2 3 4 5

A≻B

6-25

conclude that the larger the lifespan difference between the power plants, the more useful

compression is and the more valuable LCOE is as a metric. In this case, it was achieved by

moving members of the population who had dropped out of the Simplifying class (indicating

that applying heuristic decision making was inducing errors) into the Useful class (indicating

that the application of compression corrected those errors). No meaningful movement was

observed in the Irrelevant or Counterproductive classes.

Next, one of the classic findings of the behavioral decision-making literature is the

asymmetry between gains and losses, with many decision makers demonstrating loss

aversion, suggesting that the framing of choices as gains or losses could potentially bias

decision making. Shelley [1994], among many others, demonstrated the existence of Gain-

Loss Asymmetry in risky intertemporal choice, concluding that discount rates were smaller

for gains than for losses. Recall that the original definition of LCOE was as an expense-only

measure, meaning that all lotteries were framed in terms of costs, or losses. I contrast this

with a more complete cash flow measure (Cash Available for Finance) that includes

revenues, and therefore has outcomes framed as both gains and losses. The set of hypotheses

for this evaluation is provided in Exhibit QQQ and the results are presented in Exhibit RRR.

6-26

Relative Lifespan the prospects are divided into subgroups by the ratio of the longer-lived plant’s lifespan to the shorter-lived plant’s lifespan

Choice Outcome Characterization

Hypotheses about the percentage of the decision-

maker population characterized in each way in each prospect subgroup Hypothesis Rationale

Projects have same

lifespan

Project lifespan

differential is 2x

Simplifying > Fewer time biases are initially present when projects have identical lifespans.

Counterproductive = No reason to believe levelizing would introduce error into an initially correct choice.

Irrelevant > Levelizing is not likely to correct a bias not likely to have originally been caused by time differences.

Useful < If the initial choice was non-normative and due to lifespan differences, levelizing more likely to correct.

Bad No prediction Hypotheses follow from individual components.

Change <

Exhibit OOO: Relative Life Hypotheses and Short-Long Asymmetry

Exhibit PPP: Population Classification According to the Relative Lifespans of the Prospects, Measured as Longer Lifespan Divided by Shorter Lifespan

0% 20% 40% 60% 80% 100%

Simplifying

Counterproductive

Irrelevant

Useful

Bad

Change

2.00 1.75 1.50 1.25 1.00

p < 0.001

No prediction

p < 0.001

p = n.s.

p = n.s.

p < 0.001

6-27

Cash Flow Profile Framing the prospects are divided into subgroups by whether or not they include only the expense-related cash flows or all the project net cash flows

Choice Outcome Characterization

Hypotheses about the percentage of the decision-

maker population characterized in each way in each prospect subgroup Hypothesis Rationale

Expense-only cash

flows

Net cash available for

finance

Simplifying <

Biases are less prominent when cash flows are mixed or predominantly positive. As a result, errors are less likely to be made initially and remain unchanged by levelizing.

Counterproductive <

If the initial choice was made normatively, for levelizing to be counterproductive, it most likely involves a sign change, which is only possible under the cash available for finance framing.

Irrelevant >

Although biases are more likely to be present in the loss framing of expenses-only, levelizing the cash flows does nothing to change their sign, and therefore initial biases are more likely to remain in place.

Useful < If an error was made initially, levelizing the full cash flows is more likely to preserve their (positive) sign.

Bad > Hypotheses follow from individual components.

Change <

Exhibit QQQ: Cash Flow Framing Hypotheses and Gain-Loss Asymmetry

Exhibit RRR: Population Classification According to Cash Flow Profile Framing

0% 20% 40% 60% 80% 100%

Simplifying

Counterproductive

Irrelevant

Useful

Bad

Change

Expenses Only Cash Available for Finance

p < 0.001

p < 0.001

p < 0.001

p < 0.001

p < 0.01

p < 0.1

6-28

Inclusion of Incentives the prospects are divided into subgroups according to whether or not their cash flows include government-provided (i.e., project external) tax incentives for renewable electricity generation

Choice Outcome Characterization

Hypotheses about the percentage of the decision-

maker population characterized in each way in each prospect subgroup Hypothesis Rationale

Projects include

incentives

Projects do not include incentives

Simplifying No prediction

Counterproductive > Levelizing reverses the perceived acceleration of benefits from incentives, potentially leading to a preference reversal opposing the normative choice.

Irrelevant No prediction

Useful <

The absence of incentives increases the likelihood of realizing negative cash flows, which would trigger loss aversion, but would be reversed when levelizing restores a positive perceived valence to the cash flows.

Bad No prediction Hypotheses follow from individual components.

Change >

Exhibit SSS: Incentive Hypotheses and Short-Long Asymmetry

Exhibit TTT: Population Classification According to Use of Incentives

0% 20% 40% 60% 80% 100%

Simplifying

Counterproductive

Irrelevant

Useful

Bad

Change

Both Renewable, No Incentives Both Renewable with Incentives

p < 0.001

p < 0.001

p < 0.001

No prediction

No prediction

No prediction

6-29

Project Type the prospects are divided into subgroups based on whether or not they are comparing two power projects of the same type or of different types

Choice Outcome Characterization

Hypotheses about the percentage of the decision-

maker population characterized in each way in each prospect subgroup Hypothesis Rationale

Projects are the same

type

Projects are different

types

Simplifying > Projects of the same type are less likely to succumb to biases initially, and levelizing is not likely to introduce further bias.

Counterproductive > Levelizing should be more helpful on different types of projects, not less helpful.

Irrelevant < Comparing different types of projects is more likely to be problematic to begin with, and levelizing may not correct those problems.

Useful < Levelizing would be expected to help correct the errors associated with comparing different types of projects.

Bad No prediction Hypotheses follow from individual components.

Change <

Exhibit UUU: Project Type Hypothesis and Gain-Loss and Magnitude Asymmetries

Exhibit VVV: Population Classification Across Project Types vs. Within Project Types

0% 20% 40% 60% 80% 100%

Simplifying

Counterproductive

Irrelevant

Useful

Bad

Change

Different Plant Types Same Plant Types

p < 0.001

No prediction

p < 0.001

p = n.s.

p < 0.001

p < 0.001

6-30

Third, both Short-Long Asymmetry and Gain-Loss Asymmetry can impact the

comparison of projects presented with and without tax-related incentives. The inclusion of

incentives in a project’s cash flows tilts the cash flow profile of the project toward more

present-biased returns. Similarly, many renewable projects are likely to show losses at

various periods of time without the incentive payments, raising the influence of loss aversion

on decision makers. The comparisons here must be made carefully, as the inclusion of tax

incentives in a project’s cash flows can only be positive from a normative perspective. Thus,

the comparison of interest is not between projects with and without incentives, but within

each class (i.e., between two projects presented with incentives or between two projects

presented without incentives). For example, when projects are compared without inclusion

of incentives, the resulting cash flows are more likely to be negative. In those cases, a loss

aversion bias may present, which would be mitigated by levelizing those cash flows (and

thus returning them to uniformly positive), making levelizing more Useful for projects

presented without incentives. In contrast, when incentives are present, losses are less likely,

and therefore only the Short-Long Asymmetry effect is likely to be present. In those cases,

levelizing reverses the acceleration of perceived benefits, leading to more weight being

placed on future benefits contrary to the normative choice rule. The set of hypotheses for

this evaluation is provided in Exhibit SSS and the results are presented in Exhibit TTT.

Fourth, levelizing is less likely to be useful for projects of the same type, which are

more likely to exhibit similar cash flow profiles. In comparing projects of different types

(e.g., nuclear vs. wind, solar vs. NGCC), both Gain-Loss Asymmetry and Magnitude

Asymmetry may have an effect. Magnitude Asymmetry results in perceived discount rates

being higher for larger payoffs [Thaler, 1981]. Projects of different types are more likely to

have per-period payoffs of different magnitudes, making decision makers considering them

more susceptible to Magnitude Asymmetry. Projects of the same type are more likely to

have similar cash flow profiles and fewer instances of differential gain and loss occurrence.

In other words, when projects are similar and both succumb to similar biases, the effects

may tend to “cancel each other out.” Therefore, compression is more likely to be a beneficial

force in comparing projects of different types.

6-31

The set of hypotheses for this evaluation is provided in Exhibit UUU and the results

are presented in Exhibit VVV. Interestingly, most of the hypotheses related to plant type

similarity were not supported. Levelizing proved to be more Simplifying for different plant

types and more Useful for the same plant types, both in contradiction to my hypotheses.

These effects reverse, however, if I also control for whether or not the plants are renewable

(wind or solar). If the comparison is limited only to renewable projects, the original

hypotheses become well supported (except for the very small Counterproductive class).

Exhibit WWW illustrates the differences. I would speculate that the renewable project types,

which tend to have the most variable cash flow profiles due to their incentives, are more

likely to emphasize the differences that would create the expected effect from similar or

different plant types.

Exhibit WWW: Refining the Population Classification Across Project Types by Controlling for Renewable Power Types

Lastly, I examine the influence of each of the prospect characteristics on the outcome

classifications. Exhibit XXX illustrates a considerable amount of similarity in which

prospect characteristics are influential on the role of compression. To help clarify the results,

I limited the analysis only to cases where the effects were greater than 75% of the population

or less than 25% of the population for each class. Prospect characteristics that do not seem

to matter include the ages of the plants being compared, the trajectory of their cash flows

(other than through incentives), and the probabilities associated with their capital cost and

operating expenses.82 In contrast, characteristics that do matter for outcome classification

are: (i) whether or not the power plants are renewables, (ii) the capacity factors of the plants,

82 The somewhat surprising finding that probabilities alone do not appear to matter is reminiscent of March and Shapira’s [1987] claims about managerial insensitivity to estimates of outcome probabilities.

Hypothesis

Change < Not supported p < 0.001 Supported p < 0.001

Bad No prediction No prediction No prediction

Useful < Not supported p < 0.001 Supported p < 0.001

Irrelevant < Not supported n.s. Supported p < 0.05

Counterproductive > Supported p < 0.001 Not supported p < 0.05

Simplifying > Not supported p < 0.001 Supported p < 0.001

Original Result Renewable-only Result

6-32

(iii) the presence of incentives for renewable energy, (iv) whether the projects are described

on an expense-only basis, and (v) the risks associated with decommissioning expenses for

nuclear power projects. In each of those five cases, dividing the prospects along that

characteristic produced a significant difference in the outcome classification, suggesting that

the use of levelizing in projects with those characteristics is likely to have an impact on the

choices made.

Exhibit XXX: Influence of Prospect Characteristics on Decision Problems with Compression

To conclude, it should be noted that these impacts are not necessarily negative ones.

In fact, the results suggest that roughly two-thirds of the time, presentation compression

through levelizing is a Simplifying metric when comparing power projects. More

importantly, however, between 20% and 40% of the time, compression through levelizing is

a Useful metric, meaning that it corrects for biases that would otherwise lead decision makers

astray from the normative choices in comparing power projects.

t statistic p value t statistic p value t statistic p value t statistic p value t statistic p value t statistic p value

A - Renewable -4.19 **** -6.49 **** 1.51 3.08 *** -0.16 3.55 ***

A - Age -0.69 0.32 -0.87 1.34 -0.89 1.59

A - Capacity Factor 6.67 **** 6.62 **** -3.45 *** -5.71 **** -1.27 -5.38 ****

A - Incentives -3.88 **** -7.65 **** -2.40 ** 8.19 **** -3.73 **** 6.58 ****

A - Trajectory -0.99 -5.22 **** 1.18 0.61 0.44 0.69

A - Expenses Only -10.25 **** -10.55 **** 14.34 **** 10.51 **** 9.73 **** 6.80 ****

A - Cost Probability 0.53 -3.77 **** 1.11 -1.28 0.66 -1.63

A - Operating Probability -0.29 0.21 0.83 -0.56 0.65 -0.10

A - Decommissioning Probability 7.93 **** 6.44 **** -7.48 **** -4.79 **** -4.74 **** -4.15 ****

B - Renewable -4.59 -12.25 **** 10.54 **** 1.42 * 5.72 **** -1.06 **

B - Age 0.71 -5.77 **** -5.32 1.84 -6.32 2.40

B - Capacity Factor -0.22 -6.20 **** -0.61 1.42 ** -1.14 *** 1.16 *

B - Incentives 0.97 * 9.49 **** 0.85 **** -2.34 **** 3.37 **** -1.81 ****

B - Trajectory -1.97 -8.37 -3.91 7.22 -5.43 5.30

B - Expenses Only 0.53 **** -1.61 **** -0.03 **** -0.23 **** -0.10 **** -0.13 ****

B - Cost Probability -10.25 -10.55 ** 14.34 10.51 9.73 ** 6.80

B - Operating Probability -0.56 2.33 1.63 -1.16 2.08 -0.39 **

B - Decommissioning Probability 1.74 **** -0.29 * -0.45 **** -1.19 -0.50 *** -2.05

**** = significance at the 0.001 level

*** = significance at the 0.01 level

** = significance at the 0.05 level

* = significance at the 0.10 level

Bad ChangeSimplifying Counterproductive Irrelevant Useful

6-33

6.4.4 Compression and a Heterogeneous Population of Decision Makers

Having explored the effect of compression on prospects with different

characteristics, I now ask the question in the other direction: for what types of decision

makers is compression likely to be more or less beneficial? In the previous section, I reported

the percentage of the population exhibiting specific choice outcomes (e.g., Simplifying,

Useful). By extending the analysis backward into the simulated population of decision

makers, however, I can examine the characteristics of decision makers for which

compression is categorized by each outcome classification.

Such an analysis is important because if investors can be “typed,” then information

and problem presentations can be tailored to be of particular use to them (or even against

their interests, if persuasion is the goal). Is compression, for example, more beneficial to a

particular subset of the population of decision makers? If a particular decision maker is

known to be extremely loss averse, for example, should or should not compression be used

as a metric? On the other hand, if the choice outcomes resulting from use of compression

are broadly stable across a population, then one may conclude that it has considerable value

(assuming, of course, that the analysis described in Section 6.4.3 indicated that compression

was also a beneficial force relative to the prospect characteristics).

I hypothesize that compression (here as levelizing as applied to power projects) will

be disproportionately useful for more loss-averse decision makers (large ), and by

extension, for decision makers with elevated levels of risk seeking in the domain of losses

(smaller ), and for decision makers with more nonlinear probability weighting for losses

(smaller ). Because levelizing moderates the appearance of extreme outcomes, which

might otherwise bias decision makers’ choices, decision makers with those characteristics

are likely to be disproportionately benefitted by compression.

At first glance in Exhibit YYY, only three coefficients appear to have meaningful

differences in mean when the population of decision makers is divided by outcome class.

Although the large sample sizes mean that all of the differences are statistically significant,

6-34

the differences only appear meaningful for , , and . The effects on the remaining

coefficients are de minimis. Exhibit ZZZ illustrates, for example, the entire distribution for

the coefficient when the group is further divided by renewable generator and by

presentation as expense only or CAFF. I do not consider the coefficients without meaningful

differences further.

Exhibit YYY: Percentage Variation of Subgroup Mean Coefficient Value from Population Coefficient Means

Exhibit ZZZ: Example of De Minimis Impact on from Further Dividing the Group

-12%

-10%

-8%

-6%

-4%

-2%

0%

2%

4%

6%

8%

Alpha Beta Lambda Gamma+ Gamma- Psi

Dev

iatio

n fr

om P

opul

atio

n M

ean

Simplifying Counterproductive Irrelevant Useful

0%

20%

40%

60%

80%

100%

0.3 0.4 0.5 0.6 0.7 0.8 0.9

Cum

ulat

ive

Pro

babi

lity

AlphaRenewable-Expense Only Not Renewable-Expense OnlyRenewable-CAFF Not Renewable-CAFFTotal Population

6-35

The inclusion of as a meaningful variable, however, is somewhat surprising.

Because levelizing does not change the duration of cash flow profiles, I had not expected the

population of decision makers to subdivide on that coefficient. However, the shifting of cash

flows within terms of the same duration appears to have a meaningful impact on how

different proportions of the population of decision makers responds. I explore each

meaningful coefficient in turn.

The hypothesis for beta was that increasing risk-seekingness (smaller ) would be

associated with compression being more beneficial. The two primary effects found in

Exhibit YYY support this pattern. Decision makers with higher (those that are less risk-

seeking), find compression Simplifying, in that they are less likely to be prone to biases

initially, and therefore levelizing allows for task simplification without additional effect. In

contrast, decision makers with lower (those that are more risk-seeking), find compression

Useful, in that their increased susceptibility to biases allows levelizing to mitigate the effects

of such biases. If one peers further into the data, additional separation is apparent. The

separation of the population into less and more risk-seeking in the Simplifying and Useful

classes appears to be driven entirely by choices made regarding non-renewable projects

using full CAFF profiles. Exhibit AAAA illustrates the entire distribution for each cross

between decision maker characteristic and project characteristic for the Simplifying and

Useful outcome classes. The Simplifying result is obtained primarily by predominantly less

risk-seeking decision makers confronted with non-renewable and full CAFF projects; in

contrast, the Useful result is obtained primarily by predominantly more risk-seeking decision

makers confronted with those same problems.

The hypothesis for lambda was that compression would be more beneficial for

decision makers with higher levels of loss aversion (larger ). As Exhibit YYY illustrates,

the results here are similar. The Simplifying class is associated with increased levels of loss

aversion. In contrast, the Useful) class is associated with lower levels of loss aversion. In

terms of the beneficial or “Good” (Simplifying + Useful) classes, the results are roughly off-

setting. More loss-averse decision makers find compression Simplifying, but less loss-averse

decision makers are the ones finding compression Useful. Exhibit BBBB further

6-36

decomposes these results by relating them to prospect characteristics. The Simplifying and

Irrelevant classes are largely consistent in their response to different prospect types. More

variation between prospect types is apparent in the Counterproductive and Useful classes. In

those cases, the populations divide along the cash flow presentation lines, with decision

makers with lower levels of loss aversion finding compression Counterproductive under the

expense-only presentation and Useful under the full CAFF presentation.

Exhibit AAAA: Connection of Decision Maker Characteristics ( ) to Project Characteristics for the Simplifying and Useful Outcome Classes

0%

20%

40%

60%

80%

100%

0.30 0.50 0.70 0.90Cum

ulat

ive

Pro

babi

lity

Beta - Simplifying Only

Renewable-Expense Only

Not Renewable-Expense Only

Renewable-CAFF

Not Renewable-CAFF

0%

20%

40%

60%

80%

100%

0.30 0.50 0.70 0.90Cum

ulat

ive

Pro

babi

lity

Beta - Useful Only

Renewable-Expense Only

Not Renewable-Expense Only

Renewable-CAFF

Not Renewable-CAFF

6-37

Exhibit BBBB: Connection of Decision Maker Characteristics ( ) to Project Characteristics for All Outcome Classes

0%

20%

40%

60%

80%

100%

1.00 1.25 1.50 1.75 2.00 2.25Cum

ulat

ive

Pro

babi

lity

Lambda - Simplifying Only

Renewable-Expense Only

Not Renewable-Expense Only

Renewable-CAFF

Not Renewable-CAFF

0%

20%

40%

60%

80%

100%

1.00 1.25 1.50 1.75 2.00 2.25Cum

ulat

ive

Pro

babi

lity

Lambda - Counterproductive Only

Renewable-Expense Only

Not Renewable-Expense Only

Renewable-CAFF

Not Renewable-CAFF

0%

20%

40%

60%

80%

100%

1.00 1.25 1.50 1.75 2.00 2.25Cum

ulat

ive

Pro

babi

lity

Lambda - Irrelevant Only

Renewable-Expense Only

Not Renewable-Expense Only

Renewable-CAFF

Not Renewable-CAFF

0%

20%

40%

60%

80%

100%

1.00 1.25 1.50 1.75 2.00 2.25Cum

ulat

ive

Pro

babi

lity

Lambda - Useful Only

Renewable-Expense Only

Not Renewable-Expense Only

Renewable-CAFF

Not Renewable-CAFF

6-38

Exhibit CCCC: Connection of Decision Maker Characteristics ( ) to Project Characteristics for All Outcome Classes

0%

20%

40%

60%

80%

100%

0.00 0.25 0.50 0.75 1.00Cum

ulat

ive

Pro

babi

lity

Psi - Simplifying Only

Renewable-Expense Only

Not Renewable-Expense Only

Renewable-CAFF

Not Renewable-CAFF

0%

20%

40%

60%

80%

100%

0.00 0.25 0.50 0.75 1.00Cum

ulat

ive

Pro

babi

lity

Psi - Counterproductive Only

Renewable-Expense Only

Not Renewable-Expense Only

Renewable-CAFF

Not Renewable-CAFF

0%

20%

40%

60%

80%

100%

0.00 0.25 0.50 0.75 1.00Cum

ulat

ive

Pro

babi

lity

Psi - Irrelevant Only

Renewable-Expense Only

Not Renewable-Expense Only

Renewable-CAFF

Not Renewable-CAFF

0%

20%

40%

60%

80%

100%

0.00 0.25 0.50 0.75 1.00Cum

ulat

ive

Pro

babi

lity

Psi - Useful Only

Renewable-Expense Only

Not Renewable-Expense Only

Renewable-CAFF

Not Renewable-CAFF

6-39

I had not originally hypothesized an effect for psi, but Exhibit YYY illustrated a clear

effect. Compression is likely to lead to a Change (Counterproductive + Useful) outcome for

more present-biased ( → 1) decision makers, while the No Change (Simplifying +

Irrelevant) classes were realized primarily by less present-biased ( → 0) decision makers

(or those closer to exponential discounting). These mixed results are more complicated to

interpret, but also suggest more concern regarding the application of compression, since

particular classes of decision makers appear predisposed to outcomes when faced with

certain prospects that could be either good or bad.

Exhibit CCCC further decomposes the psi results according to prospect

characteristics. Here, it is the Counterproductive decomposition that is of interest. Especially

among moderately present-biased decision makers, but also across the range of the degree

of hyperbolicity exhibited, decision makers faced with non-renewable projects were 20-30

percentage points more likely to end up classified as Counterproductive. Because the

primary distinguishing (cash flow) feature of renewable projects (vis-à-vis non-renewable

projects) is the presence of incentives that accelerate the realization of value across time, it

is understandable that renewable projects may be more impacted by compression, which by

equalizing cash flows over time shifts more of the accelerated gains back into the future

where they may be perceived to have more value. Such results are then less likely to be

classified as Counterproductive than their non-renewable peers.

6.5 Applications and Implications

The purpose of this chapter is to investigate decision making relative to problem

presentation. This is not a new area of research. The particular contribution of my research

comprises multiple distinct elements. First, the novel computational decision-making

simulation approach developed in Chapter 5 is applied to a specific set of corporate finance

questions involving risky intertemporal choice. Second, a heuristic choice framework is

developed to allow for the assessment of compression as a useful form of presentation and

levelized cost as an efficient metric. Third, effort is made to confront the simulated subjects

with prospects designed to exhibit a high degree of realism as power project investments.

6-40

Fourth, the computational approach allows for the examination of a heterogeneous pool of

prospect design elements in combination with a heterogeneous pool of decision makers. By

connecting these approaches, linkages can be established between decision maker

characteristics and prospect characteristics that can assist in allowing compression to be

more effectively used in power plant investment decision making.

In practical terms, my research suggests that users of the compressed LCOE

presentation form should be informed as to areas where reliance on that presentation is likely

to trigger biases and thereby cause them to make non-normative choices. Just as Joskow

[2011] has shown that LCOE is “not a useful way to compare generating technologies [that

have] different production profiles” (e.g., baseload (nuclear) vs. intermittent (wind)), this

work shows that LCOE is also not a universally reliable way for decision makers with certain

cognitive characteristics to compare technologies with certain risk profiles (e.g., high fixed

cost vs high variable cost) or distributions of costs and benefits across time (e.g., heavily-

incentivized renewables vs fossil or nuclear). Specifically, this lack of universal reliability

is because compression resulting from the metric may tend to alter the decision problem’s

characteristics in ways that are known to trigger biases. Compression, for example, obscures

the presence of risk by replacing explicit probabilities with expected values. Certainty-risk

asymmetry results in decision makers applying higher discount rates to certain outcomes.

Likewise, compression explicitly “levelizes” cash flows over time, and short-long

asymmetry results in discount rates declining as events are pushed into the future (which

levelizing, in effect, does with the accelerated incentives provided for renewable power

projects). In many cases, however, it is the removal of these details via compression that

mitigates biases. Although Joskow’s [2011] recommendation was to “abandon” levelized

cost comparisons, I propose a less drastic response for cognitively-constrained decision

makers.

A heuristic is “good” if it allows a simpler decision process to be substituted (in the

sense of Kahneman and Frederick’s [2002] “attribute substitution”) reliably for a more

complicated but normative decision process. This work identified classes of areas where the

6-41

use of LCOE leads heuristics to become unreliable, but also areas where compression as a

metric and its related heuristic could be a beneficial force and useful for debiasing.

At the most general level, the use of compression in power-investment decision

making is beneficial for a majority of projects and decision makers. In most cases, it is

Simplifying. However, this research also identifies particular circumstances for which

compression is not a beneficial force. As I noted at the outset, for heuristics to be used

effectively, their strengths and weaknesses must be well understood. Accordingly, the results

of this study should inform the use of compression (levelizing) as a metric. To summarize

the practical implications of these findings, this research shows that:

1. Compression is more Useful when comparing projects with large lifespan

differences. Because different types of power project tend to have different

estimated lifespans, project type can be a proxy for lifespan in many applications.

2. Compression is more Useful when projects are evaluated with their full cash

flows, rather than only the expenses, as is commonly done with levelized cost.

3. In fact, use of the expense-only framing results in approximately twice as many

Bad (Counterproductive or Irrelevant) outcomes as the full CAFF framing. This

is, in a sense, restating Joskow’s [2011] conclusion in more decision-making

language, even if the underlying sentiment is similar.

4. Levelizing is more Useful in no-incentive comparisons. Levelizing tends to

reverse the acceleration of value provided by many incentives for renewable

power projects. As a result, any attempt that shifts any perceived value into the

future may be overvalued by present-biased decision makers, but contrary to

what a normative decision maker should prefer. As levelized cost tends to be

disproportionately used for evaluating renewable power projects, this result

should prompt some caution.

5. Project type matters only for renewable power projects. It is Useful for comparing

among types of renewable power projects, but not for comparing renewable

projects to non-renewable projects.

6-42

6. Three parameters show meaningful separation by outcome classification: risk-

seekingness under losses, loss aversion, and present bias.

7. The application of compression by less risk-seeking or more loss-averse decision

makers tends to produce Simplifying outcomes, while the application of

compression by more risk-seeking or less loss-averse decision makers tends to

produce Useful outcomes. These results are driven primarily by comparisons

involving non-renewable projects, together with full CAFF framing.

8. The results for present bias (degree of hyperbolicity) were mixed, suggesting that

both beneficial and harmful outcomes could occur in certain circumstances.

9. For moderately present-biased decision makers and non-renewable projects, such

decision makers are 20-30 percentage points more likely to end up with a

Counterproductive outcome.

6.5.1 Compression as a Tool for Debiasing

Although in this chapter I have asked the question from a “top down” or “information

supplier” perspective, inquiring as to whether letting decision makers use compressed

metrics is beneficial, it is also worth contemplating a “bottom up” or “information

consumer” interpretation of this problem. Since many business decision makers see the

compressed metrics (such as LCOE or NPV) first, one might ask whether there is value in

additionally requesting full information about a problem. Such a question is rarely

considered in normative analysis because additional information always has non-negative

value. Numerous researchers, however, have questioned the value of providing more

information to cognitively-constrained decision makers [Camerer, Loewenstein, and Weber,

1989; Kleinmuntz and Schkade, 1993; Iyengar and Lepper, 1999].

In fact, consider the cognitively-constrained information consumer’s most basic

question: “how much information should I request or consider?” A simple objective function

for such a question is the percent of the time the requested information results in a “correct”

outcome (in that the option selected is consistent with a normative choice rule). By

examining the outcomes of choices made by each of the 500 decision makers in the simulated

6-43

population for each of the 6,000 prospect comparisons in the population of problems,

answers to this question emerge. Exhibit DDDD tabulates these results.

Compressed

Correct Incorrect

Full Correct

69% (Simplifying)

2% (Counterproductive)

71%

Incorrect 22%

(Useful) 7%

(Irrelevant) 29%

91% 9%

Exhibit DDDD: Information Consumer Choice Strategy Outcomes

A decision maker using the full presentation can expect to achieve the normatively

correct outcome 71% of the time (ranging from 50% to 90% across all decision makers).

However, that same decision maker using the compressed LCOE presentation instead can

expect to achieve the normatively correct outcome fully 91% of the time (ranging from 88%

to 99% across all decision makers). For these cognitively-constrained decision makers,

requesting less information improves their decision performance, suggesting that the biases

they exhibit in processing the full information can be mitigated mostly by compressing much

of that detail. I also look at the decision maker-by-decision maker and comparison-by-

comparison performance of such a rule. For 100% of decision makers, the frequency of

Useful outcomes exceeds the frequency of Counterproductive outcomes. Likewise, for 96%

of all project comparisons, the frequency of Useful outcomes exceeds the frequency of

Counterproductive outcomes. The performance of the compression heuristic first-order

stochastically dominates decisions made using the full presentation form.

As a result, a decision strategy that comprises “request the compressed information

only and act on it” proves to be a powerful tool for improving the performance of

cognitively-constrained decision makers. LCOE may have normative problems, but

compression is a broadly beneficial heuristic for bias-prone decision makers. The benefits it

provides from allowing such decision makers to avoid the consequences of their biases

appears to exceed the costs of LCOE’s normative failings.

6-44

The compression heuristic is sufficiently powerful that there does not appear to be

incremental value in using more information with it. Consider the case of a decision maker

with the compressed presentation who is offered the full presentation result as well. In this

case, the decision maker observes two outcomes that either agree or disagree. The outcomes

agree 76% of the time (the diagonal results in Exhibit DDDD) and disagree 24% of the time

(the off-diagonal results in Exhibit DDDD). But if there is agreement (i.e., the full

presentation matches the compressed presentation), the decision maker remains with the

outcome precipitated by the compressed presentation. Meanwhile, if there is disagreement

(i.e., the full presentation conflicts with the compressed presentation), the performance of

the compressed presentation remains better. As a result, the decision maker’s behavior is

unchanged and therefore there is no additional value in obtaining both problem

presentations.83 However, because in most circumstances requesting more information does

not impact the choice made, it can nevertheless be entertained if some ancillary benefit

results (e.g., it improves post-decision satisfaction).

These results concerning decision rule use are significantly impacted, however, by

the cognitive profile of the decision maker (as represented by the simulated 7-tuple of

prospect theory and hyperbolic discounting parameters). Decision makers who are more

loss-averse, more risk-seeking, and more present-biased than the population median can shift

the likelihood of a Counterproductive (or Useful) outcome given that a change in choice

occurs by as much as 30%. Exhibit EEEE provides a “heuristic map” of where different

cognitive subsets of the general population are more or less likely to realize

Counterproductive or Useful outcomes as a result of changing their choices upon receipt of

full information. Likewise, as illustrated in Exhibit FFFF, the usefulness of the LCOE

heuristic varies across problem characteristics and decision maker characteristics as well.

The exhibit illustrates the accuracy of the full and compressed heuristics across various

subpopulations of prospects and decision makers (based on a median split of decision maker

83 76% of the time, the two presentations result in the same choice. At that point, the decision maker can nominally elect to remain with the Compressed (C) choice or switch to the Full (F) choice. However, as they are the same in this branch, there is no choice, and the correct outcome results in 69/76 of the cases. In contrast, 24% of the time the two presentations disagree. In that case, remaining with C results in the correct outcome 22/24 of the time. Because 76% × (69/76) + 24% × (22/24) = 69 + 22 = 91%, the additional information has no incremental value over the “request the compressed information and act on it” strategy.

6-45

subpopulations). Although the compressed presentation is more accurate than the full

presentation in every instance, the performance of the compressed presentation is

particularly high in prospect comparisons involving full cash flows (i.e., CAFF) and

different technologies. This conclusion was noted previously, but I add here that it holds

across different decision-maker subpopulations as well.

If, as results such as Albert [1967] suggest, businesspeople differ “significantly”

from the general population of decision makers, it becomes important to be able to evaluate

decisions conditional on the characteristics of that subpopulation. The ability of the

simulation approach developed in Chapter 5 and applied here to specify such subpopulations

against, for example, simple calibration tasks, makes it especially well-suited to evaluate

such decision-making environments.

Although this chapter has focused specifically on decision making involving power

plant investments, there is a broader message in the results. Heuristic decision making can

be a powerful tool for reducing cognitive load. Likewise, the metrics so commonly used in

finance, but rarely contemplated from a decision-making perspective, can be beneficial, but

as with all tools, their proper use is required to make most effective use of their benefits.

This chapter examines an application to a single domain; other problem domains may not

find similar benefits for compression. The simulation approach developed in Chapter 5 and

applied here, however, allows for the in-depth examination of decision problems with

realistic levels of complexity among a diverse and flexible artificial population. The

identified advantages and weaknesses of compression—regardless of domain—should be

used by policy and investment decision makers to improve the effectiveness of information

given to problem stakeholders and optimize the impact of heuristic decision making.

6-46

Exhibit EEEE: Heuristic Map of Change-in-Choice Consequences

0.00

0.20

0.40

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6-47

Exhibit FFFF: Rule Accuracy by Prospect and Decision Maker Characteristics

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7-1

7 Final Thoughts & Future Directions

7.1 Securities Design

The virtually limitless bundling and unbundling of risks possible in theoretical

finance faces a very pedestrian challenge in the real world: “consumer” marketing. In the

absence of arbitrage bounds in tradable markets for novel securities, issuers must take into

account the ability of potential buyers to understand the risks being transferred, to price them

rationally, and to believe in the lack of informational asymmetry in the transaction. This is

often a tall order when firms tend toward design complexity as a means of exerting oligopoly

power [Henderson and Pearson, 2011]. This oligopoly power, which manifests in larger-

than-equilibrium bid-ask spreads in novel securities is a two-edged sword though: issuer and

market-maker profits increase right up to the point where buyers withdraw from the market.

The first essay in this dissertation developed eight categories of design features that

can affect the successful marketing of a novel security to investors motivated by heuristic

decision making. Although the application addressed was the securitization of catastrophic

risk, which suffered from an initial reluctance of investors to participate, the resulting design

principles can be extended to other securities.

For example, Shefrin [2000], among others, has noted that the lottery bonds issued

by several countries (the U.K., Sweden, and others) remain popular investments. Lottery

bonds are bonds for which the investor is guaranteed return of principal, but in lieu of a

coupon, receives a “lottery ticket” entitling them to a chance at winning a large prize. These

bonds, in many ways, are strikingly similar to catastrophe bonds if viewed abstractly (they

have uncorrelated returns, they have features that result in small probabilities of large

changes in value, etc.). And yet, they are perceived very differently by investors. Cat bonds

are less attractive than they “should” be; lottery bonds are more attractive than they “should”

be. The implication of my investigation into cat bonds is that, when attempting to appeal to

7-2

investor clienteles in the creation of novel securities, issuers should take a more holistic view

of investors’ preferences and biases.

The areas of financial innovation and securities design have significant practical

relevance, but have received relatively little attention from a behavioral economics

perspective. Future work could explore other novel securities, but perhaps more importantly,

it could serve to guide the creation of novel securities. Finance has dealt extensively with

the notions of clienteles formed by tax policy, by regulatory policy, and by market frictions,

but has generally not sought to cater explicitly (or at least openly) to clienteles formed by

investors’ decision-making practices. This path of research potentially also provides a way

to test whether the involvement of high stakes can be used to incentivize investors to engage

in debiasing behavior. Could behaviorally-prompted securities innovations endure, for

example, if they prove to be suboptimal investments?

For corporations, this research suggests that it should be possible to design a security

to exploit investors’ biases in such a way as to lower the issuer’s cost of capital. My analysis

of cat bonds suggested that they were (initially and unintentionally) designed almost as

counterproductively as possible, triggering a variety of biases and behaviors that made

investors averse to owning them. One might ask whether it would be similarly possible (with

intention) to design securities to take advantage of as many biases and behaviors as possible.

Lottery bonds appear to be a good example, but how much further could structures be

pushed?

For regulators, this research suggests that disclosures and communication about

securities offerings could be evaluated for material that, while not intentionally misleading

or false, may be likely to trigger suboptimal choice among investors. Whether or not this is

a legitimate function of government regulators is a separate question. Should corporations

be allowed to design securities in a way that appeals to the non-normative preferences of

investors? While government may have a legitimate interest in preventing inaccurate or

misleading disclosure to potential investors, it is far from clear that barring corporations

from designing securities to appeal explicitly to investors’ preferences (whether rational or

7-3

not) would be equally legitimate (e.g., gambling is generally legal, but arguably not

“rational”).84

The co-evolution of this problem space, between issuer, investor, and regulator

interests, suggests a rich area for future research. Future research in this area may also benefit

from the structured computational analysis of risky intertemporal choice developed in

Chapter 5. A framework for the design of novel securities could be developed as a

constrained nonlinear optimization problem that seeks to maximize prospect theory values

while holding expected values constant by changing the structure of the cash flows. The

objective of this effort would be to increase the attractiveness of a security to a potential

investor while minimizing its expected cash cost to the issuer.

7.2 Regulatory Intermediation

Electric power regulators are charged with protecting both the public interest and the

economic stability of utilities. Neither of these mandates implies that rates for electric power

or utility profits cannot either increase or decrease over time. Many valid potential reasons

exist for their variation. My research, however, has shown that utilities’ authorized return

premiums (and earned returns such as net income) have generally increased over the past 35

years. Additionally, my research has failed to find any significant economic justification for

this steady increase. Thus, given that underlying riskless rates of return have generally

decreased over that period, profits to utilities have expanded significantly more than can be

explained by traditional theories in finance.

This is a problem that is somewhat unique to the regulated world. In a competitive

market, excess returns would be subject to the self-correcting forces of competition. But in

regulated markets, it is the intermediation of regulators that is intended to provide such

“correction.” Stakeholders, then, are relying on the judgment and decision making of those

84 This is not an abstract philosophical question. Traditionally, the U.S. Securities and Exchange Commission would take the position that so long as disclosure is complete, caveat emptor would prevail with regard to securities design and private contracts. The much newer Consumer Financial Protection Bureau (stated objective: “We protect consumers from unfair, deceptive, or abusive practices”) may have a different posture.

7-4

regulators to serve as an objective proxy for the market. In my work, the hypothesis that

cannot be rejected is that regulators are subject to biased judgments, and that a money

illusion-type effect has impeded allowed returns from dropping below a subjective 10%

threshold, thus increasing the risk premiums implicitly granted to utilities.

Over the last decade, retail prices for electricity have increased, while wholesale

prices for electricity have decreased. At a general level, the spread between retail and

wholesale prices, which I shall refer to as a gross spread, reflects profits to power generators.

This spread has increased significantly in many regions (see Exhibit GGGG). This growing

spread can be partially explained by the growing risk premiums authorized by regulators.

Exhibit GGGG: Gross Margin Trends in California, Pennsylvania, and Texas

If the growing risk premiums authorized cannot be explained as reasonable

additional compensation for additional risks borne by utilities, and if they are instead

explained by regulatory biases, then the consequence of these biases may be, in part,

responsible for billions of dollars in additional costs. These biases may be deemed

consequential enough so as to justify even costly (in a general sense) debiasing. If regulators

cannot be debiased, this research suggests that the public interest may be better served by

adopting a model that standardizes and “automates” the determination of rates of return for

0

2

4

6

8

10

12

2007 2008 2009 2010 2011 2012 2013 2014

Gro

ss M

argi

n (c

ents

/kw

h)

PA TX CA

+112%

–2%

+66%

7-5

utilities (as the Canadian model does). In other words, the public as a whole may be better

off by instantiating this part of the regulatory function in a fixed model and thus removing

it from the discretionary judgment of potentially fallible regulators.

A brief examination of the direct influence of regulatory posture can be seen by

including a “score” for public utilities commissions based on their reputation for energy

regulation. Although the analysis briefly described here and presented in Exhibit HHHH

below is only suggestive, it does seem to indicate that commission posture (or at least the

reputation of that posture) has an influence on authorized rate of return spreads (but virtually

no additional explanatory power as the Akaike (“AIC”) and Bayesian Information Criterion

(“BIC”) results are conflicting). To be sure, the “scoring” used here [Winegarden and Miles,

2014] is merely one subjective assessment for one static point in time and therefore, cannot

account for the trend in spreads over the 35 years studied. Here, the results suggest merely

that higher spreads are associated with “less accommodating” commissions—which is

something of a paradox.85 Further, to be sure, the authorized rate of return is merely one

lever a regulator has to influence earnings (varying the size of the allowed rate base is another

that is not addressed here).

I leave further exploration to future work, where several paths of research are

immediately obvious. Is this behavior unique to electricity regulation, or is it also present in

regulation of natural gas utilities or FERC regulation of transmission, or pipelines? Is this

behavior unique to the U.S. regulatory system, or does it manifest (perhaps in different form)

under other system as well? Looking forward, the behavior of regulators as interest rates

steadily renormalize will be of interest. Will authorized returns become “sticky” in the

opposite direction, as returns trend back over 10% with rising riskless rates?

85 On one hand, state regulatory risk is non-diversifiable for franchise utilities, and therefore, an additional risk premium may be warranted for such utilities. On the other hand, the perception of such commissions as less accommodating would seem to be at odds with their provision of higher risk premiums.

7-6

Baseline With PUC Score ln ln

, Constant -5.638**** -5.913**** (0.151) (0.209)

, Asset beta,ln -0.184**** -0.184**** (0.027) (0.027)

, Capital structure,ln 1 1 -0.487**** -0.449****

(0.116) (0.116)

, Market risk premium,ln -0.957**** -0.959**** (0.039) (0.039)

, State regulator score, ln Score 0.138* (0.072) R-squared 42.6% 42.9% Adjusted R-squared 42.4% 42.7% F statistic 345.3**** 260.1**** No. of observations 1,402 1,389 AIC 1,627.5 1,625.9 BIC 1,653.7 1,657.3

Standard errors are reported in parentheses. *, **, ***, and **** indicate significance at the 90%, 95%, 99%, and 99.9% levels, respectively. PUC scores were not provided for the District of Columbia, resulting in fewer data points.

Exhibit HHHH: Regression Results Examining Commission Reputation on Spreads

Additionally, although I have examined the link between theory-implied rates of

return and authorized rates of return, and then authorized rates of return and earned rates of

return, a third step is obvious: connecting earned rates of return to the stock performance of

regulated utilities. If there are excess returns in fact being provided and earned, who is

earning them? Either stockholders are realizing excess rates of return or utilities are

demonstrating expense-preference behavior and using regulatory munificence to counteract

the drag of expense inefficiency. Williamson [1963] and Edwards [1977] find evidence of

expense preference in regulated industries, but Awh and Primeaux, Jr. [1985] fail to find

similar evidence in a small sample of regulated electric utilities. Each of these studies,

however, is now dated and not reflective of the state of regulation prevailing during the

period covered by the dataset that I explore in Chapter 4.

7-7

Finally, the consequences of correcting any regulatory biases could also be explored.

If regulators are, in fact, providing utilities with excess returns, correction of that behavior

would reduce utility revenues and potentially alter their capital investment behavior. What

impact would that have on grid reliability, compliance with environmental regulations, and

trends toward either re-regulation or further de-regulation of the industry?

7.3 Toward a Computational Approach to Behavioral Decision Theory

Behavioral decision making represents a fertile field for application of the

computational methods developed in Chapter 5. Such approaches have not generally been

employed in this area, but several decades of extensive experimental work have provided a

large set of data on how human behavior can be characterized. Employing computational

methods expands the ability of behavioral decision making to extend beyond individual-by-

individual analysis of behavior of toward atomistic examination of populations. Likewise, it

allows for extending the nature of analysis beyond whether or not an effect exists, and toward

determining for whom it exists, and under what conditions.

Returning to an application discussed in Section 7.1, the design of financial securities

represents an attractive domain in which to apply computational methods. Many securities

design analyses estimate market share potential for a new security on the basis of the optimal

fraction of wealth that investors should allocate to it in equilibrium (based on mean-variance

preferences, etc.). While an obvious calculation for rational investors, it may provide neither

an upper nor lower bound in practice. Instead, investors—especially in financial innovations

designed with retail investors in mind—may over- or under-respond to such securities based

on the value and risks that they perceive such novel securities to have, as filtered through a

suite of potential biases. A computational platform for examining securities (both new and

existing) could be used both to estimate characteristics of an investor base, but also to

measure the impact of changes to design on the population of investors.

An additional path of research for the computational approach is the parallel conduct

of experiments in both virtual and real worlds as a means of separating intrinsic bias from

7-8

presentation (or experimental design) bias. Researchers are (or should be) scrupulously

attentive to the impact that their own behavior or the manner in which tasks are presented to

subjects have on outcomes. However, the basis for comparison in such circumstances is often

judgment based. There has not been a means, previously, by which to “remove” problem

presentation from problems presented to subjects. The application of computational methods

may provide such a means.

An additional path of exploration in this area would involve enriching the virtual

population’s diversity. Although the majority of studies appear to have converged toward

models that contain prospect theory-like and hyperbolic discounting-like elements, those

theoretical models are not universally accepted. I have demonstrated how the decision

demographics of a population can be estimated and employed under the assumption that

cumulative prospect theory and hyperbolic discounting are the models underlying individual

decision-making behavior. This approach could easily be extended, however, to account for

a more diverse population of decision makers that use other non-expected utility and non-

exponential discounting theories. Alternatively, the approach could also be narrowed to

explore subpopulations of decision makers where such analyses were appropriate (e.g.,

different forms of compensation for corporate managers may cause them to act more risk-

seeking than average [Jensen, 1986; MacCrimmon and Wehrung, 1990], corporate

accounting requirements that may induce elevated levels of loss aversion [Burgstahler and

Dichev, 1997]).

7.4 Presentation Compression in Risky Intertemporal Choice

The practice of finance has traditionally given scant attention to the decision-making

aspects of investment and corporate finance. Despite the reality that financial analysts and

managers are routinely called upon to evaluate complex choices and identify optimal

solutions, most (finance) researchers have been content simply to “wave their hands” at

assertions involving estimation of a particular performance or valuation metric and then its

application to a complex problem. Criticism of work of the type addressed in this dissertation

is commonly given along the lines of “people don’t actually behave like that in reality” and

7-9

“no one would look only at a single metric to make an investment decision.” And yet, a

classic article on managerial decision-making quoted finance executives as saying “[n]o one

is interested in getting quantified measures” and “[…] you don’t quantify the risk, but you

have to be able to feel it.” [March and Shapira [1987]

To be sure, corporate decision makers are called upon to be “risk neutral” when

evaluating corporate investments. All positive expected net present value investments should

be accepted. The reality, of course, is far more nuanced. However risk neutral that firms are

expected to be, the individuals that run them are human and generate very human levels of

risk-averse and risk-seeking behavior [Wiseman and Gomez-Mejia, 1998]. Admonitions to

“feel it” open the door to heuristic decision making, which would suggest that understanding

how the heuristics, and metrics on which they are based, are used and perceived should be

important.

Although some work has examined the role of behavior in corporate finance (e.g.,

Statman and Tyebjee [1985], Statman and Caldwell [1987]), it has mostly focused on

forecasting-related biases. This body of work has not gone far enough. However, to be fair,

the identification and solicitation of meaningful groups of human subjects for such analysis

that also have sufficient domain knowledge of corporate or investment finance is small. As

a result, the simulation approach developed in Chapter 5 and applied to a specific problem

in Chapter 6 shows more promise if the decision-making characteristics of the relevant

subpopulation can be modeled.

Levelized cost is not the only metric used in finance. Nor are heuristics limited to

investments in the power sector. The approach taken in Chapter 6 could be extended to a

wide variety of financial decision making, both at the corporate and individual level.

Financial analysts will commonly forecast cash flows only for a handful of years and then

use a “terminal multiple” to represent all value beyond that point in a project. Many

commercial property tax assessments are based on the “direct capitalization” approach,

meaning that an asset’s entire lifetime of operation is reduced to a single “representative”

year for assessment purposes. The role of compression, as defined and evaluated in Chapter

7-10

6, turns out to be fairly ubiquitous in finance. The notion that using a simplified metric that

is objectively identical to (or at least highly correlated with) a full presentation of a problem

has value in a world in which decision makers’ perceptions are not influenced by problem

presentation. But if the “lossy” compression employed in such processes alters the problem

presentation in a way that changes decision-makers’ perceptions, it becomes essential to

understand how, and why, and what to do about it.

R-1

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