Introduction To Risk Aversion

Introduction to Risk Aversion in Enterprise Risk Management

22 March 2011

Presented by:John LehmanManaging DirectorSDG-Galway Energy Strategy Practice

Page 2©2011 Strategic Decisions Group International LLC. All Rights Reserved. www.sdg.com

There are (at least*) three standards for ERM, and their treatments of risk and risk aversion differ.

Casualty Actuarial Society (CAS) – “Overview of Enterprise Risk Management” (2003)

• Does not define risk.

• Makes virtually no mention of attitude toward risk. Corporations are implicitly assumed risk neutral.

Committee of Sponsoring Organizations (COSO) – “Enterprise Risk Management – Integrated Framework” (2004)

• “Risk – The possibility that an event will occur and adversely affect the achievement of objectives”.

• “Risk appetite: The broad-based amount of risk a company or other entity is willing to accept in pursuit of its mission (or vision).”

− “Risk appetite, established by management with oversight of the board of directors, is a guidepost in strategy setting.”

• “Risk tolerances are the acceptable levels of variation relative to the achievement of objectives.”

• Risk appetite is treated as a prior, fixed limit within which decisions are made.*RIMS had a standard for Risk Management, but appears to have adopted ISO31000.


There are three standards for ERM, and their treatments of risk and risk aversion differ.

International Standards Organization (ISO) – “ISO 31000 Risk Management — Principles and Guidelines” (2009)

• Risk – “Effect of uncertainty on objectives”.

• Risk Attitude – “Organization’s approach to assess and eventually pursue, retain, take or turn away from risk”.

• Risk Appetite – “Amount and type of risk that an organization is willing to pursue or retain”.

• Risk Tolerance – “Organization's or stakeholder's readiness to bear the risk after risk treatment in order to achieve its objectives”.

• Risk Aversion – “Attitude to turn away from risk”.


Your textbook adds a few other definitions into the mix.

From Chapter 9 – “How to Create and Use Corporate Risk Tolerance”

• “Risk is commonly referred to as the chance, possibility, or uncertainty of outcome or consequences.”

• “…risk exposures are simply the extent to which you are exposed to a risk…”

• “…risk tolerance…is the risk exposure an organization determines is appropriate to take or avoid taking.”

o “…you need to understand the concept of “appropriate”. Determining what is appropriate requires applying judgment.”

• “Risk attitude is a person’s propensity to take risk.”

o “The term ‘person’ should be read to include an individual, group of individuals, or an organization.”

So what are we to believe?


If we’re going to manage risk, it’s a good idea to know what it is!

“Risk is uncertainty with the potential for ex post regret.”


Let’s begin with a brief history of rational decision-making, starting with Blaise Pascal and expected value.

• Blaise Pascal was instrumental in developing the mathematics of probabilities, particularly as applied to games of chance.

• In 1654, Pascal tackled the “Problem of Points”, which dealt with the proper way of dividing the stakes of a game that was interrupted prior to completion.

• From this Pascal developed the mathematical concept of “expected value” and suggested that the standard for rational decision making was expected value maximization.


The mathematically rigorous treatment of risk began with Daniel Bernoulli in 1738.

• Bernoulli attempted to explain the St. Petersburg Paradox which involved observed behavior when people were offered the chance to play a game with an infinite expected value.

• It was noted that people would only pay small amounts to play the game, showing that they were not acting on expected values.

• Bernoulli developed “expected utility theory”:

− “The determination of the value of an item must not be based on the price, but rather on the utility it yields…. There is no doubt that a gain of one thousand ducats is more significant to the pauper than to a rich man though both gain the same amount.”

• Bernoulli referred to mathematical utility functions, even suggesting one, log utility, that would resolve the St. Petersburg Paradox.


In 1944 John Von Neumann and Oskar Morgenstern advanced expected utility theory when they defined “rational choice” axiomatically.

• Von Neumann and Morgenstern asserted four principals or “axioms” of rational choice: transitivity, completeness, independence and continuity.

• Adherence to these four principals define Von Neumann-Morgenstern rationality, which allows the behavior of a rational agent to be described by reference to a “utility function”.

• For a rational agent as defined by Von Neumann-Morgenstern, risk aversion is a result of diminishing marginal utility for wealth, as Bernoulli suggested in 1738.


If your wealth-impacting decisions follow the von Neuman-Morgenstern axioms, we can define a utility function for you.

How do we define “utility”? What is it? Where does it come from?


Fortunately, this problem was entirely taken care of by Jeremy Bentham in the 18th century!

Jeremy Bentham’s “Felicific Calculus”• There are 12 pains and 14 pleasures.

• For each, calculate the hedons and dolors according to:1. Intensity: How strong is the pleasure/pain?2. Duration: How long will the pleasure/pain last?3. Certainty or uncertainty: How likely or unlikely is it

that the pleasure/pain will occur?4. Propinquity or remoteness: How soon will the

pleasure/pain occur?5. Fecundity: The probability that the action will be

followed by sensations of the same kind.6. Purity: The probability that it will not be followed by

sensations of the opposite kind.7. Extent: How many people will be affected?

• Sum the resulting hedons and dolors… Voila’!


So, accepting the notion that utility is not directly observable, calculable or comparable, let’s keep going…*

4.1 utils

2.2 utils

1.3 utils

0.8 utils

0.4 utils

* In the words of Kenneth Arrow, “Now here we have a serious problem that we have to face. Let’s face it. And now, let’s move on.”


The utility changes with each wealth increment, giving us the marginal utility of wealth.

4.1 utils

2.2 utils

1.3 utils

0.8 utils

“What’s risk got to do with it?”


Our subject has diminishing marginal utility for wealth, so let’s offer her a 50/50 gamble.

3.5

6.8 utils

2.35Certain Equivalent

½ of total distance

½ of total distance

The outcome if she loses.

The outcome if she wins.

50%(1) + 50%(6) = 3.5


Next we’ll look at a subject with increasing marginal utility for wealth.

3.5

1.5 utils

4.35Certain

Equivalent

What happens to people like this?


In the 1960’s, Kenneth Arrow and John W. Pratt developed a mathematical definition of absolute risk aversion and tolerance.

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Absolute Risk Aversion

Absolute Risk Tolerance

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Absolute Risk Tolerance


“Birds do it, bees do it…also apes”

Takahashi, T.; “Biophysics of risk aversion based on neurotransmitter receptor theory”, Neuro Endocrinology Letters, 2008 Aug;29(4):399-404.

Lee, D.; “Neuroeconomics: making risky choices in the brain”, Nature Neuroscience, 2005 Sep;8(9):1129-30.

Caraco,Thomas; “Aspects of risk-aversion in foraging white-crowned sparrows” Animal Behaviour, Volume 30, Issue 3, August 1982, Pages 719-727.

Marsh, B. & Kacelnik, A.; “Framing effects and risky decisions in starlings” Proceedings of the National Academy of Science, USA, 2002, 99, 3352–3355.

Real, Leslie A.; “Animal Choice Behavior and the Evolution of Cognitive Architecture”, Science, 30 August 1991, 980-986.

Heilbronner, Sarah R., Alexandra G. Rosati, Jeffrey R. Stevens, Brian Hare and Marc D. Hauser; “A fruit in the hand or two in the bush? Divergent risk preferences in chimpanzees and bonobos”, Biology Letters, (2008) 4, 246–249.

A Modest Selection of Papers


Now, let’s change direction and ask a couple of simple questions.

What is a corporation?• “The private corporation or firm is simply one form of legal fiction which

serves as a nexus for contracting relationships and which is also characterized by the existence of divisible residual claims on the assets and cash flows of the organization…”*

Why do corporations exist?• Adopting the corporate form lowers the costs of contracting between and

among the owners of factors of production/claimants to the assets and cash flows of the organization.

What is the role of corporate equity holders?• Equity holders own the residual value of the corporation – they are residual

claimants – and thus bear the bulk of the business risk of the organization.

For whom does the management of a public corporation work?

*Jensen, Michael and William Meckling; “Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure”, Journal of Financial Economics, October, 1976, V. 3, No. 4, pp. 305-360


Let’s summarize what we have learned thus far and ask a few critical questions.

• Risk aversion is strictly a function of diminishing marginal utility.• Utility is not directly observable, calculable or comparable across individuals.• There are mathematical definitions of risk aversion and risk tolerance.• Risk aversion is found in humans and other animals and appears to have

origins in natural selection. (Competition weeds out risk preferrers.)• The mechanism by which risk aversion becomes manifest appears to be

neurochemical.

• Corporations are legal fictions that serve as connecting points for contracts among providers of factors of production.

• Corporations exist to lower the costs of contracting among these providers.• Equity owners are “residual claimants” to corporate assets and cash flows.• Residual claimants provide risk-bearing service to the other claimants to the

firm’s assets and cash flows.• Management acts on behalf of the equity owners/residual claimants.


When we speak of the “risk aversion” of a corporation, what in the #%$@ are we talking about?

• Risk aversion is strictly a function of diminishing marginal utility.• Utility is not directly observable, calculable or comparable across individuals.• There are mathematical definitions of risk aversion and risk tolerance.• Risk aversion is found in humans and other animals and appears to have

origins in natural selection. (Competition weeds out risk preferrers.)• The mechanism by which risk aversion becomes manifest appears to be

neurochemical.

• Corporations are legal fictions that serve as connecting points for contracts among providers of factors of production.

• Corporations exist to lower the costs of contracting among these providers.• Equity owners are “residual claimants” to corporate assets and cash flows.• Residual claimants provide risk-bearing service to the other claimants to the

firm’s assets and cash flows.• Management acts on behalf of the equity owners/residual claimants.


Management acts on behalf of the residual claimants – what can we say about their risk aversion?

Remember CAPM and Modern Portfolio Theory? What did that tell us about the risk aversion of the market?

• Shareholders can diversify away idiosyncratic (or “random”) risk at a very low cost.

• Unless the corporation can shed idiosyncratic risk cheaper, the market will not reward the equity holders (through a higher market price) for management’s attempting to do so.

• Remember conglomerate mergers? How did that work out?

• So the market price of the residual claims will be discounted only for systematic risk, and the types of random risks typically considered by ERM can be ignored.

• Note that the derivation of CAPM begins with a utility function for wealth in which utility increases in expected value and decreases in variance.

• In fact, bond covenants generally contain provisions that prohibit management from increasing risks in order to benefit equity holders!


To see how increasing risk might help shareholders, let’s look at a simplified example of a corporation.

For our example we will look at an imaginary company that holds a single asset and a single liability.

• Asset: 10,000mmbtus of natural gas to be delivered exactly one year from today.

• Liability: An obligation to pay exactly $30,000 in one year from today (i.e. $3.00/mmbtu in the forward contract).


First, let’s take assume that there is no risk in the value of the contract at expiration.

Forward Purchase of Natural Gas• The firm has a single asset, a forward natural gas contract for delivery of 10,000

mmbtus of gas in exactly one year.• Upon delivery, the firm is obligated to make a payment of $30,000.• The riskless rate of interest is 5.0%.• The gas will be sold at the spot price immediately upon receipt.• The current one-year forward price of natural gas is $3.50.

Cash $0

Forward Contract

Total $33,293 Total

Zero-Risk Balance Sheet

Assets Liabilities and Equity

$33,293

$33,293

Price of $3.50 times 10,000 mmbtu’s discounted at the riskless rate.

$28,537 Debt

The present value of the $30,000 obligation discounted at the riskless rate.

$4,756 Equity

The asset value less the value of the debt.


To see how increasing risk might help shareholders, let’s look at a simplified example of a corporation.

For our example we will look at an imaginary company that holds a single asset and a single liability.

• Asset: 10,000mmbtus of natural gas to be delivered exactly one year from today.

• Liability: An obligation to pay exactly $30,000 in one year from today (i.e. $3.00/mmbtu in the forward contract).

While the approach we will illustrate is perfectly general, this simplified example will allow us to focus on the result of changing risk levels rather than the details of risk assessment, measurement, etc.

• The company is subject to a single risk – the risk that the price of natural gas in one year will change from today’s observed forward price.

• The metric for price risk on such contracts has been standardized (volatility) and can, in many instances, be derived directly from the market.


Next we will introduce risk in the form of random price volatility of 35%. Using option pricing, we develop a market value balance sheet.

Market Value Balance SheetAssets Liabilities and Equity

Cash $0 $26,215 DebtForward Contract $33,293 $7,078 Equity

Total $33,293 $33,293 Total

Price of $3.50 times 10,000 mmbtu’s discounted at the riskless rate.

The value of a one-year call option on a forward contract with:

• Strike Price = $3.00 x 10,000 mmbtus• Volatility = 35%• Riskless Rate = 5%• Asset Value = $3.50 x 10,000 mmbtus

Asset Value – Equity Value

• The equity value is the value of an option, and the debt value is the PV of the future cash flows (at the riskless rate) less the extrinsic value of the equity option.

• The market value of the debt is $26,215 with the 35% volatility, which is $2,322 lower than the value without risk. The implied market debt yield here is 13.48% or 848 bps above the riskless rate.

• By increasing the asset volatility from 0% to 35% the shareholders have expropriated $2,322 of the debtholders’ wealth for themselves!


“So, we don’t care about risk? That’s nuts! I want my tuition back!”

Please remain seated and try to stay calm…


However we define ERM, it must be directed toward the maximization of shareholder wealth.

There must be an understood causal relationship between the actions prescribed and the value of residual claims. Unsupported assertions of “corporate risk aversion” do not suffice. Here are some candidates for value-adding risk management activities:

• Ideation – Attempts to add value often focus on incremental revenue generation or high probability cost lowering (e.g. production rationalization). Actions that lower the chance or severity of bad outcomes may have positive value but be overlooked.

• De-biasing – Humans are prone to cognitive biases leading to over-optimism, many of which relate to the treatment of risks. ERM can formalize processes for de-biasing estimates and improve decision making.

• Cost of risk capital in strategic decisions – Decisions of a scale sufficient to alter the probability of financial distress by definition involve corporate risk capital, whose cost is seldom recognized.

• Value of real options – The value of management flexibility as resolution of uncertainty improves is often missed in analysis and implementation.


Introduction to Risk Aversion in Enterprise Risk Management

22 March 2011

Presented by:John LehmanManaging DirectorSDG-Galway Energy Strategy Practice

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Introduction To Risk Aversion