Optimal Decentralized ALM © Michael W. Brandt 2008

Optimal Decentralized ALM

Jules H. van Binsbergen, Stanford University

Michael W. Brandt, Duke University and NBER

Ralph S.J. Koijen, University of Chicago

Rotman ICPM Forum, TorontoJune 3-4 2008

© Michael W. Brandt, 2008 All rights reserved without exception

Motivation

Optimal Decentralized ALM© Michael W. Brandt 2008 *

Decentralized investment management

• Institutions decentralize investment decisions along asset classes

– Example

– Why? Division of labor

Specialization ) Generating value (i.e., lower transaction cost or positive alpha) within an asset class requires specialized skill

CIO

Fixed Income Portfolio Manager

Equities Portfolio Manager

Motivation


Misalignment of objectives

1. Suboptimal diversification

– Joint optimization by CIO over all assets dominates best combination of portfolios optimized by portfolio managers within asset-classes

– Sharpe (1981) and Elton and Gruber (2004)

2. Different risk preferences

– Portfolio managers take more or less risk than CIO desires

– CIO does not generally know the managers’ risk preferences

– van Binsbergen, Brandt, and Koijen (2008)

3. Mismatch risk between assets and liabilities

– Portfolio managers do not consider liabilities in their optimization

– Main motivation for this project

Motivation


Benchmarking

• Performance benchmarks are commonly used to evaluate and compensate portfolio managers

– Emphasis is on measuring effort or skill

– Benchmarks are taken as exogenously given (e.g., cash or index)

• We examine to what extent optimally designed benchmarks can alleviate the misalignment induced by decentralization

• To be realistic, we focus on

– Benchmarks that are tradable portfolios and can be matched by the portfolio managers (i.e., no cross-benchmarking)

– Benchmarks that do not depend on unknown quantities

– Unconditional benchmarks

Motivation


Objective of our study

• Quantify in an intuitive way the economic cost of decentralization

– How much active skill do delegated portfolio managers have to have in order to justify decentralization?

• Show how to construct benchmarks that perfectly align objectives and achieve the same outcome as if the investment process was centralized and the CIO had the skills of the portfolio managers

– Full benefits of diversification

– Optimal mismatch risk

– Optimal alpha overlay

Motivation


Objective of our study (cont)

• Show how to operationalize our approach

– Our optimally constructed benchmarks depend on the portfolio managers’ risk tolerances and active skill levels

– Three possibilities Take an ex-ante stance on both sets of parameters Construct an empirical cross-sectional distribution and

incorporate the resulting “parameter uncertainty” Limit the role of both sets of parameters through constraints

Motivation

Integrated and fully operational approach for decentralized liability driven investment (LDI) management

Problem setup


Pension fund

• CIO

– Liabilities

Exogenous with Treasury-like dynamics

– Assets

Centralized portfolio management (7 assets)– Fixed income indices (Aaa, Baa, and Treasuries)– Equity indices (Growth, Intermediate, Value)– Cash

Decentralized portfolio management (3 assets)– Fixed income manager

– Indices + orthogonal alpha technology

– Equities manager– Indices + orthogonal alpha technology

– Cash

– Preferences = power utility over AT/LT

Problem setup


Portfolio managers

• Fixed income manager (4 assets)

– Indices (Aaa, Baa, Treasuries)

– Independent alpha technology

– No cash position

– Preferences = power utility over A1T/B1T

• Equities manager (4 assets)

– Indices (Growth, Intermediate, Value)

– Independent alpha technology

– No cash position

– Preferences = power utility over A2T/B2T

• Two types of benchmarks (cash or optimally chosen)

Problem setup

Cost of decentralization

Optimal Decentralized ALM© Michael W. Brandt 2008

Decomposition

*


Cost of Decentralization

Suboptimal Diversification

Asset/Liability Mismatch

Alpha

=

+

-


Suboptimal diversification

• Cash benchmarks

• No alpha technologies

• Portfolio managers have relative risk aversion of 10

*



• CIO’s optimal allocation to the 6 risky assets

• Note

– No liability hedging with ° = 1 (log utility)

– Full liability immunization as ° ! 1

*

Centralized ALM


max SR weights liability hedging weights


Centralized ALM (cont)



• Both portfolio managers maximize their (absolute) SR

with

which includes their alpha technologies (technically ¤ ¤C)

• CIO invests optimally in the 2 managed portfolios and cash

*

Decentralized ALM with cash benchmarks



Decentralized ALM with cash benchmarks (cont)




• How much alpha do the portfolio managers have to add for the CIO to be indifferent between centralized and decentralized ALM?

*


IR

Optimal benchmarks for delegated ALM


Optimal benchmarks

• Response of the portfolio managers to benchmark with weights ¯i

• Note

– Benchmarks are ineffective with ° = 1 (log utility)

– Tracking error volatility ! 0 as ° ! 1

*

Optimal benchmarks for decentralized ALM


Optimal benchmarks (cont)

• Understanding how portfolio managers respond to benchmarks, the CIO’s optimal benchmark choice is

where xiC is the CIO’s optimal allocation to the portfolio manager’s

assets including the manager’s alpha technology

• These benchmarks induce the first-best solution– Full benefits of diversification– Optimal mismatch risk– Optimal alpha overlay

*


Optimal benchmarks achieve the same outcome as if the investment process was centralized and the CIO had the

skills of the portfolio managers



*




*


Practical implementation


Unknown quantities

• The optimal benchmarks depend on two unknown quantities

– Portfolio managers’ risk tolerance

– Portfolio managers’ active skill (IC)

• Unknown quantities can be dealt with the same way as they usually are in portfolio choice problems

– “Plug-in” = pick values and proceed as if they known

– Bayesian = construct a subjective cross-sectional distribution of risk tolerance and active skill levels (be careful, they are likely highly correlated) and then integrate out the unknown quantities



Empirical solution

• Looking at past returns on active managers through the lens of a structural model of delegated portfolio management (like ours), we can learn a lot about managers’ risk preferences and skill

) Koijen (2008)

• Intuition

– Structural models predict how much beta exposure and active risk managers take on as a function of their risk aversion and skill

– Beta exposure and active risk can be measured fairly accurately (especially when compared to historical alpha estimates)

– These estimates can then be inverted to risk aversion and skill



Empirical solution (cont)

• E.g., cross-sectional distribution of relative risk aversion of U.S. mutual fund managers


Extensions and conclusions


Extensions

• Long-only constraints

• Risk constraints at the portfolio manager level

• Alternative CIO preferences (van Binsbergen and Brandt, 2007)

• Other suggestions?

Extension and conclusions


Conclusions

• Three contributions

– Quantify in an intuitive way the economic costs of decentralization

– Show how to construct benchmarks that perfectly align objectives and achieve the same outcome as if the investment process was centralized and the CIO had the skills of the portfolio managers

– Show how to operationalize our approach

• Integrated and fully operational approach for decentralized ALM

Extension and conclusions

Documents

Optimal Decentralized ALM © Michael W. Brandt 2008