1. 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, Toronto June 3-4 2008 © Michael W. Brandt, 2008 All rights reserved without exception

2. Motivation

3. Optimal Decentralized ALM© Michael W. Brandt 2008  3  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

4. Optimal Decentralized ALM© Michael W. Brandt 2008  4  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

5. Optimal Decentralized ALM© Michael W. Brandt 2008  5  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

6. Optimal Decentralized ALM© Michael W. Brandt 2008  6  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

7. Optimal Decentralized ALM© Michael W. Brandt 2008  7  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

8. Problem setup

9. Optimal Decentralized ALM© Michael W. Brandt 2008  9  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 A T /L T Problem setup

10. Optimal Decentralized ALM© Michael W. Brandt 2008  10  Portfolio managers Fixed income manager (4 assets) –Indices (Aaa, Baa, Treasuries) –Independent alpha technology –No cash position –Preferences = power utility over A 1T /B 1T Equities manager (4 assets) –Indices (Growth, Intermediate, Value) –Independent alpha technology –No cash position –Preferences = power utility over A 2T /B 2T Two types of benchmarks (cash or optimally chosen) Problem setup

11. Cost of decentralization

12. Optimal Decentralized ALM© Michael W. Brandt 2008 Decomposition  12  Cost of decentralization Cost of Decentralization Suboptimal Diversification Asset/Liability Mismatch Alpha = + -

13. Optimal Decentralized ALM© Michael W. Brandt 2008 Suboptimal diversification Cash benchmarks No alpha technologies Portfolio managers have relative risk aversion of 10  13  Cost of decentralization

14. Optimal Decentralized ALM© Michael W. Brandt 2008 CIO’s optimal allocation to the 6 risky assets Note –No liability hedging with ° = 1 (log utility) –Full liability immunization as ° ! 1  14  Centralized ALM Cost of decentralization max SR weightsliability hedging weights

15. Optimal Decentralized ALM© Michael W. Brandt 2008  15  Centralized ALM (cont) Cost of decentralization

16. Optimal Decentralized ALM© Michael W. Brandt 2008 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  16  Decentralized ALM with cash benchmarks Cost of decentralization

17. Optimal Decentralized ALM© Michael W. Brandt 2008  17  Decentralized ALM with cash benchmarks (cont) Cost of decentralization

18. Optimal Decentralized ALM© Michael W. Brandt 2008 Cost of decentralization How much alpha do the portfolio managers have to add for the CIO to be indifferent between centralized and decentralized ALM?  18  Cost of decentralization IR

19. Optimal benchmarks for delegated ALM

20. Optimal Decentralized ALM© Michael W. Brandt 2008 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  20  Optimal benchmarks for decentralized ALM

21. Optimal Decentralized ALM© Michael W. Brandt 2008 Optimal benchmarks (cont) Understanding how portfolio managers respond to benchmarks, the CIO’s optimal benchmark choice is where x i C 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  21  Optimal benchmarks for decentralized ALM Optimal benchmarks achieve the same outcome as if the investment process was centralized and the CIO had the skills of the portfolio managers

22. Optimal Decentralized ALM© Michael W. Brandt 2008 Optimal benchmarks (cont)  22  Optimal benchmarks for decentralized ALM

23. Optimal Decentralized ALM© Michael W. Brandt 2008 Optimal benchmarks (cont)  23  Optimal benchmarks for decentralized ALM

24. Practical implementation

25. Optimal Decentralized ALM© Michael W. Brandt 2008  25  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 Practical implementation

26. Optimal Decentralized ALM© Michael W. Brandt 2008  26  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 Practical implementation

27. Optimal Decentralized ALM© Michael W. Brandt 2008  27  Empirical solution (cont) E.g., cross-sectional distribution of relative risk aversion of U.S. mutual fund managers Practical implementation

28. Extensions and conclusions

29. Optimal Decentralized ALM© Michael W. Brandt 2008  29  Extensions Long-only constraints Risk constraints at the portfolio manager level Alternative CIO preferences (van Binsbergen and Brandt, 2007) Other suggestions? Extension and conclusions

30. Optimal Decentralized ALM© Michael W. Brandt 2008  30  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