Investment Course III – November 2007

1. Investment Course III – November 2007 Topic Seven: Portfolio Optimization: Case Studies

2. Portfolio Optimization Example #1:2003 Texas Teachers’ Retirement System • Background: Texas Teachers’ Retirement System (TRS) is a public defined-benefit pension fund dedicated to delivering retirement benefits and related services for more than 1,000,000 public education employees and their annuitants in the state of Texas. It currently has more than USD 90 billion of assets under management. • Investment Problem: The Board of Trustees at TRS faces a typical “asset-liability” management problem in that they must invest so as to simultaneously satisfy the income needs of current retirees and beneficiaries as well as provide sufficient asset growth to provide for future funding needs. The system is currently underfunded relative to actuarial liabilities, largely due to the fact that contributions from the state legislature have not kept pace with needs. • Portfolio Optimization Application: Mean-variance optimization approach across multiple asset classes, including U.S. equity, non-U.S. equity, fixed-income, private equity, “strategically traded” (i.e., hedge funds), and real estate. • Miscellaneous Issues: - Ennis Knupp Associates in the main economic consultant to the TRS Board - TRS is required by state law to revisit strategic allocation process every 3-5 years

3. TRS: Initial Strategic Allocation & Comparable Portfolios

4. Texas Teachers’ Retirement System: Optimization Process Overview

5. TRS: Steps in the Process • Establish assumptions and simulate key economic variables • Inflation (price and wage) • Interest rates • Asset class returns, volatility and correlations • Use simulations to develop plan financial results over forecast period • Summarize and graph results • Trends • Range and distribution of results (i.e. uncertainty or risk) • Test impact of alternative equity allocation targets

6. TRS: Unfunded Status • A contribution from the State of Texas of about (12% x Pay) would be required to fund the normal cost plus amortize a $22 billion unfunded actuarial liability over 30 years

7. TRS: Economic Assumptions for the Forecast • Each forecast reflects a specific scenario for future rates of inflation, wage increases, bond yields and asset class returns • These variables will be different than the actuarial assumptions, thus producing “actuarial gains or losses” that are recognized in the forecast results – just as happens in each year’s actuarial valuation results • For the baseline forecast, best estimate assumptions are used • For simulation runs, the model produces 500 different scenarios with year-to-year fluctuations in each economic variable – but the average result across all 500 scenarios will closely match the best estimate assumptions from the baseline forecast

8. TRS: Example of Simulation-Based Forecasting Process 10-yr. Bond Yield Price Inflation* Wage Inflation** * Compound average price inflation over 15 years is 3.00%. ** Compound average wage inflation over 15 years is 4.00%. A merit/promotional increase is added to wage inflation to get the total salary increase rate.

9. TRS: Asset Class Mix and Assumptions

10. TRS: Gross Return Simulations with Different Equity Levels in Portfolio 8.52% 4.65% 7.36% 70% Equity 100% Equity 0% Equity 30% Fixed 0% Fixed 100% Fixed 70% Equity 100% Equity 0% Equity

11. TRS: Forecast Results With Full Simulation • Six different sets of results, based on two key variables • Three different rates of employer contribution (as % of pay) • 6% (current) • 10% (constitutional max) • 14% (approximate rate for 30-year amortization of UAL, plus a 2% cushion) • Two different assumptions for ad hoc benefit increases to retirees • No ad hoc increases • Increases to match CPI each year • Funded ratio results = actuarial value of assets / actuarial value of liabilities • Based on current actuarial assumptions in almost all scenarios • Only in some of the scenarios where market interest rates move to (and stay at) extreme levels do we assume that changes in the actuarial assumptions would be made

12. Question: How Much Equity to Include in the TRS Portfolio? • First analysis is for the result set that puts the lowest emphasis on the need for high equity returns to maintain funded status: • Assume contributions are at 14% of pay • Assume no ad hoc increases for retirees • Look at distribution of final (year 15) funded position and the contribution required to fund it • Final unfunded liability = final actuarial liability minus final market value of assets • Calculate the additional contribution (% pay) that would be required over the 15 year forecast period to fully fund the final unfunded liability – call this the “full funding cost add-on” • Put no weight on any final surplus assets (i.e. the required contribution above is never less than zero) • Repeat for various equity allocation targets • Perform risk / reward analysis • Reward = average of all 500 simulated scenarios • Risk = average of the worst 100 simulated scenarios • Plot the changes in risk and reward measures vs. current policy • Repeat analysis using a result set that puts more emphasis on the need for high equity returns to maintain funded status (10% contributions & full ad hocs)

13. Example of Simulation Analysis on Final Funded Ratio: 14% Contributions & No Ad Hocs

14. TRS: Notion of Risk-Reward Analysis Benchmark ( = current mix) Lower cost Less risk Avg. Cost Savings (% Pay) (All 500 scenarios) More risk Higher cost Avg. Risk Increase (% Pay) (Worst 100 scenarios) Change in cost relative to “benchmark” values 2.19

15. TRS: Risk-Reward Analysis for Different Equity Levels Benchmark ( = current 70%) 60% Avg. Cost Savings (% Pay) (All 500 scenarios) 50% 80% 90% 40% Avg. Risk Increase (% Pay) (Worst 100 scenarios) Conclusion: Based on this analysis, a reduction in the equity allocation to as low as 40% could be justified. At 60% equity, risk is reduced, but the average cost remains essentially unchanged. 2.20

16. TRS: Mean-Variance Optimization Inputs and Results

17. Texas Teachers’ Retirement System (cont.)

18. Texas Teachers’ Retirement System (cont.)

19. Texas Teachers’ Retirement System – 2007 Update

20. Texas Teachers’ Retirement System – 2007 Update (cont.)

21. Portfolio Optimization Example #2:2004 Chilean Pension System (Source: Fidelity Investments) • Background: System of private pension accounts since 1980. Beneficiaries select among several different investment managers (i.e., AFPs), which in turn over five different asset allocation alternatives. Constraints exist as to how much non-CLP investment can occur and what form the foreign investments must take. • Investment Problem: What are the optimal strategic asset allocations for the Chilean pension funds? • Portfolio Optimization Application: Augmented mean-variance optimization using three Chilean asset classes (stocks, bonds, cash) and four foreign asset classes (U.S. stocks, U.S. bonds, Developed Non-U.S. stocks, Developed Non-U.S. bonds) • Miscellaneous Issue: Optimization process uses the “Resampled Frontier” approach to reduce estimation error problems

22. Two Approaches to the Chilean Pension Investment Problem • Defined Benefit (DB) - Immunize the future liability stream (or manage the surplus) - All individuals treated identically within the overall plan • Defined Contribution (DC) - Maximize wealth at retirement subject to risk - Provide efficient portfolios in absolute return/risk space - Individuals select risk/return profile based on preferences • Analysis requires: - Long-term expected asset class returns - Asset class covariances - Appropriate portfolio construction

23. Chile: Base Case Assumptions • Base Case Assumptions: • Expected real returns based on 1954 – 2003 risk premiums • Real returns for developed market stocks and bonds areGDP-weighted excluding US (equally-weighted returns for stocks and bonds are 5.73% and 1.39%, respectively) • Chilean risk-premium volatility estimates exclude the period 1/72 – 12/75

24. Chile: Base Case Assumptions (cont.) - Correlation matrix is based on real returns from the period 1/93 – 6/03 using Chilean inflation and based in Chilean pesos - Real returns for developed market stocks and bonds areGDP-weighted excluding US

25. Chile: Notion of a Resampled Efficient Frontier • Problems with traditional mean-variance optimization • Rare events such as unusually low or high returns greatly affect the result of the optimization (maximizing sampling error) • Length of data series is crucial -- the longer the forecasting period, the longer data series are required • “Optimal” efficient frontier may not be optimal and should not be used to make all asset allocation decisions

26. Chile: Notion of a Resampled Efficient Frontier (cont.) • Created by Richard Michaud, resampling is a Monte Carlo technique for estimating the inputs of a mean-variance efficient frontier that results in well-diversified portfolios. • Concept of a Resampled Efficient Frontier: • Take a random sample of observation from a universe of asset class returns (e.g., 30 of 60 months) and calculate the efficient frontier • Divide this efficient frontier into 20 regions by risk or expected return and look at the median allocation in each of these regions • Repeat these steps for a new sampling of the asset class return universe • Generate a large collection of efficient frontiers by repeated sampling of the return universe (e.g., 500-1000 trials) • Average all of the “regional” allocations across the collection of optimization trials – this is the resampled efficient frontier

27. Chile: Notion of a Resampled Efficient Frontier (cont.) • Resampling provides a more realistic and reliable risk/return structure • Robust estimate of underlying distributions • While the weights on the actual frontier change erratically, the resampled weights are evenly distributed along the points on the efficient frontier • With the actual efficient frontier, a marginal change in risk or return can bring about a dramatic change in the optimal allocation. With the resampled frontier, the changes in weights are always smooth • Potential shortcomings of resampling: • Lack of theory (i.e., no reason why resampled portfolios will be optimal) • No framework for incorporating tactical views

28. Chile: Traditional vs. Resampled Efficient Frontier

29. Chile: Base Case Unconstrained Resampled Frontier

30. Chile: Base Case Unconstrained Resampled Frontier (cont.)

31. Chile: Base Case Unconstrained Resampled Frontier (cont.) Unconstrained Frontier:

32. Chile: Modifying the Unconstrained Optimization Constraint Set:

33. Chile: Modifying the Unconstrained Optimization (cont.) Constrained Frontier for Fund A:

34. Chile: Comparing Optimal Allocations Across Constraints Asset Allocations of Various Funds Using Point 20 on Unconstrained Frontier:

35. Chile: Comparing Optimal Allocations Across Constraints (cont.) Asset Allocations of Various Funds Using Point 15 on Unconstrained Frontier:

36. Portfolio Optimization Example #3:2005 University of Texas Investment Management Company • Background: The University of Texas Investment Management Company (UTIMCO) is a private company whose only client is the public endowment fund holding the assets of the University of Texas and Texas A&M University Systems. It currently has about USD 16 billion under management. • Investment Problem: The Board of Directors of UTIMCO faces a multi-dimensional investment problem that involves both short- and intermediate-term funding needs for the various campuses in the UT and A&M systems as well as long-term growth goals. Although UT is a public university, the UTIMCO staff feels that it must produce investment returns that are comparable to the endowments of Harvard and Yale Universities. • Portfolio Optimization Application: Mean-downside risk optimization approach across multiple asset classes, including U.S. equity, non-U.S. equity, fixed-income, private equity, hedge funds, and real estate. • Miscellaneous Issues: • The downside risk threshold is the funding rate that is projected by the System’s Board of Regents, which consists of politically appointed members. • Cambridge Associates is the primary economic consultant to the UTIMCO Board

37. UTIMCO: Initial Asset Allocation and Issues to Address • Benchmark for Developed International and Emerging Markets • Target and Upper Limit Identical in Hedge Funds • Target and Upper Limit Identical in Private Equity • Target and Lower Limit Identical in Fixed Income • Remove REITS From US Equity Category • Remove TIPS From Fixed Income Category • Reinstate Inflation Hedge Category • Liquidity Policy is Inconsistent With Asset Allocation Policy May, 2005 36

38. UTIMCO: How Competitive is the Current Allocation Policy? May, 2005 37

39. UTIMCO: Recent Performance Relative to Large Endowment Peers May, 2005 38

40. UTIMCO: Inputs for the Asset – Obligation Optimization Process • The Asset – Obligation Optimization Process Requires the Following Assumptions: • Expected Returns • Expected Risk and Risk Profile • Correlations Between Expected Returns Across Asset Categories • The Minimum Acceptable Return (or MAR) March, 2005 16

41. UTIMCO: Developing Return Assumptions Through the Risk Premium Approach March, 2005 18

42. UTIMCO: Developing Return Assumptions by Building Economic Return Components March, 2005 19

43. UTIMCO: Notion of Potential Value Added (PVA) • Potential Value-Added (PVA) is the opportunity to increase returns beyond those generally available in an asset class through active management, • PVA takes two forms: • PVA by an active manager is the result of effective security selection usually based on extensive research and analysis skills, • PVA by staff can result from a wide range of sources including skill in manager selection, term negotiations, manager monitoring, responses to periodic special opportunities in the markets, and risk control. • The objective at UTIMCO is to focus on high PVA opportunities, developing or purchasing the skills necessary to earn attractive returns. March, 2005 23

44. UTIMCO: Measuring PVA Across Asset Classes • High value-added spread equals high PVA, • PVA spreads measure the opportunity for value-added • Realistic assumptions on future value-added spreads are the basis for PVA projections • A realistic evaluation of staff and external manager skills leads to an estimated “Capture Ratio” that defines the portion of the total value-added spreads we expect to earn in excess returns March, 2005 24

45. UTIMCO: Efficient Frontier With PVA

46. UTIMCO: Recommended 2005 Return and Risk Assumptions With PVA May, 2005 45

47. UTIMCO: Recommended 2005 Return and Risk Assumptions With PVA (cont.) May, 2005 46

48. UTIMCO: Risk Framework

49. UTIMCO: Developing Return Correlations Assumptions May, 2005 48

50. UTIMCO: Developing Return Correlations Assumptions (cont.) May, 2005 49