Investment Course III

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Investment Course III November 2007

• Topic Seven
• Portfolio Optimization Case Studies

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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

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TRS Initial Strategic Allocation Comparable
Portfolios
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Texas Teachers Retirement System Optimization
Process Overview
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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

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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

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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 years
  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

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TRS Example of Simulation-Based Forecasting
Process
10-yr. Bond Yield
Wage Inflation
Price 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.
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TRS Asset Class Mix and Assumptions
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TRS Gross Return Simulations with Different
Equity Levels in Portfolio
8.52
4.65
7.36
100 Equity
0 Equity
70 Equity
30 Fixed
0 Fixed
100 Fixed
100 Equity
70 Equity
0 Equity
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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

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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)

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Example of Simulation Analysis on Final Funded
Ratio 14 Contributions No Ad Hocs
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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
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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
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TRS Mean-Variance Optimization Inputs and Results
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Texas Teachers Retirement System (cont.)
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Texas Teachers Retirement System (cont.)
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Texas Teachers Retirement System 2007 Update
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Texas Teachers Retirement System 2007 Update
(cont.)
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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

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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

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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

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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
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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

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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

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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

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Chile Traditional vs. Resampled Efficient
Frontier
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Chile Base Case Unconstrained Resampled Frontier
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Chile Base Case Unconstrained Resampled Frontier
(cont.)
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Chile Base Case Unconstrained Resampled Frontier
(cont.)
Unconstrained Frontier
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Chile Modifying the Unconstrained Optimization
Constraint Set
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Chile Modifying the Unconstrained Optimization
(cont.)
Constrained Frontier for Fund A
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Chile Comparing Optimal Allocations Across
Constraints
Asset Allocations of Various Funds Using Point 20
on Unconstrained Frontier
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Chile Comparing Optimal Allocations Across
Constraints (cont.)
Asset Allocations of Various Funds Using Point 15
on Unconstrained Frontier
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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 AM 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 AM 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 Systems Board of
  Regents, which consists of politically appointed
  members.
• Cambridge Associates is the primary economic
  consultant to the UTIMCO Board

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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
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UTIMCO How Competitive is the Current Allocation
Policy?
May, 2005
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UTIMCO Recent Performance Relative to Large
Endowment Peers
May, 2005
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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
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UTIMCO Developing Return Assumptions Through the
Risk Premium Approach
March, 2005
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UTIMCO Developing Return Assumptions by Building
Economic Return Components
March, 2005
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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
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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
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UTIMCO Efficient Frontier With PVA
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UTIMCO Recommended 2005 Return and Risk
Assumptions With PVA
May, 2005
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UTIMCO Recommended 2005 Return and Risk
Assumptions With PVA (cont.)
May, 2005
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UTIMCO Risk Framework
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UTIMCO Developing Return Correlations Assumptions
May, 2005
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UTIMCO Developing Return Correlations
Assumptions (cont.)
May, 2005
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UTIMCO Recommended Return Correlations
Assumptions
May, 2005
50
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UTIMCO Developing the Downside Risk Threshold
May, 2005
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UTIMCO Some Thoughts About Investment
Restrictions

• Constraints Should be Considered Carefully
• They Might be Useful to Express Uncertainty
  Rather Than Aversion
• Constraints Should Define Unacceptable, Not Just
  Undesirable, Alternatives
• Remember That Every Constraint Has a Real Cost
  (We will show the estimated costs of all
  constraints adopted.)

May, 2005
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UTIMCO The Cost of Constraint - 2003 Allocation
March, 2005
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UTIMCO Existing and Recommended Constraints
May, 2005
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UTIMCO Existing and Recommended Constraints
(cont.)
May, 2005
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UTIMCO Mean-Downside Risk Optimization
Candidate Policy Portfolios Derived From 2005
Capital Market Assumptions
May, 2005
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UTIMCO 2005 Candidate Policy Portfolios No
Constraints
May, 2005
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UTIMCO 2005 Candidate Policy Portfolios 30
Hedge Fund Constraint
May, 2005
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UTIMCO Selecting a Strategic Asset Allocation

• The portfolio optimization processregardless how
  the investment problem is framedresults in an
  optimal set of asset allocations that are
  efficient in the sense each optimal allocation
  minimizes risk for a given return goal
• Once the efficient frontier is established,
  investors must next answer the following
  question Which single allocation (or range of
  allocations) from the efficient frontier is
  appropriate for them?
• Decisions Factors represent one approach to this
  problem. A decision factor is a measure or
  characteristic which may be used to relate
  specific goals to a particular decision.

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UTIMCO How Decision Factors Work
Idea A portfolio optimization simulation can be
designed to determine which potential asset
allocation would be optimal for each decision
factor (or combination of factors).
May, 2005
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UTIMCO Specific Decision Factors Voting Process
12.2
12.2
18.3
6.1
24.4
18.3
6.1
2.4
May, 2005
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UTIMCO Decision Factor Scores for Candidate
Policy Portfolios
May, 2005
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UTIMCO 2005 Policy Asset Allocation Comparison
May, 2005
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UTIMCO 2007 Update Asset Classification
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UTIMCO 2007 Update Asset Allocation