Is Portfolio Optimization Dead?

Sébastien Page CFASébastien Page, CFAHead of the Portfolio and Risk Management Group

State Street AssociatesState Street Global Markets

The Portfolio and Risk Management Group• The Portfolio and Risk Management Group specializes in quantitative, client-focused advisory research

deployed across a wide variety of asset classes and markets. The group has established strategic researchdeployed across a wide variety of asset classes and markets. The group has established strategic research partnerships with over 280 of the largest and most sophisticated institutional investors worldwide by providing advice on the macro issues of investment management, including:

1. How to determine the optimal asset allocation2. How to determine the appropriate currency exposurepp p y p3. How to structure exposure to alpha4. How to measure and manage exposure to loss5. How to determine an optimal rebalancing schedule6. How to incorporate assets with non-normal return distributions7 H t t t f7. How to structure manager fees

• In 2008, the team delivered over 732 customized asset allocation and risk management studies to clients worldwide and published 13 articles in academic journals.

Asset Managers30%Asset Owners

Client BreakdownNumber of Customized Analyses

127268

404549

732

2

70%23127

2003

2004

2005

2006

2007

2008

Data Requirements

Portfolio Reallocation Analysis

• Asset allocation

• Asset class benchmarks

Manager Reallocation Analysis

• Manager allocation

• Manager track records

Currency Hedging Analysis

• Asset allocation

• Asset class benchmarks

Optimal Rebalancing Analysis

• Asset allocation

• Asset class benchmarksAsset class benchmarks Manager track records

• Manager benchmarks

Asset class benchmarks Asset class benchmarks

Optional Optional Optional Optional

• Constraints

• Peer group allocation

• Duration of liabilities

R t i k d

• Constraints

• Expected returns

• Return, risk, and correlation assumptions

• Current hedging policy

• Constraints

• Current rebalancing policy

• Constraints

• Transaction cost assumptions

• Return, risk, and correlation assumptions • Return, risk, and

correlation assumptions

T d tiT d ti T d ti T d ti

3

Turnaround time ranges from two days to three

weeks.

Turnaround time ranges from two days to three

weeks.

Turnaround time ranges from two days to three

weeks.

Turnaround time ranges from two weeks to three

weeks.

Is Portfolio Optimization Dead?

• Bernartzi and Thaler (2001) demonstrate that equally weighted diversification (“1/N” diversification) is ingrained in human behavior.

• Previous research shows that 1/N portfolios outperform optimized portfolios out of sample. See: Jobson and Korkie (1981), DeMiguel, Garlappi, and Uppal (2007), and Duchin and Levy (2009).

• DeMiguel, Galarppi, and Uppal’s study is particularly convincing because the authors evaluate fourteen models on seven empirical datasets Theythe authors evaluate fourteen models on seven empirical datasets. They find that none of the fourteen models consistently outperforms 1/N.

4

Better Behaved Portfolios?

• In practice, most investors employ constraints when they optimize their portfolio.

• Jorion (1986, 1991) introduces the Bayes-Stein approach, which compresses expected returns towards the minimum-variance portfolio.

• Michaud (1989) discusses error maximization and Michaud (1998) introduces re-sampling as a method to reduce estimation error.

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Better Behaved Portfolios?

• Black and Litterman (1992) combine views with equilibrium expected returns to reduce extreme allocations.

• Chow (1995) achieves the same objective by augmenting the mean-variance objective function with a benchmark tracking error term, which yields better outcomes than imposing ad-hoc constraints.

• Chevrier (2009) uses economic theory – together with advances in Bayesian estimation – to build optimal portfolios The resulting portfoliosBayesian estimation – to build optimal portfolios. The resulting portfolios are better behaved than, and outperform, 1/N.

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The Problem with Previous Research“Past Performance Is Not Indicative of Future Results”

Five-Year Equity Risk Premium (1926 - 2009 YTD)(1926 2009 YTD)

15%20%25%

-5%0%5%

10%

-15%-10%

5%

1930

1935

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1955

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1965

1970

1975

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YTD

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2009

Questioning Conventional Wisdom

• Fisher and Statman (1997) argue that extreme allocations are not due to estimation errors. Optimal portfolios may include extreme positions even when the true parameters are used. Kritzman (1998) explains that no-one likes to be wrong and alonelikes to be wrong and alone.

• Scherer (2002) demonstrates that resampling converges to the mean-variance solution when short sales are allowed.

• Kritzman (2003) dismisses the adage “garbage in – garbage out” and• Kritzman (2003) dismisses the adage garbage in – garbage out and Kritzman (2006) demonstrates that high sensitivity to inputs occurs when assets have similar expected returns and risk.

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Our Experiment

• We perform backtests to compare the out-of-sample performance of – The 1/N portfolio– The market portfolio– Optimized portfolios

• However, instead of rolling historical returns, we use simple models of expected returns that do not require forecasting skill.

• Our study covers 13 datasets comprised of 1 028 data series representing• Our study covers 13 datasets comprised of 1,028 data series representing 4.4 million data points. We construct over 50,000 optimized portfolios and evaluate their out-of-sample performance.

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Asset-Liability Management

Asset Class Source Start EndDomestic Equity S&P 500 Feb 1973 Dec 2008

Foreign Equity MSCI EAFE Feb 1973 Dec 2008Foreign Equity MSCI EAFE Feb 1973 Dec 2008

Domestic Government Barclays US Govt Feb 1973 Dec 2008

Domestic Corporate Barclays US Corp Feb 1973 Dec 2008

REITs FTSE/NAREIT Feb 1973 Dec 2008

Commodities S&P GSCI Feb 1973 Dec 2008

Cash Ken French (1m T-bill) Feb 1973 Dec 2008

Liabilities (Remeaned) Barclays US Govt Long Feb 1973 Dec 2008

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Betas

Asset Class Source Start End10 Industries CRSP/Ken French Jul 1926 Dec 2008

30 Industries CRSP/Ken French Jul 1926 Dec 200830 Industries CRSP/Ken French Jul 1926 Dec 2008

10 Size Deciles CRSP/Ken French Jul 1926 Dec 2008

10 Book-to-market deciles CRSP/Ken French Jul 1926 Dec 2008

10 Dividend yield deciles CRSP/Ken French Jul 1927 Dec 2008y

10 Momentum deciles CRSP/Ken French Jan 1927 Dec 2008

10 Long-term reversal deciles CRSP/Ken French Jan 1931 Dec 2008

10 Short-term reversal deciles CRSP/Ken French Feb 1926 Dec 2008

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Alphas

Asset Class Source Start EndSecurity selection (500 stocks) S&P 500 Constituents Dec 1998 Dec 2008

21 Commodities S&P/GSCI Jan 1971 Dec 200821 Commodities S&P/GSCI Jan 1971 Dec 2008

14 Hedge fund styles HFRI Jan 1996 Dec 2008

15 Asset managers Yahoo May 1987 Dec 2008

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Constituents: Commodities

Wheat Cotton PlatinumLive Cattle Live Hogs Crude OilCorn Copper CocoaCorn Copper CocoaSoybeans Gold AluminiumGrains Coffee ZincSilver Petroleum NickelSugar Heating Oil Natural Gas

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Constituents: Hedge Fund Styles

Equity Market Neutral Private Issues – Reg D CorporatesQuant Directional Merger Arbitrage Asset-BackedShort Bias Systematic Diversified Yield AlternativesShort Bias Systematic Diversified Yield AlternativesTech - Healthcare Multi-StrategyEnergy Convertible Arbitrage

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Constituents: Asset Managers

American Funds Investors Fidelity Growth Company Fidelity Equity-IncomeDavis NY Venture A American Funds A Columbia Acorn ZVanguard American Funds Was Mutual A T Rowe Mid-Cap GrowthVanguard American Funds Was. Mutual A T. Rowe Mid-Cap GrowthAmerican Funds Growth Dodge & Cox Stock Fidelity ValueFidelity Contrafund Vanguard Windsor II Perkins Mid Cap Value

Fund Screener:• Any U.S. Stock Funds• Manager Tenure: Longer than 10 Years• Net Assets: >$5 billion• Remove redundant fundsRemove redundant funds

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Backtesting

( )

Expected Returns: Minimum Variance, Constant Risk Premium, and All-Data Risk Premium.

Covariance Matrix: Equally-Weighted (5,10, and 20 Years, All-Data, and 3-Year Daily for Security Selection).

10%15%20%25% ( )wwwMax

wΣ×− ˆˆ '

*λµ

0≥iw

10%-5%0%5%

10% i

-15%-10%

1930

1935

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1975

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009

YTD

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20

Expected Returns: Minimum Variance

ValueValue Deciles

1 0.0%

2 0.0%

3 0.0%

4 0 0%

15%20%25%

4 0.0%

5 0.0%

6 0.0%

7 0.0%

8 0.0%

5%0%5%

10% 9 0.0%

10 0.0%

-15%-10%-5%

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YTD

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2

2009

Expected Returns: Minimum Variance

ValueValue Deciles

1 25%

2 22%

3 18%

4 17%

15%20%25%

4 17%

5 15%

6 14%

7 14%

8 12%

5%0%5%

10% 9 10%

10 10%

-15%-10%-5%

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YTD

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1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2

2009

The All-Data Approach

25%Estimate Covariance Matrix

and Risk Premium Updates (Growing Sample)

5%10%15%20%

-10%-5%0%5%

-15%

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YTD

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Asset-Liability Management

Average Sharpe Ratios (Surplus)

1.4

1.11.11.2

1.4

1.6

0.7 0.7

0 6

0.8

1

0.4

0.6

MarketPortfolio

1/N MinimumVariance

Constant RiskPremium

In-Sample

5-Year Trailing Covariance Matrix With Constant Risk Premium10-Year Trailing Covariance Matrix With Constant Risk Premium20-Year Trailing Covariance Matrix With Constant Risk PremiumAll-Data Covariance Matrix and Risk Premium (Growing Sample)

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All Data Covariance Matrix and Risk Premium (Growing Sample)

Assuming 40 bps round-trip transaction costs, the estimated impact of transaction costs on Sharpe ratios are: -0.02 for 1/N, -0.04 for Minimum Variance, and -0.05 for Constant Risk Premium.

Betas

Average Sharpe Ratios

0.72

0.590 6

0.7

0.8

0 36

0.490.54

0.4

0.5

0.6

0.36

0.3

0.4

MarketPortfolio

1/N MinimumVariance

Constant RiskPremium

In-Sample

5-Year Trailing Covariance Matrix With Constant Risk Premium10-Year Trailing Covariance Matrix With Constant Risk Premium20-Year Trailing Covariance Matrix With Constant Risk PremiumAll-Data Covariance Matrix and Risk Premium (Growing Sample)

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All Data Covariance Matrix and Risk Premium (Growing Sample)

Assuming 40 bps round-trip transaction costs, the estimated impact of transaction costs on Sharpe ratios are: -0.002 for 1/N, -0.008 for Minimum Variance, and -0.009 for Constant Risk Premium.

Alphas

Sharpe Ratios1 51 60

1.2

0.98

1.3

1.5

0.9

1.21.20

1.60

0.20.3

0.4

0.160 07

0.28

0.5 0.50.4 0.4

0.40

0.80

0.07

0.00Market Portfolio 1/N Minimum

VarianceIn-Sample

S it S l ti (S&P 500)Security Selection (S&P 500)CommoditiesHedge FundsAsset Managers

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Assuming 40 bps round-trip transaction costs, the estimated impact of transaction costs on Sharpe ratios for minimum variance are: -0.04 for security selection, -0.02 for commodities, -0.17 for hedge funds, and -0.06 for asset managers; for 1/N the estimated impact is -0.01 in all cases. Results are preliminary.

Better Risk Estimates

• Risk parameters, such as standard deviation and correlation, estimated from full samples provide unreliable measures of the hedging and diversification properties of assets during turbulent markets (Chow, Jacquier Kritzman and Lowry 1999)Jacquier, Kritzman, and Lowry, 1999).

• It is possible to use multivariate outliers to measure market turbulence.

• By measuring turbulence, we can estimate risk parameters more reliably– estimate risk parameters more reliably,

– build portfolios that are more resilient to turbulent markets, and – build dynamic regime-switching models (Kritzman, Lowry, and Van Royen,

2001).

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Higher Moments

• Mean-variance optimization assumes either that returns are normally distributed or quadratic utility is a good approximation of investor preferences.

• Full-scale optimization (Cremers, Kritzman, and Page, 2005, Adler and Kritzman, 2007, Chua, Kritzman, and Page, 2009), also called direct utility maximization (Sharpe, 2007) identifies the optimal portfolio given any set of return distributions and based on any description of investor preference.

• Full-scale optimization has been shown to outperform mean-variance optimization out-of-sample.

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Full-Scale vs Mean-Variance Optimization

• Hedge fund returns are notoriously non-normal (see Alexiev 2004, Davies et al., 2003, Fung and Hsieh, 2000, Gregoriou and Gueyie, 2003, Kat and Lu, 2002, Lo, 2001, Lo 2005, and McFall, 2003).

• Using a sample of 32 hedge funds from 1994-2003 and four utility functions, Adler and Kritzman demonstrate that full-Scale optimization outperforms mean-variance optimization out-of-sample:

Increase in Frequency of1994-1998 Utility FS > M-V UtilityKinked at -1% 24% 67%Kinked at 1% 24% 67%Kinked at -5% 316% 85%S-shaped at 0% 2% 93%S-shaped at 0.5% 4% 98%

1999-2003

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Kinked at -1% 6% 61%Kinked at -5% 4% 56%S-shaped at 0% 4% 78%S-shaped at 0.5% 36% 91%

Conclusion

• DeMiguel, Garlappi, and Uppal (2007) claim that 1/N outperforms mean-variance optimization.

• Their results are highly dependent on the assumption that we can model expected returns using trailing 60-month and 120-month historical returns.

• Our contribution is not to build clever models of expected returns; we simply show that by removing our reliance on rolling mean returns, the value of optimization becomes evident.

• Quantitative and fundamental practitioners should focus on building models of expected returns that will combine with – and improve on – the risk-

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minimizing portfolio.

Candidats 2009