Investment Symposium March 2012 P2: Portfolio Construction: Asset Allocation versus Risk/Strategy Buckets Marc Carhart Radu Gabudean Moderator Timothy Wilson
Beyond Modern Portfolio Theory Radu C. Gabudean Barclays Research Asset Allocation: Historical Evolution Portfolio Building Blocks Market Risk Premia Alternative Risk Premia Geographical Diversification Equity Rates Credit.. Alt Assets Equity Rates Credit Commods EM Equity Fixed Income Commods Equity Fixed Income Today 2000s 1990s 1980s 1970s Portfolio Construction Method 4. Risk Parity, Most Diversified Portfolio, Equal Volatility, 3. Capacity & liquidity constraints: Constrained optimization 2. Estimation error: Black Litterman, shrinkage, robust optimization 1. Tail-risk: Sortino 60/40 Modern Portfolio Theory - MVO
Building a Portfolio The objective of any portfolio: Maximize i Performance vs Risk Requires forecast of building blocks properties Performance (E.g. Expected Returns) Risk (E.g. Volatilities) Joint behavior (E.g. Correlations) If Risk = Volatility then Mean Variance Optimization i (MVO) Why Portfolio Building Blocks Matter If forecasts are perfect, building blocks do not matter Historical data often produces unreliable forecasts Particularly for building blocks with unstable properties and high correlations Check historical estimates against intuition Must be able to form views on future performance and risk Combine historical estimates with pre-defined views For clarity and practicality, define building blocks based on sources of performance Risk Premia = Sources of Performance
Risk Premia as Portfolio Building Blocks Intuitive performance May have low correlation More stable correlations and volatilities Easier to forecast from historical data More stable portfolio weights Offer a systematic way to cover all sources of performance Views about various premia differ across investors Portfolio differs across investors Market-cap portfolio is not optimal Asset Allocation Example: Building Blocks Liquid risks that carry a premium, diversified across geography & style BetaFactors Alternative Beta Factors Diversifiers Global Equity Markets Russell 1000 MSCI EAFE Global Rates Markets US Rates US TIPS Carry/Curve/Value Premia MSCI EM Rates 2/10 USD FX Carry EU Rates EU Linkers Commodities Markets Energy Industrials CDX IG EM Sov USD Agriculture Livestock Credit Spreads CDX HY itraxx IG Rates 2/10 EU Commodities Curve Commodities Value Rates Liquidity Volatility Curve Equity Value Equity M&A Long Volatility Tail Hedge Gold
Which Portfolio Construction Method? Many alternative methods to Mean-Variance Optimization E.g. Most Diversified, Equal Volatility, Risk Parity, Equal Weights Still use estimates of performance and/or risk All may be interpreted as robust MVO The properties forecasts combine estimates with pre-defined values Hard to give them another interpretation without departing from the objective of Maximize Performance vs Risk Allows for clear comparison and selection across methods The pre-defined values must be appropriate Robust Mean Variance Mean Variance Most Diversified Minimum Volatility Risk Parity Equal Weights... Robust MVO Construction Methods: Examples Name Volatility forecast Correlation forecast Sharpe forecast Equal Volatility Historical The same The same Max Diversified Portfolio Risk Parity Historical Historical The same Historical Historical & Zero Minimum Volatility Historical Historical Shrinkage (Ledoit & Wolf) Black Litterman Your own Historical Historical & Historical&/or Historical & The same Historical & Historical&/or The same Inverse of volatility Historical Historical & Historical&/or
From MVO to Tail-Risk Maximize Performance / Risk; Risk =Tail-Risk Issue: Joint behavior = Multivariate joint distribution Portfolio construction with tail-risk hedges: Robust Mean-Variance Optimization on nonhedges Overlay tail-hedges using tail-risk criteria Account for tail-hedges in MVO Capacity and the Market-weight Portfolio Capacity constraints: Tilts the portfolio towards market-cap weights because of trading costs Optimum Portfolio w/out Trading Costs Market-Cap Portfolio Optimum Portfolio with Trading Costs Market-cap portfolio is not always optimal, but it is still special Implement capacity constraints with a layered approach: Group risks into buckets of comparable importance
Asset Allocation Example: Methodology Compare models: 1. 60/40 on US Equity and US Fixed Income 2. MVO on US Equity, US Fixed Income and Commodities using historical estimates for performance and risk 3. Robust methodology to historical estimates, tail-hedge and capacity constraints on Global Liquid Risk Premia Average Weight Equities FI / Rates Commodities Spreads Alternative Premia Tail-Hedge 60/40 60% 40% Historical MVO 23% 59% 18% Robust Risk-premia 5% 30% 7% 25% 27% 6% Standard Deviation of Weights Equities FI / Rates Commodities Spreads Alternative Premia Tail-Hedge Historical MVO 30% 37% 24% Robust Risk-premia 1% 5% 2% 5% 5% 0% Source: Barclays, Bloomberg Asset Allocation Example: Results Pie Charts: Realized Risk Contributions 190 160 60/40 FI Equities Historical MVO Equities Commods FI Diversified, Tail hedged, Risk Parity Hedge Equities Alternatt Spreads Rates Commods Vol=2.4% Vol = 6.9% 130 Vol = 10% 100 70 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Source: Barclays, Bloomberg 2010 2011 2012
Conclusion Standard approach is a good theoretical start Practical adjustments t Risk premia instead of assets Methodology robust to estimation errors Tail-risk included in the picture Capacity constraints: tilt towards market portfolio Appendix
Risk-Parity and MVO 1 1 w S Volatilities; Correlation Matrix; S Sharpe Ratios MVO Portfolio weights w: MVO assuming all Sharpes are the same = Most Diversified Portfolio: w i w 1 1 N i N MVO assuming all Sharpes are the same and all correlations are 0 = Equal Volatility Portfolio: w I i 1 1 N N I w i N N i N I N Is a vector of ones Is the identity matrix Risk Parity weights satisfy the equation: Is the element-by- I N w w in i N element product Risk-parity equations are a product of the equations satisfied by the MD Portfolio with the equations satisfied by the EV Portfolio A particular combination between the historically-estimated correlation matrix and the identity one It penalizes more correlations that cause larger deviations from vol-weights From Risk-Parity to Risk Budgeting Generalize Risk Parity when Sharpe ratios are not the same: I w w S S I N Left side is Total Contributions to Portfolio Risk (TRC) 2 For an asset i we have: TRCi S i The risk budget of a position is proportional to the Sharpe ratio squared
Risk Premia & Alpha: Evolution Over Time Before bond & equity market indices After bond & equity market indices After other asset class indices After risk premia strategy indices All returns are Manager Alpha Manager Alpha Returns of market portfolio of bond&equity are risk premia Beta Manager Alpha Additional market risk premia Other Market Beta Beta Manager Alpha Alternative Risk Premia Other Market Beta Beta Risk Premia: A Taxonomy Merger-arbitrage in equities (deal-failure risk premium) Equities Commodities Rates Credit Currencies Volatility Market Carry Curve Value Momentum Liquidity Event X Currency carry (crash-risk premium in high yielding currencies) Term premium in global interest rate markets (duration risk premium) Roll congestion strategies in commodity markets (liquidity risk premium)
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