Next Generation Fund of Funds Optimization

Transcription

1 Next Generation Fund of Funds Optimization Tom Idzorek, CFA Global Chief Investment Officer March 16, Morningstar Associates, LLC. All rights reserved. Morningstar Associates is a registered investment advisor and wholly owned subsidiary of Morningstar, Inc. The Morningstar name and logo are registered marks of Morningstar, Inc. This presentation includes proprietary material of Morningstar Associates. Reproduction, transcription or other use, by any means, in whole or in part, without the prior written consent of Morningstar Associates is prohibited. For Financial Professionals Only. Not For Public Distribution.

2 How does one implement an asset allocation? Strategic Asset Allocation Policy Asset Classes or Risk Factors Fund Specific Portfolio Mutual Funds, ETFs, Hedge Funds? 2 For Financial Professionals Only. Not For Public Distribution.

3 Alpha-Tracking Error Optimization Version 1.0 Strategic Asset Allocation Policy Asset Classes or Risk Factors Alpha-Track Error Optimizer Fund Specific Portfolio Mutual Funds, ETFs, Hedge Funds? 3 For Financial Professionals Only. Not For Public Distribution.

4 Alpha-Tracking Error Optimization Version 2.0 Strategic Asset Allocation Policy Asset Classes or Risk Factors Alpha-Track Error Optimizer Fund Specific Portfolio Mutual Funds, ETFs, Hedge Funds 2.0? Markowitz 2.0 Fund of Funds Optimization For Financial Professionals Only. Not For Public Distribution.

5 Agenda The Modern Investment Management Process Strategic Asset Allocation The Beta Decision Portfolio Construction The Alpha (Product) Decision Fund of Funds Optimization Version 1.0 Fund of Funds Optimization Version For Financial Professionals Only. Not For Public Distribution.

6 The Modern Investment Management Process Separating Beta and Alpha 6 For Financial Professionals Only. Not For Public Distribution.

7 The Modern Investment Management Process Monitor Portfolio Construction α Ψ Capital Market Assumptions Manager Research Asset Allocation Step 1: Capital Market Assumptions Identify opportunity set of asset classes Long-term expected returns Standard deviations Skewness Kurtosis Step 2: Strategic Asset Allocation Mean-conditional value-at-risk optimization Liability-relative optimization Mean-variance optimization Resampling Yield (Income) preference optimization Sensitivity analysis and stress testing Step 3: Manager Research 5 qualitative pillars Parent, People, Process, Performance, Price Quantitative alpha liquidity, momentum Holdings-based style analysis Returns-based style analysis Step 4: Portfolio Construction Alpha-tracking error fund-of-funds optimization Active risk budgeting Carve outs for non-marked to market investments Consideration of non-normal return strategies Higher moment optimization Step 5: Monitor Internal portfolio review Rebalancing Detailed performance attribution Custom benchmarking Annual review 7 For Financial Professionals Only. Not For Public Distribution.

8 Strategic Asset Allocation The Beta Decision 8 For Financial Professionals Only. Not For Public Distribution.

9 Strategic Asset Allocation History of Asset Allocation 1952, 1959 Harry Markowitz Nobel Prize Winner and 1990 Nobel Father of Modern Portfolio Theory 9 For Financial Professionals Only. Not For Public Distribution.

10 Strategic Asset Allocation History of Asset Allocation 1940 Bruno de Finetti 10 For Financial Professionals Only. Not For Public Distribution.

11 Strategic Asset Allocation Mean-Variance Optimization Review Inputs Mean-Variance Optimizer de Finetti [1940], Markowitz [1952, 1959] Capital Market Assumption Expected Returns Standard Deviations (Risks) Correlations Mean-Variance Efficient Frontier Expected Return Individual Assets Standard Deviation 11 For Financial Professionals Only. Not For Public Distribution.

12 Step 2: Strategic Asset Allocation Criticism of Mean-Variance Optimization Single-period framework in multi-period world Non-diversified asset allocations Resampling Black-Litterman Model Ignores liability Liability-Relative Optimization (Surplus Optimization) Only uses first two moments (means and standard deviations) of return dist. Higher Moment Optimization 12 For Financial Professionals Only. Not For Public Distribution.

13 The Flaw of the Bell Shaped Curve Histogram of S&P 500 Monthly Returns January 1926 to November 2008 Number of Occurrences Mean minus 3σ should occur about once every 1000 observations In this time period, 10 of the 995 observations exceed -15% Lognormal Distribution Curve S&P 500 Returns Mean less 3σ -15% Returns Source: Paul D. Kaplan, Déja Vu All Over Again, in Morningstar Advisor Magazine, February/March 2009 Performance data shown represents past performance. Past performance is not indicative and not a guarantee of future results. Indices shown are unmanaged and not available for direct investment. Performance data does not factor in transaction costs or taxes. 13 For Financial Professionals Only. Not For Public Distribution.

14 A Better Definition of Risk in a Non-Normal World Conditional Value-at-Risk (CVaR) CVaR identifies the probability weighted return of the entire tail Worst 5 th Percentile 95% of all returns are better 5% of all returns are worse 14 For Financial Professionals Only. Not For Public Distribution.

15 Strategic Asset Allocation Mean-Conditional Value-at-Risk Optimization Inputs Mean-conditional value-of-risk (improving on Markowitz [1952, 1959]) Expected Return Mean-CVaR Optimizer Mean-CVaR Efficient Frontier Individual Assets Capital Market Assumption Expected Returns Standard Deviations (Risks) Correlations Skewness Kurtosis Conditional Value-at-Risk 15 For Financial Professionals Only. Not For Public Distribution.

16 Strategic Asset Allocation Set Strategic Asset Allocation Policy Expected Return Conservative Risk Range Moderate Risk Range Risk Aggressive Risk Range % Stocks % Bonds This is a graphical representation; plot points are not necessarily meaningful. 16 For Financial Professionals Only. Not For Public Distribution.

17 Portfolio Construction The Alpha (or Product) Decision Fund of Funds Optimization Version For Financial Professionals Only. Not For Public Distribution.

18 Portfolio Construction Fund of Funds Optimization Version 1.0 Strategic Asset Allocation Policy Asset Classes or Risk Factors Fund Specific Portfolio Mutual Funds, ETFs, Hedge Funds? 18 For Financial Professionals Only. Not For Public Distribution.

19 Portfolio Construction Key Philosophical Decision Passive Fund Specific Portfolio Mutual Funds, ETFs, Hedge Funds? Active Jack Bogle vs. Warren Buffett 19 For Financial Professionals Only. Not For Public Distribution.

20 The Argument for Passive A Losing Game in the Absence of Skill % of Active Funds Outperforming Benchmark Benchmark Returns (%) as of June 30, 2009 Source: Morningstar 20 For Financial Professionals Only. Not For Public Distribution.

21 The Argument for Active Ability to Select Good Managers Matters Difference in 5-Year Returns (between 10 th Percentile and 90 th Percentile Funds) 27.5% 10 th Percentile: 19.7% 90 th Percentile: -7.8% 10th Percentile: 18.6% 90th Percentile: -13.2% 31.8% 36.1% 10 th Percentile: 27.0% 90 th Percentile: -9.1% Source: Morningstar Direct. Data represents the difference between five-year cumulative returns of the 10th percentile and 90th percentile funds in each Morningstar, Inc. mutual fund category as of December 31, For informational purposes only. Past performance does not guarantee future results. 21 For Financial Professionals Only. Not For Public Distribution.

22 Separating Alpha from Beta Returns-Based Style Analysis Journal of Portfolio Management, Winter For Financial Professionals Only. Not For Public Distribution.

23 Fund Returns Come From Betas Plus an Alpha Returns-Based Style Analysis Betas - Style analysis attempts to attribute manager returns to the return of passive indexes (i.e. beta exposures that are available for free ) Beta Factors Cash European Bonds Non-European Bonds Global High Yield Germany European Stocks ex Germany World Stocks ex. Europe Emerging Markets Global Real Estate Fund X 23 For Financial Professionals Only. Not For Public Distribution.

24 Fund Returns Come From Betas Plus an Alpha Returns-Based Style Analysis Alphas After adjusting for the beta exposures (i.e. a fund specific custom composite benchmark), did the manager add value? Beta Factors Cash European Bonds Non-European Bonds Global High Yield Germany European Stocks World Stocks ex. Europe Emerging Markets Global Real Estate Fund X Alpha.5% Analysis determines variability of alpha, a.k.a fund specific risk 24 For Financial Professionals Only. Not For Public Distribution.

25 Manager Research Converting Academic Research into Practice From academic research to real world solutions Estimating Credit Risk and Illiquidity Risk in Guaranteed Investment Products The Liquidity Style of Mutual Funds Combining Liquidity and Momentum to Pick Top-Performing Mutual Funds Working Paper Working Paper Working Paper James Xiong, Ph.D., CFA Senior Research Consultant Thomas M. Idzorek, CFA Global Chief Investment Officer Current Version: October 2010 Thomas M. Idzorek, CFA Global Chief Investment Officer James Xiong, Ph.D., CFA Senior Research Consultant Roger Ibbotson, Ph.D. Chairman Zebra Capital Management Current Version: October 2010 Thomas M. Idzorek, CFA Global Chief Investment Officer James Xiong, Ph.D., CFA Senior Research Consultant Roger Ibbotson, Ph.D. Chairman Zebra Capital Management Current Version: October 2010 Investment Management Investment Management Investment Management 25 For Financial Professionals Only. Not For Public Distribution.

26 Manager Research Forecasting Alpha Downside Risk Premiums for U.S. Equity Funds ( to ) Quintile Quintile-5 Q1-Q5 Excess-CVaR 6.97% 6.71% 6.24% 5.64% 4.30% 2.67% alpha t-stat Coskewness 6.72% 6.29% 6.01% 5.97% 4.87% 1.85% alpha t-stat Cokurtosis 6.51% 6.15% 6.43% 5.85% 4.91% 1.59% alpha t-stat Downside-β 6.22% 6.07% 6.17% 5.95% 5.42% 0.80% alpha t-stat For Financial Professionals Only. Not For Public Distribution.

27 Manager Research Forecasting Alpha Downside Risk Premiums for Non-U.S. Equity Funds ( to ) Quintile Quintile-5 Q1-Q5 Excess-CVaR 6.33% 6.44% 5.98% 4.93% 3.80% 2.53% alpha t-stat Coskewness 6.20% 6.27% 5.43% 4.94% 4.66% 1.54% alpha t-stat Cokurtosis 5.69% 6.03% 6.18% 5.73% 3.90% 1.79% alpha t-stat Downside-β 4.49% 6.24% 6.10% 5.20% 5.41% -0.92% alpha t-stat For Financial Professionals Only. Not For Public Distribution.

28 Manager Research Forecasting Alpha Tail Risk Premium ( ) Fund Categories 1 Low Excess- CVaR High Excess- CVaR Q1 - Q5 All US Equity 6.97% 6.71% 6.24% 5.64% 4.30% 2.67% Large 6.13% 5.73% 5.77% 5.26% 4.43% 1.70% Medium 6.77% 7.49% 7.52% 6.93% 4.95% 1.82% Small 6.84% 7.33% 7.11% 5.79% 4.08% 2.76% Blend 6.59% 6.39% 6.00% 5.55% 4.29% 2.30% Growth 6.57% 6.81% 6.61% 6.06% 5.69% 0.87% Value 6.93% 6.27% 5.42% 5.36% 4.23% 2.70% Non-US Equity 6.33% 6.44% 5.98% 4.93% 3.80% 2.53% Bonds 2.90% 2.62% 2.68% 2.59% 2.82% 0.08% 28 For Financial Professionals Only. Not For Public Distribution.

29 Portfolio Construction Fund of Funds Optimization Version For Financial Professionals Only. Not For Public Distribution.

30 Portfolio Construction Fund of Funds Optimization Version 1.0 Strategic Asset Allocation Policy Asset Classes or Risk Factors Alpha-Track Error Optimizer Fund Specific Portfolio Mutual Funds, ETFs, Hedge Funds? 30 For Financial Professionals Only. Not For Public Distribution.

31 Strategic Asset Allocation Set Strategic Asset Allocation Policy Expected Return 0 Cash Conservative TIPS Risk Range Moderate Risk Range US Bonds Risk 10 Private Equity Emerging Markets 90 US Small Cap Aggressive Non-US Developed US Large Cap Risk Range Commodities % Stocks % Bonds Liability (Short TIPS-like characteristics) This is a graphical representation; plot points are not necessarily meaningful. 31 For Financial Professionals Only. Not For Public Distribution.

32 Portfolio Construction Fund of Funds Optimization Version 1.0 Expected Return Alpha 0 Tracking Error Risk This is a graphical representation; plot points are not necessarily meaningful. 32 For Financial Professionals Only. Not For Public Distribution.

33 Portfolio Construction Fund of Funds Optimization Version 1.0 Combinations of funds Expected Return Alpha 0 Tracking Error Risk Combinations of asset classes This is a graphical representation; plot points are not necessarily meaningful. 33 For Financial Professionals Only. Not For Public Distribution.

34 Portfolio Construction Fund of Funds Optimization Version 1.0 Alpha Better funds lead to better implementation frontiers Expected Return 0 Tracking Error Risk This is a graphical representation; plot points are not necessarily meaningful. 34 For Financial Professionals Only. Not For Public Distribution.

35 Portfolio Construction An Alpha-Tracking Error Optimization occurs for Each Strategic Asset Allocation Expected Return 0 Risk % Stocks % Bonds This is a graphical representation; plot points are not necessarily meaningful. 35 For Financial Professionals Only. Not For Public Distribution.

36 Version 1.0 Inputs Mean-Variance Optimization Asset Class Expected Total Returns Asset Class Correlations Asset Class Standard Deviations Fund of Funds Optimization ---- Asset Class Correlations Asset Class Standard Deviations Manager Expected Alphas Standard Deviation of Alphas Correlations of Alphas Manager Asset Class Exposures 36 For Financial Professionals Only. Not For Public Distribution.

37 Portfolio Construction Fund of Funds Optimization Version 1.0 Alpha Return Asset Class Misfit Risk Manager Specific Risk Aversion to Misfit Risk Alpha Penalty for Tracking Error Aversion to Manager Specific Risk 37 For Financial Professionals Only. Not For Public Distribution.

38 Portfolio Construction Portfolio Alpha α P Portfolio Alpha( ) α P = h T m α m hm α m = = Manager Holdings or Weights (M x 1 column vector) Manager Alphas (M x 1 column vector) 38 For Financial Professionals Only. Not For Public Distribution.

39 Portfolio Construction Tracking Error Tracking Error ( ) Ψ P Ψ = Asset Allocation Misfit Risk ( T T ) T ( T T ) T h mx hb Vk hmx hb + hmvmh m hm = Manager Holdings (m x 1 column vector) Manager Specific Risk X hb = = Manager Asset Class / Style Exposures (m x k matrix, where k is the number of asset classes and m is the number of managers) Benchmark Holdings (k x 1 column vector) Vk Vm = = Asset Class Covariance Matrix (k x k matrix) Manager Specific Risk Covariance Matrix (k x k matrix) 39 For Financial Professionals Only. Not For Public Distribution.

40 Portfolio Construction The Alpha (or Product) Decision Fund of Funds Optimization Version For Financial Professionals Only. Not For Public Distribution.

41 Strategic Asset Allocation Non-Normal Asset Class Returns Skewness and Kurtosis ( ) 0.5 Skewness Non-U.S Bonds. Non-U.S. REITs Cash U.S. Bonds Small Growth Non-U.S. Dev Commodity Large Growth Emerging Equities Large Value U.S. TIPS Small Value U.S. REITs -1.5 Global High Yield Kurtosis Source: The Impact of Skewness and Fat Tails On the Asset Allocation Decision by James Xiong and Thomas Idzorek (2011). 41 For Financial Professionals Only. Not For Public Distribution.

42 Portfolio Construction Fund Returns can Depart Significantly from the Normal Distribution Worst 5 th Percentile Fund Mutual Funds Hedge Funds Skewness (5th) Kurtosis (5th) CVaR (5th) - Monthly For Financial Professionals Only. Not For Public Distribution.

43 Portfolio Construction Fund Returns can Depart Significantly from the Normal Distribution Worst 1 st Percentile Fund Mutual Funds Hedge Funds Skewness (1st) Kurtosis (1st) CVaR (1st) - Monthly For Financial Professionals Only. Not For Public Distribution.

44 Portfolio Construction Converting Academic Research into Practice From academic research * The Tail Risk Premium and Portfolio Construction to real world solutions Fund of Funds Optimization in a Non-Normal World Working Paper Working Paper James Xiong, Ph.D., CFA Senior Research Consultant Thomas M. Idzorek, CFA Global Chief Investment Officer Thomas M. Idzorek, CFA Global Chief Investment Officer James Xiong, Ph.D., CFA Senior Research Consultant Current Version: Not Released Current Version: Not Released Investment Management Investment Management * Not authored by a Morningstar Investment Management author. 44 For Financial Professionals Only. Not For Public Distribution.

45 Portfolio Construction Fund of Funds Optimization Version 2.0 Strategic Asset Allocation Policy Asset Classes or Risk Factors Alpha-Track Error Optimizer Fund Specific Portfolio Mutual Funds, ETFs, Hedge Funds 2.0? Markowitz 2.0 Fund of Funds Optimization For Financial Professionals Only. Not For Public Distribution.

46 Version 2.0 Inputs Mean-CVaR Optimization Asset Class Expected Total Returns Asset Class Correlations Asset Class Standard Deviations Asset Class Skewness Asset Class Kurtosis Fund of Funds Optimization Asset Class Returns Asset Class Correlations Asset Class Standard Deviations Manager Expected Alphas Standard Deviation of Alphas Correlations of Alphas Manager Asset Class Exposures Manager Expected Total Returns Manager Standard Deviations Manager Skewness Manager Kurtosis 46 For Financial Professionals Only. Not For Public Distribution.

47 M Portfolio Construction Fund of Funds Optimization Version 2.0 Total Portfolio Return (Benchmark Return + Active Beta Return + Manager Alpha Return) Penalty for CVaR Penalty for Misfit Risk 47 For Financial Professionals Only. Not For Public Distribution.

48 M Portfolio Construction Fund of Funds Optimization Version 2.0 Total Portfolio Return (Benchmark Return + Active Beta Return + Manager Alpha Return) Penalty for CVaR Subject to: Asset Class Constraints or Asset Class Misfit Risk 48 For Financial Professionals Only. Not For Public Distribution.

49 Portfolio Construction Fund of Funds Optimization Comparison Out of Sample Test: Fund of Funds Optimizer Version Equity Funds Each Month: Rank Funds by Standard Deviation Create 25 Opportunity Sets Each with 16 Funds Fund of Funds Optimizer Version For Financial Professionals Only. Not For Public Distribution.

50 Portfolio Construction Fund of Funds Optimization Comparison Out of Sample Test: Return 16% 12% 8% Version 2 Version 1 Equal Weights 4% 0% 10% 14% 18% 22% 26% Standard Deviation 30% 50 For Financial Professionals Only. Not For Public Distribution.

51 Portfolio Construction Fund of Funds Optimization Comparison The last 12 years: Version 1.0 Two Moments Not well suited for alternatives The Near Future: Version 2.0 Four Moments Well suited for alternatives Fund of Funds Optimizer Version 1.0 Fund of Funds Optimizer Version For Financial Professionals Only. Not For Public Distribution.

52 52 For Financial Professionals Only. Not For Public Distribution.

53 Downside-β The Regular β is defined as β = cov(r i, r m ) / var(r m ) The downside-β is introduced by Bawa and Lindenberg (1977) as β - = cov(r i, r m r m < 0) / var(r m r m < 0) The relative downside-β is introduced by Ang, Chen and Xing (2005) as β - - β 53 For Financial Professionals Only. Not For Public Distribution.

54 54 For Financial Professionals Only. Not For Public Distribution. Coskewness The coskewness is calculated as (Harvey and Siddique, 2000): Coskewness ~ cov(r i, r m2 ) ) ( ) (, ] [ ] [ ] [,,,,,, 2, 2, 2,, t M t M t m ft t M i ft t i t i t M t i t M t i r avg r r r r r E E E Coskewness = = = ε β ε ε ε ε ε

55 55 For Financial Professionals Only. Not For Public Distribution. Cokurtosis The cokurtosis is calculated as Cokurtosis ~ cov(r i, r m3 ) ) ( ) (, ] [ ] [ ] [,,,,,, 3, 2, 3,, t M t M t m ft t M i ft t i t i t M t i t M t i r avg r r r r r E E E Cokurtosis = = = ε β ε ε ε ε ε

56 Tail Risk - Excess-CVaR The Conditional Value-at-risk (CVaR) for a normal distribution is μ *Þ Excess-CVaR is defined as: CVaR - (μ *Þ) (Xiong and Idzorek, 2012) 56 For Financial Professionals Only. Not For Public Distribution.