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© 2012 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.
Next GenerationFund of Funds Optimization
Tom Idzorek, CFAGlobal Chief Investment OfficerMarch 16, 2012
2 For Financial Professionals Only. Not For Public Distribution.
How does one implement an asset allocation?
Strategic Asset Allocation PolicyAsset Classes or Risk Factors
?
Fund Specific PortfolioMutual Funds, ETFs, Hedge Funds
3 For Financial Professionals Only. Not For Public Distribution.
Alpha-Tracking Error Optimization – Version 1.0
Strategic Asset Allocation PolicyAsset Classes or Risk Factors
?
Fund Specific PortfolioMutual Funds, ETFs, Hedge Funds
Alpha-Track ErrorOptimizer
4 For Financial Professionals Only. Not For Public Distribution.
Alpha-Tracking Error Optimization – Version 2.0
Strategic Asset Allocation PolicyAsset Classes or Risk Factors
?
Fund Specific PortfolioMutual Funds, ETFs, Hedge Funds
Alpha-Track ErrorOptimizer
Markowitz
2.0Fund of Funds Optimization
2.0
2.0
5 For Financial Professionals Only. Not For Public Distribution.
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 2.0
6 For Financial Professionals Only. Not For Public Distribution.
The Modern Investment Management ProcessSeparating Beta and Alpha
7 For Financial Professionals Only. Not For Public Distribution.
αΨ
αΨ
Capital Market Assumptions
AssetAllocation
ManagerResearch
PortfolioConstruction
Monitor
Step 1: Capital Market AssumptionsIdentify opportunity set of asset classesLong-term expected returnsStandard deviationsSkewnessKurtosis
Step 2: Strategic Asset AllocationMean-conditional value-at-risk optimizationLiability-relative optimizationMean-variance optimizationResamplingYield (Income) preference optimizationSensitivity analysis and stress testing
Step 3: Manager Research5 qualitative pillars – Parent, People,
Process, Performance, PriceQuantitative alpha – liquidity, momentumHoldings-based style analysisReturns-based style analysis
Step 4: Portfolio ConstructionAlpha-tracking error fund-of-funds optimizationActive risk budgetingCarve outs for non-marked to market
investmentsConsideration of non-normal return strategiesHigher moment optimization
Step 5: MonitorInternal portfolio reviewRebalancingDetailed performance attributionCustom benchmarkingAnnual review
The Modern Investment Management Process
8 For Financial Professionals Only. Not For Public Distribution.
Strategic Asset AllocationThe Beta Decision
9 For Financial Professionals Only. Not For Public Distribution.
Strategic Asset AllocationHistory of Asset Allocation
Harry MarkowitzNobel Prize Winner and“Father” of Modern Portfolio Theory
1952, 1959 1990 Nobel
10 For Financial Professionals Only. Not For Public Distribution.
Strategic Asset AllocationHistory of Asset Allocation
Bruno de Finetti1940
11 For Financial Professionals Only. Not For Public Distribution.
Mean-Variance Optimizer
Inputs
Expe
cted
Ret
urn
Mean-Variance Efficient Frontier
Individual Assets
Standard Deviation
Strategic Asset AllocationMean-Variance Optimization Review
► de Finetti [1940], Markowitz [1952, 1959]
► Capital Market Assumption
► Expected Returns
► Standard Deviations (Risks)
► Correlations
12 For Financial Professionals Only. Not For Public Distribution.
► 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
Step 2: Strategic Asset AllocationCriticism of Mean-Variance Optimization
13 For Financial Professionals Only. Not For Public Distribution.
Mean less 3σ≈ -15%
Mean minus 3σ should occur about once every 1000 observations
In this time period, 10 of the 995 observations exceed -15%
Returns
Histogram of S&P 500 Monthly Returns – January 1926 to November 2008
S&P 500 ReturnsLognormal Distribution Curve
Source: Paul D. Kaplan, “Déja Vu All Over Again,” in Morningstar Advisor Magazine, February/March 2009Performance 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.
The Flaw of the Bell Shaped CurveN
umbe
r of O
ccur
renc
es
14 For Financial Professionals Only. Not For Public Distribution.
A Better Definition of Risk in a Non-Normal WorldConditional Value-at-Risk (CVaR)
∞
CVaR identifies the probability weighted return of the entire tail
Worst 5th Percentile
95% of all returns are better5% of all returns are worse
15 For Financial Professionals Only. Not For Public Distribution.
Mean-CVaR Optimizer
Inputs
Expe
cted
Ret
urn
Mean-CVaR Efficient Frontier
Individual Assets
Conditional Value-at-Risk
Strategic Asset AllocationMean-Conditional Value-at-Risk Optimization
► Mean-conditional value-of-risk(improving on Markowitz [1952, 1959])
► Capital Market Assumption
► Expected Returns
► Standard Deviations (Risks)
► Correlations
► Skewness
► Kurtosis
16 For Financial Professionals Only. Not For Public Distribution.
0Expe
cted
Ret
urn
Strategic Asset AllocationSet Strategic Asset Allocation Policy
This is a graphical representation; plot points are not necessarily meaningful.
Risk
AggressiveRisk Range
10
90
ModerateRisk Range
60 40
ConservativeRisk Range
2080
% Stocks% Bonds
17 For Financial Professionals Only. Not For Public Distribution.
Portfolio ConstructionThe Alpha (or Product) Decision
Fund of Funds Optimization – Version 1.0
18 For Financial Professionals Only. Not For Public Distribution.
Portfolio ConstructionFund of Funds Optimization – Version 1.0
Strategic Asset Allocation PolicyAsset Classes or Risk Factors
?
Fund Specific PortfolioMutual Funds, ETFs, Hedge Funds
19 For Financial Professionals Only. Not For Public Distribution.
Portfolio ConstructionKey Philosophical Decision
vs.Warren BuffettJack Bogle
Passive Active
?
Fund Specific PortfolioMutual Funds, ETFs, Hedge Funds
20 For Financial Professionals Only. Not For Public Distribution.
Source: Morningstar
The Argument for PassiveA Losing Game in the Absence of Skill
% of Active Funds Outperforming Benchmark
Benchmark Returns (%) as of June 30, 2009
21 For Financial Professionals Only. Not For Public Distribution.
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, 2011. For informational purposes only. Past performance does not guarantee future results.
31.8%
36.1%
27.5% 10th Percentile: 19.7%90th Percentile: -7.8%
10th Percentile: 27.0%90th Percentile: -9.1%
10th Percentile: 18.6%90th Percentile: -13.2%
Difference in 5-Year Returns (between 10th Percentile and 90th Percentile Funds)
The Argument for ActiveAbility to Select Good Managers Matters
22 For Financial Professionals Only. Not For Public Distribution.
Separating Alpha from BetaReturns-Based Style Analysis
Journal of Portfolio Management, Winter 1992
23 For Financial Professionals Only. Not For Public Distribution.
× Betas - Style analysis attempts to ‘attribute’ manager returns to the return of passive indexes (i.e. beta exposures that are available for ‘free’)
Cash
European Bonds
Non-European Bonds
Global High Yield
Germany
European Stocks ex Germany
World Stocks ex. Europe
Emerging Markets
Global Real Estate
Fund XBeta Factors
Fund Returns Come From Betas Plus an AlphaReturns-Based Style Analysis
24 For Financial Professionals Only. Not For Public Distribution.
× Alphas – After adjusting for the “beta” exposures (i.e. a fund specific custom composite benchmark), did the manager add value?
Fund Returns Come From Betas Plus an AlphaReturns-Based Style Analysis
Cash
European Bonds
Non-European Bonds
Global High Yield
Germany
European Stocks
World Stocks ex. Europe
Emerging Markets
Global Real Estate
Alpha
.5%
Analysis determines variability of alpha, a.k.a fund specific risk
Beta Factors Fund X
25 For Financial Professionals Only. Not For Public Distribution.
Manager ResearchConverting Academic Research into Practice
From academic research… …to real world solutions
The Liquidity Style of Mutual Funds
Working Paper
Thomas M. Idzorek, CFAGlobal Chief Investment Officer
James Xiong, Ph.D., CFASenior Research Consultant
Roger Ibbotson, Ph.D.Chairman – Zebra Capital Management
Current Version: October 2010
Investment Management
Combining Liquidity and Momentum to Pick Top-Performing Mutual Funds
Working Paper
Thomas M. Idzorek, CFAGlobal Chief Investment Officer
James Xiong, Ph.D., CFASenior Research Consultant
Roger Ibbotson, Ph.D.Chairman – Zebra Capital Management
Current Version: October 2010
Investment Management
Estimating Credit Risk and Illiquidity Risk in Guaranteed Investment Products
Working Paper
James Xiong, Ph.D., CFASenior Research Consultant
Thomas M. Idzorek, CFAGlobal Chief Investment Officer
Current Version: October 2010
Investment Management
26 For Financial Professionals Only. Not For Public Distribution.
Manager Research – Forecasting AlphaDownside Risk Premiums for U.S. Equity Funds (01-1980 to 07-2011)
Quintile-1 2 3 4 Quintile-5 Q1-Q5Excess-CVaR 6.97% 6.71% 6.24% 5.64% 4.30% 2.67%alpha t-stat 1.23 2.55 1.24 -0.77 -3.24 2.63
Coskewness 6.72% 6.29% 6.01% 5.97% 4.87% 1.85%alpha t-stat 1.65 0.50 -0.87 -0.47 -2.07 1.99
Cokurtosis 6.51% 6.15% 6.43% 5.85% 4.91% 1.59%alpha t-stat 1.79 0.77 1.18 -1.53 -2.64 2.35
Downside-β 6.22% 6.07% 6.17% 5.95% 5.42% 0.80%alpha t-stat 0.64 0.95 1.16 -0.42 -1.87 1.40
27 For Financial Professionals Only. Not For Public Distribution.
Manager Research – Forecasting AlphaDownside Risk Premiums for Non-U.S. Equity Funds (01-1980 to 07-2011)
Quintile-1 2 3 4 Quintile-5 Q1-Q5Excess-CVaR 6.33% 6.44% 5.98% 4.93% 3.80% 2.53%alpha t-stat 0.14 1.41 1.09 -0.74 -1.65 1.12
Coskewness 6.20% 6.27% 5.43% 4.94% 4.66% 1.54%alpha t-stat 0.80 1.43 -0.19 -1.24 -1.34 1.34
Cokurtosis 5.69% 6.03% 6.18% 5.73% 3.90% 1.79%alpha t-stat 0.15 0.71 1.12 0.03 -1.43 0.98
Downside-β 4.49% 6.24% 6.10% 5.20% 5.41% -0.92%alpha t-stat -1.34 1.45 1.03 -0.52 -0.52 -0.67
28 For Financial Professionals Only. Not For Public Distribution.
Manager Research – Forecasting AlphaTail Risk Premium (1980.1-2011.7)
Fund Categories
1 Low Excess-CVaR
2 3 4 5 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%
29 For Financial Professionals Only. Not For Public Distribution.
Portfolio ConstructionFund of Funds Optimization – Version 1.0
30 For Financial Professionals Only. Not For Public Distribution.
Portfolio ConstructionFund of Funds Optimization – Version 1.0
Strategic Asset Allocation PolicyAsset Classes or Risk Factors
?
Fund Specific PortfolioMutual Funds, ETFs, Hedge Funds
Alpha-Track ErrorOptimizer
31 For Financial Professionals Only. Not For Public Distribution.
0Expe
cted
Ret
urn
Strategic Asset AllocationSet Strategic Asset Allocation Policy
This is a graphical representation; plot points are not necessarily meaningful.
Risk
AggressiveRisk Range
10
90
ModerateRisk Range
60 40
ConservativeRisk Range
2080
% Stocks% Bonds
Emerging Markets
Non-US Developed
US BondsTIPS
Cash
Private Equity
Commodities
US Small Cap
US Large Cap
Liability(Short TIPS-like characteristics)
32 For Financial Professionals Only. Not For Public Distribution.
0Expe
cted
Ret
urn
Risk
This is a graphical representation; plot points are not necessarily meaningful.
Alp
ha
Tracking Error
Portfolio ConstructionFund of Funds Optimization – Version 1.0
33 For Financial Professionals Only. Not For Public Distribution.
0Expe
cted
Ret
urn
Risk
This is a graphical representation; plot points are not necessarily meaningful.
Alp
ha
Tracking Error
Portfolio ConstructionFund of Funds Optimization – Version 1.0
Combinations of asset classes
Combinations of funds
34 For Financial Professionals Only. Not For Public Distribution.
0Expe
cted
Ret
urn
Risk
This is a graphical representation; plot points are not necessarily meaningful.
Alp
ha
Tracking Error
Portfolio ConstructionFund of Funds Optimization – Version 1.0 Better funds
lead to better implementation frontiers
35 For Financial Professionals Only. Not For Public Distribution.
0Expe
cted
Ret
urn
Portfolio ConstructionAn Alpha-Tracking Error Optimization occurs for Each Strategic Asset Allocation
This is a graphical representation; plot points are not necessarily meaningful.
Risk
% Stocks% Bonds
36 For Financial Professionals Only. Not For Public Distribution.
Version 1.0 Inputs
►Asset Class Expected Total Returns
►Asset Class Correlations
►Asset Class Standard Deviations
► ----
► Asset Class Correlations
► Asset Class Standard Deviations
► Manager Expected Alphas
► Standard Deviation of Alphas
► Correlations of Alphas
► Manager Asset Class Exposures
Mean-Variance Optimization Fund of Funds Optimization
37 For Financial Professionals Only. Not For Public Distribution.
Portfolio ConstructionFund of Funds Optimization – Version 1.0
Alpha Return Asset Class Misfit Risk
Manager Specific Risk
Aversion to Misfit Risk
Aversion to Manager
Specific Risk
Alpha – Penalty for Tracking Error
38 For Financial Professionals Only. Not For Public Distribution.
Portfolio Alpha( )
mTmP αh=α
=mh Manager Holdings or Weights (M x 1 column vector)
=mα Manager Alphas (M x 1 column vector)
Pα
Portfolio ConstructionPortfolio Alpha
39 For Financial Professionals Only. Not For Public Distribution.
Tracking Error ( )
( ) ( ) mmTm
Tb
Tmk
TTb
TmP hVhhXhVhXh +−−=Ψ
=mh Manager Holdings (m x 1 column vector)
=X Manager Asset Class / Style Exposures (m x k matrix, where k is the number of asset classes and m is the number of managers)
=bh Benchmark Holdings (k x 1 column vector)
=kV Asset Class Covariance Matrix (k x k matrix)
=mV Manager Specific Risk Covariance Matrix (k x k matrix)
Manager Specific Risk
Asset Allocation Misfit RiskΨ
Portfolio ConstructionTracking Error
40 For Financial Professionals Only. Not For Public Distribution.
Portfolio ConstructionThe Alpha (or Product) Decision
Fund of Funds Optimization – Version 2.0
41 For Financial Professionals Only. Not For Public Distribution.
-2.0
-1.5
-1.0
-0.5
0.0
0.5
0 4 8 12
Kurtosis
Skew
ness
Global High Yield
Non-U.S Bonds.
U.S. REITsU.S. TIPS
Non-U.S. REITs
Small Value
Cash
Non-U.S. Dev
Emerging Equities
Commodity
Large Value
U.S. BondsSmall Growth
Large Growth
Strategic Asset AllocationNon-Normal Asset Class Returns – Skewness and Kurtosis (1990.2 – 2010.5)
Source: “The Impact of Skewness and Fat Tails On the Asset Allocation Decision” by James Xiong and Thomas Idzorek (2011).
42 For Financial Professionals Only. Not For Public Distribution.
Portfolio ConstructionFund Returns can Depart Significantly from the Normal Distribution
Mutual Funds
Hedge Funds
Skewness (5th) -1.9 -2.0Kurtosis (5th) 9.6 15.7CVaR (5th) - Monthly -17.9 -21.6
Worst 5th Percentile Fund
43 For Financial Professionals Only. Not For Public Distribution.
Portfolio ConstructionFund Returns can Depart Significantly from the Normal Distribution
Mutual Funds
Hedge Funds
Skewness (1st) -2.2 -3.6Kurtosis (1st) 17.0 31.5CVaR (1st) - Monthly -23.0 -32.0
Worst 1st Percentile Fund
44 For Financial Professionals Only. Not For Public Distribution.
Portfolio ConstructionConverting Academic Research into Practice
From academic research… …to real world solutions
The Tail Risk Premiumand Portfolio Construction
Working Paper
James Xiong, Ph.D., CFASenior Research Consultant
Thomas M. Idzorek, CFAGlobal Chief Investment Officer
Current Version: Not Released
Investment Management
*
* Not authored by a Morningstar Investment Management author.
Fund of Funds Optimizationin a Non-Normal World
Working Paper
Thomas M. Idzorek, CFAGlobal Chief Investment Officer
James Xiong, Ph.D., CFASenior Research Consultant
Current Version: Not Released
Investment Management
45 For Financial Professionals Only. Not For Public Distribution.
Portfolio ConstructionFund of Funds Optimization – Version 2.0
Strategic Asset Allocation PolicyAsset Classes or Risk Factors
?
Fund Specific PortfolioMutual Funds, ETFs, Hedge Funds
Alpha-Track ErrorOptimizer
Markowitz
2.0Fund of Funds Optimization
2.0
2.0
46 For Financial Professionals Only. Not For Public Distribution.
Fund of Funds Optimization
Version 2.0 Inputs
►Asset Class Expected Total Returns►Asset Class Correlations►Asset Class Standard Deviations►Asset Class Skewness►Asset Class Kurtosis
►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
Mean-CVaR Optimization
47 For Financial Professionals Only. Not For Public Distribution.
Portfolio ConstructionFund of Funds Optimization – Version 2.0
Total Portfolio Return(Benchmark Return + Active Beta Return + Manager Alpha Return)
Penalty for CVaR Penalty for Misfit Risk
M
48 For Financial Professionals Only. Not For Public Distribution.
Portfolio ConstructionFund 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
M
49 For Financial Professionals Only. Not For Public Distribution.
Portfolio ConstructionFund of Funds Optimization ComparisonOut of Sample Test: 1997 – 2011
400 Equity Funds
Each Month: Rank Funds by Standard
Deviation
Create 25 Opportunity Sets
Each with 16 Funds
Fund of Funds Optimizer – Version 1.0
Fund of Funds Optimizer – Version 2.0
2.0
50 For Financial Professionals Only. Not For Public Distribution.
Portfolio ConstructionFund of Funds Optimization ComparisonOut of Sample Test: 1997 – 2011
0%
4%
8%
12%
16%
10% 14% 18% 22% 26%Standard Deviation
Retu
rn
30%
Version 2
Version 1
Equal Weights
51 For Financial Professionals Only. Not For Public Distribution.
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 2.0
Portfolio ConstructionFund of Funds Optimization Comparison
2.0
53 For Financial Professionals Only. Not For Public Distribution.
Downside-β
► The Regular β is defined as β = cov(ri, rm) / var(rm)
► The downside-β is introduced by Bawa and Lindenberg (1977) as
► β- = cov(ri, rm|rm < 0) / var(rm|rm < 0)► The relative downside-β is introduced by Ang, Chen and Xing (2005) as β- - β
54 For Financial Professionals Only. Not For Public Distribution.
Coskewness
► The coskewness is calculated as (Harvey and Siddique, 2000):
► Coskewness ~ cov(ri, rm2)
)(
)(
,][][
][
,,,
,,,
2,
2,
2,,
tMtMtm
fttMifttiti
tMti
tMti
ravgr
rrrr
EE
ECoskewness
−=
−−−=
=
ε
βε
εε
εε
55 For Financial Professionals Only. Not For Public Distribution.
Cokurtosis
► The cokurtosis is calculated as
► Cokurtosis ~ cov(ri, rm3)
)(
)(
,][][
][
,,,
,,,
3,
2,
3,,
tMtMtm
fttMifttiti
tMti
tMti
ravgr
rrrr
EE
ECokurtosis
−=
−−−=
=
ε
βε
εε
εε