Next Generation Fund of Funds Optimization - …corporate.morningstar.com/euconf/presentations/mic-2012/Thomas... · Fund of Funds Optimization – Version 1.0 ... Step 5: Monitor

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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

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Fund Specific PortfolioMutual Funds, ETFs, Hedge Funds


Alpha-Tracking Error Optimization – Version 1.0


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Alpha-Track ErrorOptimizer


Alpha-Tracking Error Optimization – Version 2.0


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Markowitz

2.0Fund of Funds Optimization

2.0

2.0


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


The Modern Investment Management ProcessSeparating Beta and Alpha


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


Strategic Asset AllocationThe Beta Decision


Strategic Asset AllocationHistory of Asset Allocation

Harry MarkowitzNobel Prize Winner and“Father” of Modern Portfolio Theory

1952, 1959 1990 Nobel


Strategic Asset AllocationHistory of Asset Allocation

Bruno de Finetti1940


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


► 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


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


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


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


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


Portfolio ConstructionThe Alpha (or Product) Decision

Fund of Funds Optimization – Version 1.0


Portfolio ConstructionFund of Funds Optimization – Version 1.0


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Portfolio ConstructionKey Philosophical Decision

vs.Warren BuffettJack Bogle

Passive Active

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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


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


Separating Alpha from BetaReturns-Based Style Analysis

Journal of Portfolio Management, Winter 1992


× 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


× 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


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



Roger Ibbotson, Ph.D.Chairman – Zebra Capital Management



Estimating Credit Risk and Illiquidity Risk in Guaranteed Investment Products

Working Paper






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


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


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%






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0Expe

cted

Ret

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Strategic Asset AllocationSet Strategic Asset Allocation Policy


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)


0Expe

cted

Ret

urn

Risk


Alp

ha

Tracking Error



0Expe

cted

Ret

urn

Risk


Alp

ha

Tracking Error


Combinations of asset classes

Combinations of funds


0Expe

cted

Ret

urn

Risk


Alp

ha

Tracking Error

Portfolio ConstructionFund of Funds Optimization – Version 1.0 Better funds

lead to better implementation frontiers


0Expe

cted

Ret

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Portfolio ConstructionAn Alpha-Tracking Error Optimization occurs for Each Strategic Asset Allocation


Risk

% Stocks% Bonds


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



Alpha Return Asset Class Misfit Risk

Manager Specific Risk

Aversion to Misfit Risk

Aversion to Manager

Specific Risk

Alpha – Penalty for Tracking Error


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


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


Portfolio ConstructionThe Alpha (or Product) Decision

Fund of Funds Optimization – Version 2.0


-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).


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


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


Portfolio ConstructionConverting Academic Research into Practice

From academic research… …to real world solutions

The Tail Risk Premiumand Portfolio Construction

Working Paper



Current Version: Not Released


*

* Not authored by a Morningstar Investment Management author.

Fund of Funds Optimizationin a Non-Normal World

Working Paper



Current Version: Not Released





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Markowitz

2.0Fund of Funds Optimization

2.0

2.0


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



Total Portfolio Return(Benchmark Return + Active Beta Return + Manager Alpha Return)

Penalty for CVaR Penalty for Misfit Risk

M



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


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


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


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



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


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


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


Tail Risk - Excess-CVaR

► The Conditional Value-at-risk (CVaR) for a normal distribution is μ - 2.06*Þ

► Excess-CVaR is defined as: CVaR - (μ - 2.06*Þ) (Xiong and Idzorek, 2012)

Documents

Next Generation Fund of Funds Optimization - …corporate.morningstar.com/euconf/presentations/mic-2012/Thomas... · Fund of Funds Optimization – Version 1.0 ... Step 5: Monitor