Mutual funds: Mutual funds: performance performance evaluationevaluation

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Open-end mutual Open-end mutual fundsfunds Active vs passive (index) fundsActive vs passive (index) funds Obliged to buy/sell shares at NAVObliged to buy/sell shares at NAV

– Net Asset Value = Total Net Assets (TNA) Net Asset Value = Total Net Assets (TNA) per shareper share

Part of the fund family (run by one Part of the fund family (run by one management company)management company)

Management fee:Management fee:– Asset-based: proportional to TNAAsset-based: proportional to TNA– Performance-based: must be symmetric Performance-based: must be symmetric

around the benchmarkaround the benchmark

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MF categories MF categories (by Morningstar)(by Morningstar) Broad asset Broad asset classclass::

– Domestic: equity vs bond vs money market vs Domestic: equity vs bond vs money market vs hybridhybrid

– International: foreign, world (global), Europe, International: foreign, world (global), Europe, Pacific, etc.Pacific, etc.

(Stated) investment (Stated) investment objective objective – Equity: aggressive growth, growth, Equity: aggressive growth, growth,

growth&income, equity-income, incomegrowth&income, equity-income, income– Bond: government, municipal, corporateBond: government, municipal, corporate– Hybrid: balanced, asset allocationHybrid: balanced, asset allocation

(Estimated) investment (Estimated) investment stylestyle: 3x3 matrix: 3x3 matrix– Equity: large/mid/small-cap – value/blend/growthEquity: large/mid/small-cap – value/blend/growth– Bonds: high/medium/low credit quality – Bonds: high/medium/low credit quality –

short/intermediate/long durationshort/intermediate/long duration

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Benefits of investing Benefits of investing via MFvia MF Low transaction costsLow transaction costs

– Easy way to buy a diversified portfolioEasy way to buy a diversified portfolio Customer servicesCustomer services

– Liquidity insuranceLiquidity insurance– Easy transfer across funds within the Easy transfer across funds within the

familyfamily Professional managementProfessional management

– Selecting right stocks at right time?Selecting right stocks at right time? The objective of the research:The objective of the research:

– Check the validity of these claimsCheck the validity of these claims

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Research questionsResearch questions

Why has it become one of the largest Why has it become one of the largest financial intermediaries?financial intermediaries?

Why are there more mutual funds than Why are there more mutual funds than stocks?stocks?

How to measure fund performance adjusted How to measure fund performance adjusted for risk?for risk?

Does fund performance persist?Does fund performance persist? How do investors choose between funds?How do investors choose between funds? Which incentives does it give to fund Which incentives does it give to fund

managers?managers? How accurately do categories divide funds?How accurately do categories divide funds?

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PlanPlan

Performance evaluationPerformance evaluation– Risk-adjusted performanceRisk-adjusted performance

Absolute vs relativeAbsolute vs relative Return-based vs portfolio-basedReturn-based vs portfolio-based Selection vs timing abilitySelection vs timing ability Unconditional vs conditionalUnconditional vs conditional

– Differential performanceDifferential performance Performance persistencePerformance persistence Determinants of performanceDeterminants of performance

– Impact of survivor biasImpact of survivor bias

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PlanPlan (cont.)(cont.)

Determinants of fund flowsDeterminants of fund flows– Non-linear relation to past performance:Non-linear relation to past performance:

High and low performanceHigh and low performance Recent and distant performanceRecent and distant performance

Fund strategic behavior (to maximize Fund strategic behavior (to maximize performance and flows)performance and flows)– Risk-takingRisk-taking– Window-dressingWindow-dressing– Allocating performance within the familyAllocating performance within the family– Incubator strategiesIncubator strategies

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How to measure MF How to measure MF performance?performance? Raw returnRaw return, determined by, determined by

– Risk factorsRisk factors– Factor exposuresFactor exposures

TimingTiming ability: changing beta at right ability: changing beta at right timetime

– Selection Selection (stock-picking) ability(stock-picking) ability Choosing right stocks (for same level of Choosing right stocks (for same level of

risk)risk)

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How to measure MF How to measure MF performance?performance? Risk-adjusted returnRisk-adjusted return: :

– Difference between fund Difference between fund ii’s return and ’s return and benchmark returnbenchmark return

– Benchmark: passive portfolio with same risk as Benchmark: passive portfolio with same risk as fund fund ii

How to find a right benchmark?How to find a right benchmark?– Return-based approach: estimate based on Return-based approach: estimate based on

past returnspast returns– Portfolio-based approach: construct a portfolio Portfolio-based approach: construct a portfolio

of assets similar to those held by the fundof assets similar to those held by the fund– Relative approach: compare to performance of Relative approach: compare to performance of

other fundsother funds

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Factor modelsFactor models

Regression of excess asset returns on Regression of excess asset returns on factor returnsfactor returns

RRi,ti,t–R–RF,tF,t = α = αii + Σ + Σkkββi,ki,kFFk,tk,t + + εεtt,,– Market model: RMRFMarket model: RMRF– Fama-French: RMRF, SMB, HMLFama-French: RMRF, SMB, HML– Carhart: RMRF, SMB, HML, MOM (1y Carhart: RMRF, SMB, HML, MOM (1y

momentum)momentum)– Elton-Gruber: RMRF, SMB, HML, excess Elton-Gruber: RMRF, SMB, HML, excess

bond index returnbond index return Jensen’s alphaJensen’s alpha::

– Shows whether fund Shows whether fund ii outperforms passive outperforms passive portfolio of K factors and Rportfolio of K factors and RFF

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Mean-variance Mean-variance spanning testsspanning tests Test whether adding K new assets (MFs) to N Test whether adding K new assets (MFs) to N

old assets leads to the shift of the MV frontier:old assets leads to the shift of the MV frontier:– Three cases possible: spanning, intersection, shiftThree cases possible: spanning, intersection, shift

Regression of new asset returns r (Kx1) on old Regression of new asset returns r (Kx1) on old asset returns R (Nx1):asset returns R (Nx1):

rrtt = α + BR = α + BRtt + + εεtt

– Generalized Jensen’s alphaGeneralized Jensen’s alpha Test for intersection: there exists η s.t. Test for intersection: there exists η s.t. αα--ηη((llNN--

BBllKK)=0)=0 Test for spanning: Test for spanning: αα=0 =0 and and BBllKK==llNN

– All additional assets can be written as portfolio of old All additional assets can be written as portfolio of old assetsassets

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Other absolute ordinal Other absolute ordinal measuresmeasures Sharpe ratio: (E(RSharpe ratio: (E(Rii)-R)-RFF)/σ)/σii

Treynor ratio: (E(RTreynor ratio: (E(Rii)-R)-RFF)/)/ββii

Appraisal ratio: Appraisal ratio: ααii//σσ((εε))ii

– Called Treynor-Black ratio when Called Treynor-Black ratio when alpha based on market modelalpha based on market model

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Relative performance Relative performance measuresmeasures Use funds in the same category as a Use funds in the same category as a

benchmarkbenchmark Ordinal measures: difference with the Ordinal measures: difference with the

mean or median return in the fund’s mean or median return in the fund’s categorycategory

Cardinal measures: category ranking based Cardinal measures: category ranking based on return/on return/αα/…/…

Drawbacks:Drawbacks:– There may be substantial differences in risk There may be substantial differences in risk

within the categorywithin the category– Survivor biasSurvivor bias– Bad incentives to managers (as in a Bad incentives to managers (as in a

tournament)tournament)

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How to measure How to measure performance performance persistence?persistence? Contingency tables:Contingency tables:

– Sort funds by past and current performanceSort funds by past and current performance E.g., 2x2 (above/below median): winner-winner, WL, E.g., 2x2 (above/below median): winner-winner, WL,

LW, LLLW, LL– Check whether actual frequencies are far from Check whether actual frequencies are far from

those under the nullthose under the null Examine zero-investment portfolios formed on Examine zero-investment portfolios formed on

the basis of the basis of past performancepast performance– Sort funds into deciles by last-year returnSort funds into deciles by last-year return– Test whether top-bottom portfolio has premium Test whether top-bottom portfolio has premium

unexplained by factor modelsunexplained by factor models Cross-sectional regressions of current Cross-sectional regressions of current

performance on past performanceperformance on past performance

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Need to control forNeed to control for

Fund attritionFund attrition– Survivor biasSurvivor bias

Cross-correlation in fund returnsCross-correlation in fund returns– Fewer degrees of freedom will make Fewer degrees of freedom will make

s.e. largers.e. larger The measurement error (and The measurement error (and

mean reversion)mean reversion)– If measure both current and past If measure both current and past

performance in the same wayperformance in the same way

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Brown and GoetzmannBrown and Goetzmann (1995)(1995)

"Mutual fund performance "Mutual fund performance persistencepersistence""

Explore MF performance Explore MF performance persistencepersistence– Absolute vs relative benchmarksAbsolute vs relative benchmarks– Explicitly model survivor biasExplicitly model survivor bias– Disaggregate on the annual basisDisaggregate on the annual basis

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DataData

Common stock funds in 1976-Common stock funds in 1976-19881988– Including dead fundsIncluding dead funds– Monthly return dataMonthly return data

Table 1Table 1– # funds: 372 in 1976, 829 in 1988# funds: 372 in 1976, 829 in 1988– Total assets rose more than 4 timesTotal assets rose more than 4 times– MaxCap category became relatively MaxCap category became relatively

less popularless popular

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Average performanceAverage performance

Table 2Table 2– VW mean MF return is below VW mean MF return is below

S&P500 return by 0.4% p.a., though S&P500 return by 0.4% p.a., though above index fundabove index fund

– Dead funds heavily underperform Dead funds heavily underperform living fundsliving funds

– EW means exceed VW meansEW means exceed VW means

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Fund disappearanceFund disappearance

Disappearance: termination or Disappearance: termination or merging into another fundmerging into another fund

Table 3, determinants of Table 3, determinants of prob(death)prob(death)– Lagged relative return: -Lagged relative return: -– Lagged relative new money: -Lagged relative new money: -

But insignificant in presence of past But insignificant in presence of past performanceperformance

– Relative size: -Relative size: -– Expense ratio: +Expense ratio: +– Age: -Age: -

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Performance Performance persistencepersistence Contingency tables:Contingency tables:

– Sort funds by performance over the Sort funds by performance over the last year and the current yearlast year and the current year

– Winner/loser = above/below Winner/loser = above/below median, 2x2 matrixmedian, 2x2 matrix

– Cross-product ratio: Cross-product ratio: (WW*LL)/(WL*LW)=1 under the (WW*LL)/(WL*LW)=1 under the nullnull

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Bootstrapping Bootstrapping procedureprocedure Necessary to control for fund Necessary to control for fund

attrition and cross-correlation:attrition and cross-correlation:– Use de-meaned sample of fund Use de-meaned sample of fund

monthly returns in 1987-88monthly returns in 1987-88– For each year, select N funds without For each year, select N funds without

replacement and randomize over timereplacement and randomize over time– Assume that poorest performers after Assume that poorest performers after

the first year are eliminatedthe first year are eliminated– Repeat 100 timesRepeat 100 times

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Results Results

Table 4, odds ratio test for raw Table 4, odds ratio test for raw returns relative to medianreturns relative to median– 7 years: significant positive 7 years: significant positive

persistencepersistence– 2 years: significant negative 2 years: significant negative

persistencepersistence

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Controlling for Controlling for differences in systematic differences in systematic riskrisk Use several risk-adjusted Use several risk-adjusted

performance measures:performance measures:– Jensen’s alpha from the market modelJensen’s alpha from the market model– One-index / three-index appraisal ratioOne-index / three-index appraisal ratio– Style-adjusted returnStyle-adjusted return

Table 6, odds ratio test for risk-Table 6, odds ratio test for risk-adjusted returns relative to medianadjusted returns relative to median– Similar results: 5-7 years +, 2 years - Similar results: 5-7 years +, 2 years -

persistencepersistence

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Absolute benchmarksAbsolute benchmarks

Figure 1, frequencies of repeat Figure 1, frequencies of repeat losers and winners wrt S&P500losers and winners wrt S&P500– Repeat-losers dominate in the Repeat-losers dominate in the

second half of the sample periodsecond half of the sample period Table 6, odds ratio test for Table 6, odds ratio test for

alpha relative to 0alpha relative to 0– 5 years +, 2 years - persistence5 years +, 2 years - persistence

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Investment Investment implicationsimplications Table 7, performance of last-year Table 7, performance of last-year

return octile portfoliosreturn octile portfolios– Past winners perform better than past Past winners perform better than past

loserslosers Winner-loser portfolio generates significant Winner-loser portfolio generates significant

performanceperformance

– Idiosyncratic risk is the highest for past Idiosyncratic risk is the highest for past winnerswinners

Winner-loser portfolio return is mostly due Winner-loser portfolio return is mostly due to bad performance of persistent losersto bad performance of persistent losers

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ConclusionsConclusions

Past performance is the strongest Past performance is the strongest predictor of fund attritionpredictor of fund attrition

Clear evidence of relative Clear evidence of relative performance persistenceperformance persistence

Performance persistence is strongly Performance persistence is strongly dependent on the time perioddependent on the time period

Need to find common mgt strategies Need to find common mgt strategies explaining persistence and reversalsexplaining persistence and reversals– Additional risk factor(s)Additional risk factor(s)– Conditional approachConditional approach

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ConclusionsConclusions (cont.)(cont.)

Chasing the winners is a risky Chasing the winners is a risky strategystrategy

Selling the losers makes senseSelling the losers makes sense– Why don’t all shareholders of poorly Why don’t all shareholders of poorly

performing funds leave?performing funds leave? Disadvantaged clienteleDisadvantaged clientele

– Arbitrageurs can’t short-sell losing Arbitrageurs can’t short-sell losing MFs!MFs!

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Carpenter and Lynch Carpenter and Lynch (1999(1999)) ““Survivorship bias and attrition Survivorship bias and attrition

effects in measures of effects in measures of performance persistenceperformance persistence””

Simulation analysis of survivor bias in Simulation analysis of survivor bias in presence of heteroscedasticity in presence of heteroscedasticity in performanceperformance

When attrition depends When attrition depends – only on last-year performance: spurious only on last-year performance: spurious

performance persistence magnifiedperformance persistence magnified– on performance over several years: reversal in on performance over several years: reversal in

performance performance Look-ahead biasLook-ahead bias

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Carhart (1997)Carhart (1997)

""On persistence in mutual fund On persistence in mutual fund performanceperformance""

Survivor-bias free sampleSurvivor-bias free sample Examine portfolios ranked by lagged 1-year Examine portfolios ranked by lagged 1-year

returnreturn– The four-factor model: RMRF, SMB, HML, and 1-The four-factor model: RMRF, SMB, HML, and 1-

year momentum…year momentum…– Explains most of the return unexplained by Explains most of the return unexplained by

CAPM…CAPM…– Except for underperformance of the worst fundsExcept for underperformance of the worst funds

Fama-MacBeth cross-sectional regressions of Fama-MacBeth cross-sectional regressions of alphas on current fund characteristics:alphas on current fund characteristics:– Expense ratio, turnover, and load: negative effectExpense ratio, turnover, and load: negative effect

Conditional Conditional performance performance evaluationevaluation

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Plan for todayPlan for today

Up to now:Up to now:– Average performanceAverage performance

Jensen’s alpha: selection abilityJensen’s alpha: selection ability

– Differential performanceDifferential performance Performance persistencePerformance persistence

Today: Today: – Conditional approach to performance Conditional approach to performance

evaluationevaluation Timing abilityTiming ability Use dynamic strategies based on public info as a Use dynamic strategies based on public info as a

benchmarkbenchmark

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Problems with the Problems with the unconditional unconditional approachapproach The market model (with excess The market model (with excess

returns):returns):

rri,ti,t = = ααii + + ββiirrM,tM,t + + εεi,ti,t

– What if β is correlated with the What if β is correlated with the market return?market return?

– If cov(β, rIf cov(β, rMM)>0, the estimated )>0, the estimated αα is is downward-biased!downward-biased!

How to measure timing ability?How to measure timing ability?

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Market timing testsMarket timing tests

Assume that βAssume that βtt = β = β00 + γf(R + γf(RMM-R-RFF))

– Treynor-MazuyTreynor-Mazuy: linear function, f(·)=R: linear function, f(·)=RMM-R-RFF

– Merton-HenrikssonMerton-Henriksson: step function, : step function, f(f(··)=I{)=I{RRMM-R-RFF>0}>0}

– γ shows whether fund managers can time γ shows whether fund managers can time the marketthe market

Typical results for an average fundTypical results for an average fund– Negative alpha: no selection abilityNegative alpha: no selection ability– Negative gamma: no timing abilityNegative gamma: no timing ability

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Problems with Problems with measuring market measuring market timingtiming Benchmark assets may have option-like Benchmark assets may have option-like

characteristicscharacteristics– Gamma is positive/negative for some stocksGamma is positive/negative for some stocks

Managers may have timing ability at Managers may have timing ability at higher horizonhigher horizon– Tests using monthly data have low power of Tests using monthly data have low power of

identifying market timing on a daily basisidentifying market timing on a daily basis Positive covariance between beta and Positive covariance between beta and

market return could result from using market return could result from using public infopublic info

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Ferson and Schadt Ferson and Schadt (1996)(1996)

"Measuring Fund Strategy and "Measuring Fund Strategy and Performance in Changing Performance in Changing Economic Conditions"Economic Conditions"

Evaluate MF performance using Evaluate MF performance using conditional approachconditional approach– Both selection and timing ability Both selection and timing ability – Use dynamic strategies based on Use dynamic strategies based on

public info as a benchmarkpublic info as a benchmark Consistent with SSFEConsistent with SSFE

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MethodologyMethodology

Conditional market model:Conditional market model:

rri,t+1i,t+1 = = ααii + + ββi,ti,trrM,t+1M,t+1 + + εεi,t+1i,t+1,,– where βwhere βi,ti,t = β = β0i0i + β’ + β’1i1iZZtt (+ γ (+ γiif(rf(rM,t+1M,t+1))))– ZZtt are instruments are instruments

Estimation by OLS: Estimation by OLS:

rri,t+1i,t+1 = = ααii + ( + (ββ0i0i++ββ’’1i1iZZtt++γγiif(rf(rM,t+1M,t+1)) r)) rM,t+1M,t+1++εεi,t+1i,t+1

Extension: a four-factor modelExtension: a four-factor model– Large-cap (S&P-500) and small-cap stock Large-cap (S&P-500) and small-cap stock

returns, government and corporate bond returns, government and corporate bond yieldsyields

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DataData

Monthly returns of 67 (mostly equity) Monthly returns of 67 (mostly equity) funds in 1968-1990funds in 1968-1990

Instruments (lagged, mean-adjusted):Instruments (lagged, mean-adjusted):– 30-day T-bill rate30-day T-bill rate– Dividend yieldDividend yield– Term spreadTerm spread– Default spreadDefault spread– January dummyJanuary dummy

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ResultsResults

Table 2, conditional vs Table 2, conditional vs unconditional CAPMunconditional CAPM– Market betas are related to Market betas are related to

conditional informationconditional information 30-day T-bill rate, dividend yield, 30-day T-bill rate, dividend yield,

and term spread are significantand term spread are significant– Conditional alphas are higher Conditional alphas are higher

than the unconditional onesthan the unconditional ones

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Results (cont.)Results (cont.)

Table 3, cross-sectional distribution Table 3, cross-sectional distribution of t-stats for cond. and uncond. of t-stats for cond. and uncond. alphasalphas– Unconditional approach: there are Unconditional approach: there are

more significantly negative alphas more significantly negative alphas – Conditional approach: # significantly Conditional approach: # significantly

negative / positive alphas is similarnegative / positive alphas is similar– Very similar results for one-factor and Very similar results for one-factor and

four-factor modelsfour-factor models

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Results (cont.)Results (cont.)

Table 4, conditional vs unconditional Table 4, conditional vs unconditional market timing model for naïve strategiesmarket timing model for naïve strategies– Naïve strategies:Naïve strategies:

Start with 65% large-cap, 13% small-cap, 20% gvt Start with 65% large-cap, 13% small-cap, 20% gvt bonds, 2% corporate bonds weightsbonds, 2% corporate bonds weights

Then: buy-and-hold / annual rebalancing / fixed Then: buy-and-hold / annual rebalancing / fixed weightsweights

– Unconditional approach: positive alpha and Unconditional approach: positive alpha and negative gamma for buy-and-hold strategynegative gamma for buy-and-hold strategy

Evidence of model misspecificationEvidence of model misspecification

– Conditional approach: insignificant alpha and Conditional approach: insignificant alpha and gammagamma

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Results (cont.)Results (cont.)

Tables 5-6, conditional vs unconditional Tables 5-6, conditional vs unconditional market timing models for actual datamarket timing models for actual data– Conditional approach: the significance of Conditional approach: the significance of

alpha and gamma disappears for all alpha and gamma disappears for all categories but special (concentrating on intl categories but special (concentrating on intl investments)investments)

Table 7, cross-sectional distribution of Table 7, cross-sectional distribution of t-stats for cond. and uncond. gammast-stats for cond. and uncond. gammas– Fewer (significantly) negative gammas Fewer (significantly) negative gammas

under the conditional approachunder the conditional approach– More (significantly) positive gammas under More (significantly) positive gammas under

the conditional approach, esp. for TM modelthe conditional approach, esp. for TM model

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Interpretation of the Interpretation of the resultsresults Dynamic strategies based on instruments Dynamic strategies based on instruments

contribute negatively to fund returnscontribute negatively to fund returns Is it the active policy or mechanical Is it the active policy or mechanical

effects?effects?– The underlying assets may have gammas The underlying assets may have gammas

different from zerodifferent from zero Yet, we do not observe similar (α,β,γ) patters for Yet, we do not observe similar (α,β,γ) patters for

the buy-and-hold portfoliothe buy-and-hold portfolio

– New money flows to funds increase their cash New money flows to funds increase their cash holdings and lower betasholdings and lower betas

Edelen (1999): liquidity-motivated trading lowers Edelen (1999): liquidity-motivated trading lowers both alpha and gammaboth alpha and gamma

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ConclusionsConclusions

Conditioning on public information:Conditioning on public information:– Provides additional insights about Provides additional insights about

fund strategiesfund strategies– Allows to estimate classical Allows to estimate classical

performance measures more preciselyperformance measures more precisely The average MF performance is no The average MF performance is no

longer inferiorlonger inferior– Both selection and timing abilityBoth selection and timing ability

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Bollen and Busse Bollen and Busse (2001)(2001)""On the timing ability of mutual fund managersOn the timing ability of mutual fund managers"" Objective: use daily returns in market timing testsObjective: use daily returns in market timing tests

– Much higher power if managers time the market on a Much higher power if managers time the market on a daily basisdaily basis

Traditional tests: Traditional tests: – 40% of funds have positive gamma, 28% have negative 40% of funds have positive gamma, 28% have negative

gammagamma Cf: 33% +, 5% - based on monthly dataCf: 33% +, 5% - based on monthly data

Compare fund gammas with those for synthetic Compare fund gammas with those for synthetic portfolios:portfolios:– 1/3 of funds have positive gamma, 1/3 – negative 1/3 of funds have positive gamma, 1/3 – negative

(relative to synthetic portfolios)(relative to synthetic portfolios)

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Bollen and Busse Bollen and Busse (2001)(2001)""On the timing ability of mutual fund On the timing ability of mutual fund

managersmanagers"" Using daily returns in market timing testsUsing daily returns in market timing tests

– Much higher power if managers time the Much higher power if managers time the market on a daily basismarket on a daily basis

Traditional tests: Traditional tests: – 40% of funds have 40% of funds have γγ>0, 28% have >0, 28% have γγ<0<0

Cf: 33% +, 5% - based on monthly dataCf: 33% +, 5% - based on monthly data

Compare fund Compare fund γγ’s with those for synthetic ’s with those for synthetic portfolios (portfolios (γγBB):):– 1/3 of funds have 1/3 of funds have γγ>>γγBB, 1/3 have , 1/3 have γγ<<γγBB

Strategic Strategic behaviorbehavior

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Plan for todayPlan for today

Up to now:Up to now:– Average performanceAverage performance

Selection vs timing abilitySelection vs timing ability Unconditional vs conditionalUnconditional vs conditional

– Differential performanceDifferential performance Performance persistencePerformance persistence

Today: Today: – Strategic behavior of fund managersStrategic behavior of fund managers

Choice of risk in the annual tournamentsChoice of risk in the annual tournaments

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The objective function The objective function of MF managerof MF manager Career concernsCareer concerns

– High (low) performance leads to promotion High (low) performance leads to promotion (dismissal)(dismissal)

– High risk increases the probability of dismissalHigh risk increases the probability of dismissal CompensationCompensation

– Usually proportional to the fund’s size (and flows)Usually proportional to the fund’s size (and flows)– Convex relation between flows and performance Convex relation between flows and performance

gives strong incentives to win the MF tournamentgives strong incentives to win the MF tournament Calendar-year performance is esp importantCalendar-year performance is esp important

– Managers are usually evaluated at the end of the Managers are usually evaluated at the end of the yearyear

– Investors pay more attention to calendar yearInvestors pay more attention to calendar year performance performance

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Chevalier and Ellison Chevalier and Ellison (1997)(1997)""Risk Taking by Mutual Funds as a Risk Taking by Mutual Funds as a

Response to IncentivesResponse to Incentives"" Estimate the shape of the flow-Estimate the shape of the flow-

performance relationshipperformance relationship– Separately for young and old fundsSeparately for young and old funds

Estimate resulting risk-taking Estimate resulting risk-taking incentivesincentives

Examine the actual change in Examine the actual change in riskiness of funds’ portfoliosriskiness of funds’ portfolios– On the basis of portfolio holdings in On the basis of portfolio holdings in

September and DecemberSeptember and December

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DataData

449 growth and growth&income funds in 449 growth and growth&income funds in 1982-921982-92– Monthly returnsMonthly returns– Annual TNAAnnual TNA– Portfolio holdings in September and DecemberPortfolio holdings in September and December

About 92% of the portfolio matched to CRSP dataAbout 92% of the portfolio matched to CRSP data

Excluding index, closed, primarily Excluding index, closed, primarily institutional, merged in the current year, institutional, merged in the current year, high expense ratio (>4%), smallest high expense ratio (>4%), smallest (TNA<$10 mln) and youngest (age < 2y) (TNA<$10 mln) and youngest (age < 2y) fundsfunds

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The flow-performance The flow-performance relationshiprelationship FlowFlowtt = ΔTNA = ΔTNAtt/TNA/TNAt-1t-1 – R – Rtt

– Net relative growth in fund’s assetsNet relative growth in fund’s assets Semi-parametric regression of annual flows on Semi-parametric regression of annual flows on

last-year market-adjusted returns:last-year market-adjusted returns:

FlowFlowi,t+1i,t+1=Σ=ΣkkγγkkAgeDAgeDkkf(Rf(Ri,ti,t-R-RM,tM,t)+Σ)+ΣkkδδkkAgeDAgeDkk++αα11(R(Ri,t-1i,t-1--RRM,t-1M,t-1) +) +αα22(R(Ri,t-2i,t-2-R-RM,t-M,t-

22)+)+αα44IndFlowIndFlowi,t+1i,t+1++αα55ln(TNA)ln(TNA)i,ti,t++εεi,t+1i,t+1

– f(Rf(Ri,ti,t-R-RM,tM,t) is a non-parametric function estimated ) is a non-parametric function estimated separately for young (2-5y) and old funds separately for young (2-5y) and old funds

– AgeDAgeDkk are dummy variables for various age categories are dummy variables for various age categories– Fund’s size and growth in total TNA of equity funds Fund’s size and growth in total TNA of equity funds

are controlsare controls

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ResultsResults

Figures 1-2, Table 2: flow-Figures 1-2, Table 2: flow-performance relationship for young performance relationship for young and old fundsand old funds– Generally convex shapeGenerally convex shape

Linearity is rejected, esp for old fundsLinearity is rejected, esp for old funds

– The sensitivity of flows to performance is The sensitivity of flows to performance is higher for young fundshigher for young funds

– Flows rise with lagged performance up to Flows rise with lagged performance up to 3 years, current category flows and fall 3 years, current category flows and fall with sizewith size

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Estimation of risk-Estimation of risk-taking incentivestaking incentives Assume:Assume:

– Fees are proportional to the fund’s assetsFees are proportional to the fund’s assets– Flows occur at the end of the yearFlows occur at the end of the year– No agency problems between MF companies and No agency problems between MF companies and

their managers their managers In September of year t+1, the increase in In September of year t+1, the increase in

expected end-of-year flow due to a change in expected end-of-year flow due to a change in nonsystematic risk in the last-quarter return:nonsystematic risk in the last-quarter return:

hhkk(r(rsepsep, , σσ, , ΔσΔσ)=E[)=E[γγkk(f(R(f(Rsepsep++uu)-f(R)-f(Rsepsep++vv))]))]– After increasing nonsystematic risk by After increasing nonsystematic risk by ΔσΔσ, the last-, the last-

quarter return distribution changes from quarter return distribution changes from uu to to vv– Take Take ΔσΔσ=0.5=0.5σσ

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ResultsResults

Figure 3, risk incentives for 2y Figure 3, risk incentives for 2y and 11y fundsand 11y funds– Young funds with high (low) interim Young funds with high (low) interim

performance have an incentive to performance have an incentive to decrease (increase) risk to lock up decrease (increase) risk to lock up the winning position (catch up with the winning position (catch up with top funds)top funds) The risk incentives are reversed at the The risk incentives are reversed at the

extreme performanceextreme performance

– Insignificant pattern for old fundsInsignificant pattern for old funds

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Actual risk-taking in Actual risk-taking in response to estimated response to estimated risk incentivesrisk incentives Cross-sectional regressions of Cross-sectional regressions of

within-year change in risk on risk within-year change in risk on risk incentive measureincentive measure

Focus on the equity portion of Focus on the equity portion of funds’ portfolios (on average, funds’ portfolios (on average, about 90%about 90%– Risk measures computed based on Risk measures computed based on

prior-year daily stock dataprior-year daily stock data

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Actual risk-taking in Actual risk-taking in response to estimated response to estimated risk incentivesrisk incentives Dependent variable: change between Dependent variable: change between

September and December inSeptember and December in– St deviation of the market-adjusted return: St deviation of the market-adjusted return:

ΔΔSD(RSD(Rii-R-RMM))– Unsystematic risk: Unsystematic risk: ΔΔSD(RSD(Rii-β-βiiRRMM))– Systematic risk: Systematic risk: Δ|Δ|ββii-1|-1|

Independent variables:Independent variables:– RiskIncentive: hRiskIncentive: hkk

– Size: ln(TNA)Size: ln(TNA)– RiskIncentive*ln(TNA)RiskIncentive*ln(TNA)– September risk level: to control for mean September risk level: to control for mean

reversionreversion

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ResultsResults

Table 4Table 4– The higher risk incentives, the The higher risk incentives, the

higher actual change in total and higher actual change in total and unsystematic riskunsystematic risk

– This effect becomes less important This effect becomes less important for larger fundsfor larger funds

– No evidence of mean reversionNo evidence of mean reversion

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Actual risk-taking in Actual risk-taking in response to interim response to interim performanceperformance Dependent variable: change between Dependent variable: change between

September and December in total riskSeptember and December in total risk Main independent variable:Main independent variable:

– January-September market-adjusted return: January-September market-adjusted return: RRi,sepi,sep-R-RM,sepM,sep

Assume that change in risk is a piecewise Assume that change in risk is a piecewise linear function of interim performancelinear function of interim performance– 2 fitted kink points2 fitted kink points

Estimate separately for young and old Estimate separately for young and old fundsfunds

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ResultsResults

Table 5, Figure 4Table 5, Figure 4– Generally negative relation between actual Generally negative relation between actual

change in total risk and interim performancechange in total risk and interim performance– Most slopes and kink points are not significantMost slopes and kink points are not significant

Alternative approach to measure total Alternative approach to measure total risk: risk: – Using monthly returns: Using monthly returns: σσ(Oct-Dec)-(Oct-Dec)-σσ(Jan-Sep)(Jan-Sep)

Very noisy, esp for last quarter (only 3 points!)Very noisy, esp for last quarter (only 3 points!)

Table 6, Figure 5Table 6, Figure 5– Generally positive (!) relation between actual Generally positive (!) relation between actual

change in total risk and interim performancechange in total risk and interim performance

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ConclusionsConclusions

The flow-performance relationship is convexThe flow-performance relationship is convex This generates strategic risk-taking This generates strategic risk-taking

incentives during the yearincentives during the year Mutual funds seem to respond to these Mutual funds seem to respond to these

incentivesincentives The change in fund’s risk (measured via The change in fund’s risk (measured via

portfolio) is negatively related to its interim portfolio) is negatively related to its interim performanceperformance– Though contradictory evidence based on return-Though contradictory evidence based on return-

based approachbased approach

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Brown, Harlow, and Brown, Harlow, and StarksStarks (1996)(1996)""Of tournaments and temptations: An Of tournaments and temptations: An

analysis if managerial incentives in the analysis if managerial incentives in the MF industryMF industry""

Contingency table approach:Contingency table approach:– Sort funds by mid-year return and within-year Sort funds by mid-year return and within-year

change in total riskchange in total risk Risk-adjustment ratio based on monthly returns: Risk-adjustment ratio based on monthly returns:

σσ(7:12)/(7:12)/σσ(1:6)(1:6)– 2x2 matrix: return/RAR above/below median2x2 matrix: return/RAR above/below median– Each cell should have 25% of funds under the nullEach cell should have 25% of funds under the null

Find 27% frequency of high-return low-RAR Find 27% frequency of high-return low-RAR funds in 1980-1991funds in 1980-1991– Support the tournament hypothesisSupport the tournament hypothesis

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BusseBusse (2001)(2001)

""Another look at mutual fund Another look at mutual fund tournamentstournaments""

Same contingency table approach Same contingency table approach using daily and monthly datausing daily and monthly data– Disaggregate: annual tournamentsDisaggregate: annual tournaments

Control for cross-correlation and auto-Control for cross-correlation and auto-correlation in fund returnscorrelation in fund returns– Compute p-values from bootstrapCompute p-values from bootstrap

No significant evidence for the No significant evidence for the tournament hypothesis!tournament hypothesis!

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WermersWermers (2000)(2000)

""MF MF performance: An empirical performance: An empirical decomposition into stock-picking decomposition into stock-picking talent, style, transactions costs, talent, style, transactions costs, and expensesand expenses""

Decompose fund’s return into several Decompose fund’s return into several components to analyze the value of active components to analyze the value of active fund managementfund management– Portfolio-based approach: using portfolio Portfolio-based approach: using portfolio

holdings dataholdings data– Compare to return-based approachCompare to return-based approach

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MethodologyMethodology

Finding the benchmark: one of 125 Finding the benchmark: one of 125 portfoliosportfolios– In June of each year t, rank stocks by size In June of each year t, rank stocks by size

(current ME) and form 5 quintile portfolios (current ME) and form 5 quintile portfolios – Subdivide each of 5 size portfolios into 5 Subdivide each of 5 size portfolios into 5

portfolios based on BE/ME as of December of portfolios based on BE/ME as of December of t-1t-1

– Subdivide each of 25 size-BM portfolios into 5 Subdivide each of 25 size-BM portfolios into 5 portfolios based on past 12m returnportfolios based on past 12m return

– From July of t to June of t+1, compute monthly From July of t to June of t+1, compute monthly VW returns of 125 portfoliosVW returns of 125 portfolios

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MethodologyMethodology (cont.)(cont.)

Decomposing fund’s return: R = CS + CT + ASDecomposing fund’s return: R = CS + CT + AS– Characteristic selectivity: CS=Characteristic selectivity: CS=ΣΣjjwwj,t-1j,t-1[R[Rj,tj,t-R-Rtt(b(bj,t-1j,t-1)])]

wwj,t-1j,t-1 is last-quarter weight of stock is last-quarter weight of stock jj in the fund’s portfolio in the fund’s portfolio RRtt(b(bj,t-1j,t-1) is current return on the benchmark ptf matched to ) is current return on the benchmark ptf matched to

stock stock jj in quarter t-1 in quarter t-1 CS measures the fund’s return adjusted for 3 CS measures the fund’s return adjusted for 3

characteristicscharacteristics– Characteristic timing: CT=ΣCharacteristic timing: CT=Σjj[w[wj,t-1j,t-1RRtt(b(bj,t-1j,t-1)-w)-wj,t-5j,t-5RRtt(b(bj,t-j,t-

55)])] CT is higher if the fund increases the factor’s exposure CT is higher if the fund increases the factor’s exposure

when its premium riseswhen its premium rises– Average style: AS=ΣAverage style: AS=Σjjwwj,t-5j,t-5RRtt(b(bj,t-5j,t-5))

AS measures tendency to hold stocks with certain AS measures tendency to hold stocks with certain characteristicscharacteristics

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MethodologyMethodology (cont.)(cont.)

Comparing with return-based Comparing with return-based approach:approach:– Potentially higher power: no need to Potentially higher power: no need to

estimate factor loadingsestimate factor loadings– But: may be biased due to window-But: may be biased due to window-

dressingdressing– But: only equity portion of fund’s But: only equity portion of fund’s

portfolioportfolio

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DataData

1788 diversified equity US funds 1788 diversified equity US funds in 1975-94in 1975-94– CRSP: monthly returns, annual CRSP: monthly returns, annual

turnover, expense ratios, and TNAturnover, expense ratios, and TNA– CDA: quarterly portfolio holdings CDA: quarterly portfolio holdings

(only equity portion)(only equity portion)– No survivor biasNo survivor bias

CRSP files of US stocksCRSP files of US stocks

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ResultsResults

Table 5, decomposition of (equity portion Table 5, decomposition of (equity portion of) MF returnsof) MF returns– Gross return: 15.8% p.a. > 14.3% VW-CRSP Gross return: 15.8% p.a. > 14.3% VW-CRSP

indexindex– CS = 0.75%, significantCS = 0.75%, significant– CT = 0.02%, insignificantCT = 0.02%, insignificant– AS = 14.8%AS = 14.8%– Expense ratio = 0.79%, up from 65 to 93 b.p.Expense ratio = 0.79%, up from 65 to 93 b.p.– Transactions costs = 0.8%, down from 140 to Transactions costs = 0.8%, down from 140 to

48 b.p.48 b.p.– Non-equity portion of the fund’s portfolio: 0.4%Non-equity portion of the fund’s portfolio: 0.4%– Net return: 13.8% < 14.3% VW-CRSP index!Net return: 13.8% < 14.3% VW-CRSP index!

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Mutual funds: Mutual funds: summarysummary Many funds hardly follow their stated Many funds hardly follow their stated

objectivesobjectives On average, MFs do not earn positive On average, MFs do not earn positive

performance adjusted for risk and performance adjusted for risk and expensesexpenses

Bad performance persistsBad performance persists Money flows are concentrated among Money flows are concentrated among

funds with best performancefunds with best performance Poorly performing funds are not punished Poorly performing funds are not punished

with large outflowswith large outflows Funds try to win annual tournaments by Funds try to win annual tournaments by

adjusting riskadjusting risk