MUTUAL FUND PERFORMANCE : LUCK, SKILL, PERSISTENCE · 2008-03-31 · Skill or luck : Evidence for UK –Some top funds have ‘good skills ’, good performance is luck for most funds

MUTUAL FUND PERFORMANCE MUTUAL FUND PERFORMANCE

: LUCK, SKILL, PERSISTENCE ?: LUCK, SKILL, PERSISTENCE ?

Presentation MSc Fair Frankfurt 29Presentation MSc Fair Frankfurt 29thth March 08March 08

Dr Dirk Dr Dirk NitzscheNitzsche (E(E--mail : mail : [email protected]@city.ac.uk))

Cass Business SchoolCass Business School

�� Located in the heart of the Located in the heart of the ‘‘City of City of LondonLondon’’

�� Over 150 academic faculty, more than Over 150 academic faculty, more than 1,200 postgraduate students1,200 postgraduate students

�� Over 20 MSc Course in Finance Over 20 MSc Course in Finance –– High quality programmes combining theory High quality programmes combining theory with practice. with practice.

–– Research based business schoolResearch based business school

Asset Management Asset Management

IndustryIndustry

�� Asset Management Asset Management

–– Portfolio theory / diversificationPortfolio theory / diversification

–– Hedge funds, Mutual funds, Private equity Hedge funds, Mutual funds, Private equity

fundsfunds

–– Predicting asset returns, Performance Predicting asset returns, Performance

measuresmeasures

Private Pension SavingsPrivate Pension Savings

ContentsContents

�� Mutual fund industry : the way to diversify, the way Mutual fund industry : the way to diversify, the way to save long termto save long term

�� Models measuring performance of mutual funds (risk Models measuring performance of mutual funds (risk adjusted rate of return)adjusted rate of return)

→→ JensenJensen’’s alphas alpha

�� Questions : Questions : –– Can the fund performance be attributed to luck or skill ? Can the fund performance be attributed to luck or skill ?

–– Are fund performance persistent ? Are fund performance persistent ?

–– Can fund managers Can fund managers ‘‘market timemarket time’’ ? ?

–– Funds which look good on paper, how many are falsely Funds which look good on paper, how many are falsely discovered of being good discovered of being good –– FDR ? FDR ?

�� Active Active vsvs passive fund management passive fund management

New

spapers

New

spapers

��The Sunday Times 10.03.2002

The Sunday Times 10.03.2002

‘‘ Nine out of ten funds

Nine out of ten funds underperform

underperform

’’

��The Sunday Times 10.10.2004

The Sunday Times 10.10.2004

‘‘ Funds take half your growth in fees

Funds take half your growth in fees ’’

Evening Standard : March Evening Standard : March

20032003

Financial Times, Mon 29Financial Times, Mon 29thth

of Nov. 2004of Nov. 2004

Financial Times, Mon 21Financial Times, Mon 21stst

of March 2005of March 2005

Fund Performance : Luck or Fund Performance : Luck or

Skill ?Skill ?

Measuring Fund Performance : Measuring Fund Performance :

Equilibrium Models Equilibrium Models

Unconditional Models Unconditional Models

CAPM : (CAPM : (ERERii –– rrff))tt = = ααii + + ββii(ER(ERmm –– rrff))tt + + εεitit

FamaFama –– French 3 factor modelFrench 3 factor model

CarhartCarhart (1997) 4 factor model(1997) 4 factor model

Alphas : Unconditional Alphas : Unconditional FamaFama--

French 3 factor ModelFrench 3 factor Model

Residuals of Selected Residuals of Selected

FundsFunds

UK Mutual Fund IndustryUK Mutual Fund Industry

Interpretation of the pInterpretation of the p--Values Values

(Positive Side of Distribution)(Positive Side of Distribution)

�� Suppose highest Suppose highest ‘‘actualactual’’ alpha is 1.5 alpha is 1.5 All the highest bootstrapped alphas will be positive (by construAll the highest bootstrapped alphas will be positive (by constructions)ctions)

�� If pIf p--value is 0.20, that means 20% of the highest value is 0.20, that means 20% of the highest bootstrapped alphas (under the null of no bootstrapped alphas (under the null of no outperformanceoutperformance) are larger than the actual highest alpha ) are larger than the actual highest alpha observed in the dataobserved in the data

⇒⇒ LUCKLUCK

�� If pIf p--value is 0.02, that means only 2% of the highest value is 0.02, that means only 2% of the highest bootstrapped alphas (under the null) are larger than the bootstrapped alphas (under the null) are larger than the actual highest alpha (from data)actual highest alpha (from data)

⇒⇒ SKILLSKILL

Interpretation of the pInterpretation of the p--Values Values

(Negative Side of Distribution)(Negative Side of Distribution)

�� Suppose worst Suppose worst ‘‘actualactual’’ alpha is alpha is --3.5 3.5 All the worst bootstrapped alphas will be negative (by constructAll the worst bootstrapped alphas will be negative (by constructions)ions)

�� If pIf p--value is 0.30, that means 30% of the worst value is 0.30, that means 30% of the worst bootstrapped alphas (under the null of no bootstrapped alphas (under the null of no outperformanceoutperformance) are less than the actual worst alpha ) are less than the actual worst alpha observed in the dataobserved in the data

⇒⇒ UNLUCKY UNLUCKY

�� If pIf p--value is 0.01, that means only 1% of the worst value is 0.01, that means only 1% of the worst bootstrapped alphas (under the null) are less than the bootstrapped alphas (under the null) are less than the actual worst alpha (from data)actual worst alpha (from data)

⇒⇒ BAD SKILLBAD SKILL

Bootstrapped Results : Bootstrapped Results :

Best Funds Best Funds –– tt--alphasalphas

Actual t alpha 3.38Actual t alpha = 2.67

Bootstrapped Results : Bootstrapped Results :

Worst Funds Worst Funds –– tt--alphasalphas

Actual t-alpha = -5.358pha = -5.358

Actual t-alpha = -4.180a = -5.358

UK Results : Unconditional UK Results : Unconditional

Model (sorted by tModel (sorted by t--alpha)alpha)

0.0090.009--5.3585.358--0.2640.264WorstWorst

< 0.001< 0.001--4.2784.278--0.4000.40055thth worstworst

< 0.001< 0.001--2.5092.509--0.4350.435Min 10%Min 10%

< 0.001< 0.001--0.8730.873--0.1070.107Min 40%Min 40%

Bottom Funds Bottom Funds

0.0200.0202.5012.5010.3020.3021212thth bestbest

0.0380.0382.5452.5450.4310.4311010thth bestbest

0.1280.1283.3653.3651.4471.44722ndnd bestbest

0.4370.4373.3893.3890.4120.412Best Best

Top Funds Top Funds

BootstrBootstr. p. p--valuevalueActual tActual t--alphaalphaActual alphaActual alphaFund Position Fund Position

Persistence of Fund Persistence of Fund

PerformancePerformance

Persistence of Fund Persistence of Fund

PerformancePerformance

�� Various approaches of measuring Various approaches of measuring persistence of fund performancepersistence of fund performance–– Contingency tables Contingency tables

–– Regression based (with rebalancing)Regression based (with rebalancing)

�� Numerous papers investigate Numerous papers investigate persistence of fund returns persistence of fund returns

�� Findings : persistence exists mainly for Findings : persistence exists mainly for poor funds (poor funds (‘‘poorpoor’’ persistence). persistence).

Academic Studies Looking Academic Studies Looking

at Persistence at Persistence –– UK DataUK Data

�� Allen and Tan (1999) : Allen and Tan (1999) : –– 131 funds, 1989131 funds, 1989--1995, Persistence amongst top and bottom 1995, Persistence amongst top and bottom

performersperformers

�� Blake and Blake and TimmermannTimmermann (1998) and (1998) and LundeLunde, Blake and , Blake and TimmermannTimmermann (1999) : (1999) : –– 2,375 funds, 19722,375 funds, 1972--1995, Persistence found1995, Persistence found

�� Quigley and Quigley and SinquefieldSinquefield (1999) : (1999) : –– 752 funds, 1978752 funds, 1978--1997, Persistence found among poor 1997, Persistence found among poor

performersperformers

�� Leger (1997) : Leger (1997) : –– 72 investment trusts, 197472 investment trusts, 1974--1993, No persistence found1993, No persistence found

�� WM Company : WM Company : –– 19791979--1998, UK income and growth funds, No persistence found1998, UK income and growth funds, No persistence found

Academic Studies Looking Academic Studies Looking

at Persistence at Persistence –– US DataUS Data

�� CarhartCarhart (1997) : (1997) : –– All US equity mutual funds, 1963All US equity mutual funds, 1963--1993, Persistence amongst 1993, Persistence amongst

poor performing funds, not amongst top fundspoor performing funds, not amongst top funds

�� Chen, Chen, JegadeeshJegadeesh and and WermersWermers (2000) : (2000) : –– All US mutual funds, 1975All US mutual funds, 1975--1995, Persistence found due to 1995, Persistence found due to

momentum, No persistence when risk adjusted. momentum, No persistence when risk adjusted.

�� Elton, Gruber and Blake (1996) : Elton, Gruber and Blake (1996) : –– 188 equity mutual funds, 1977188 equity mutual funds, 1977--1993, Persistence found1993, Persistence found

�� GoetzmannGoetzmann and Ibbotson (1994) : and Ibbotson (1994) : –– 728 mutual trusts, 1976728 mutual trusts, 1976--1988, Persistence found1988, Persistence found

�� MalkielMalkiel (1995) : (1995) : –– 19711971--1991, 322 mutual funds, Persistence found during the 1991, 322 mutual funds, Persistence found during the

1970s, not in 1980s1970s, not in 1980s

Regression Analysis Based Regression Analysis Based

Persistence AnalysisPersistence Analysis

Testing for Persistence Testing for Persistence

Using Regression AnalysisUsing Regression Analysis

�� Estimation window (say 60 months) :Estimation window (say 60 months) :Estimate all the funds alphas using 12, 24, 36, Estimate all the funds alphas using 12, 24, 36,

or 60 monthly observationsor 60 monthly observations

–– Sort fund by alpha (or t of alpha) or simply Sort fund by alpha (or t of alpha) or simply

(excess) returns(excess) returns

–– Form deciles (or other portfolios)Form deciles (or other portfolios)

�� Calculation window (say 3 months) :Calculation window (say 3 months) : use use

the next 1, 3, 6 or 12 month of returns and the next 1, 3, 6 or 12 month of returns and

calculate the (monthly) portfolio returns for calculate the (monthly) portfolio returns for

each each deciledecile (equally weighted portfolios)(equally weighted portfolios)

Testing for Persistence Using Testing for Persistence Using

Regression Analysis (Cont.)Regression Analysis (Cont.)

�� Move the estimation window forward by the Move the estimation window forward by the

size of the calculation window (say 3 months) size of the calculation window (say 3 months)

and repeat the above steps. and repeat the above steps.

�� For each For each deciledecile (or other portfolio)(or other portfolio)

–– you get one (forward looking time series of portfolio you get one (forward looking time series of portfolio

returns). returns).

–– Regress the excess returns on the explanatory Regress the excess returns on the explanatory

variable(svariable(s))

–– Test the null hypothesis that Test the null hypothesis that ααii = 0. = 0.

Measuring Persistence : Measuring Persistence :

Rebalancing Top PerformersRebalancing Top Performers

Jan 1981 Dec 2002

60 month estim. window : e.g. sort alphas, invest in portfolio of ‘top’ funds

1 month ‘investment’ window : form portfolios of ‘top’ funds

Rolling this forward by the ‘investment’ window…

Measuring Persistence Measuring Persistence

(Cont.)(Cont.)

�� UK data : UK data : –– Data, data frequency and sample period : as earlierData, data frequency and sample period : as earlier

–– Models : Models : CarhartCarhart 4 factor, 4 factor, FamaFama--French 3 factor, CAPMFrench 3 factor, CAPM

�� Sorting : (Excess) Returns, alpha, tSorting : (Excess) Returns, alpha, t--alphaalpha–– Estimation window : 36 or 60 months for alpha, tEstimation window : 36 or 60 months for alpha, t--alpha; 12, alpha; 12,

6 and 3 month for returns 6 and 3 month for returns

–– Rebalancing Window : 1, 3, 6 or 12 monthsRebalancing Window : 1, 3, 6 or 12 months

For instance : For instance :

((ERERpp –– rrff))**tt = = αα + + ββ(ER(ERmm –– rrff))tt + + εεptpt

if if αα > 0 : > 0 : performance is persistentperformance is persistent

Forward Forward ‘‘ReturnsReturns’’ Regression : Regression :

4 Factor Model, Sorted t4 Factor Model, Sorted t--alphaalpha

-2.0707-0.1404-2.4729-0.1654-2.5275-0.1735-2.3797-0.142610

-1.8803-0.1150-2.7343-0.1530-3.7007-0.1753-2.6934-0.12809

-1.6559-0.0774-1.6570-0.0903-1.4459-0.0835-1.0217-0.66178

-2.5591-0.0941-2.0234-0.0815-1.9573-0.0827-1.9603-0.08877

-1.9254-0.0810-1.4618-0.0582-0.9151-0.0379-0.9522-0.03686

-1.9842-0.0940-2.7443-0.1202-1.3062-0.0599-1.9056-0.08095

-1.3863-0.05520.33860.0153-1.0825-0.0484-1.1170-0.05034

-0.1490-0.0096-1.1088-0.0648-0.6996-0.0460-1.0102-0.06463

-0.8702-0.0597-0.4811-0.0311-0.8609-0.0609-0.8468-0.06022

-0.0357-0.00290.14630.01200.09710.0078-0.0012-0.00011

t-alphaalphat-alphaalphat-alphaalphat-alphaalpha

60 / 160 / 360 / 660 /12DecileDecile

PortfPortf..

Forward Forward ‘‘ReturnsReturns’’ Regression : Regression :

4 Factor Model, Sorted t4 Factor Model, Sorted t--alphaalpha

-0.3504-0.0261-0.2813-0.0208-0.5101-0.0373-0.6762-0.050650

-0.1393-0.01130.26860.02130.02860.0023-0.1444-0.011530

0.08140.00650.44800.0369-0.0631-0.00520.02400.002025

0.01070.00090.09470.0079-0.4487-0.0382-0.2308-0.019320

0.26660.02240.78350.06820.70410.05630.50730.043410

0.95050.07661.19400.10010.94910.07370.67670.05649

0.83240.06861.21390.10891.00800.08120.39110.03428

1.40680.11401.52700.13151.01410.08270.16310.01467

1.73930.14101.70940.14491.39280.11140.26430.02376

1.97290.16291.48600.13590.93150.0784-0.1807-0.01745

2.23040.19081.34110.12070.92730.0829-0.0306-0.00294

2.25870.20821.89690.18171.53370.14670.28400.02893

1.23460.12501.26820.12261.38410.13880.80520.08592

-0.0508-0.0066-0.2758-0.03490.50440.0643-0.6412-0.09381

t-alphaalphat-alphaalphat-alphaalphat-alphaalpha

60 / 160 / 360 / 660 /12Top Top

PortfPortf..

Final Wealth : Return Final Wealth : Return

Sorted (12/12/0%)Sorted (12/12/0%)Return Sorted : 12/12/0%

0

2000

4000

6000

8000

10000

12000

Feb-99 Aug-99 Mar-00 Oct-00 Apr-01 Nov-01 May-02 Dec-02 Jun-03

Time

Fin

al W

ealth Indxe Funds

Top 5

Top 10

Top 50

Final Wealth : Return Final Wealth : Return

Sorted (12/12/2.5%)Sorted (12/12/2.5%)Return Sorted : 12/12/2.5%

0

2000

4000

6000

8000

10000

12000

Feb-99 Aug-99 Mar-00 Oct-00 Apr-01 Nov-01 May-02 Dec-02 Jun-03

Time

Fin

al W

ealth Index Funds

Top 5

Top 10

Top 50

Difference in Mean : Active versus Difference in Mean : Active versus

Passive : Return Sorted, 0% Trans. Passive : Return Sorted, 0% Trans.

CostsCosts

0.02530.84980.05140.68200.11160.45950.19830.32857

0.02260.95530.03470.80460.09010.48170.13400.44404

0.05390.50080.10590.37030.16030.27150.21400.222850

0.03550.68660.09870.46150.10130.42860.16470.330120

0.03080.75610.07240.54390.11330.42210.17700.336915

0.02610.83900.05910.62140.10380.47440.19130.326010

0.02650.83440.04730.65130.10450.47240.20230.31619

0.02250.86600.04020.70790.11240.47020.22860.28658

0.02840.87810.04450.74260.12210.42610.18060.36066

0.02310.93230.04110.73870.09220.48140.15650.40455

0.02410.90060.02220.94560.03270.63850.13290.44353

0.01691.07900.02750.94040.08270.63270.17670.42872

p-val.Testp-val.Testp-val.Testp-val.Test

12 / 112 / 312 / 612 /12TopTop

PortfPortf..

Summary of Results Summary of Results

About UK Persistence About UK Persistence

�� Persistence mainly in bad performing funds Persistence mainly in bad performing funds

�� Some persistence in Some persistence in ‘‘toptop’’ fundsfunds

�� But But ‘‘TopTop’’ portfolios still require frequent portfolios still require frequent

rebalancing rebalancing

–– No transaction costs : rebalance very frequently No transaction costs : rebalance very frequently

–– 5% transaction costs : rebalance not very 5% transaction costs : rebalance not very

frequentlyfrequently

�� Index tracker not worse. Index tracker not worse.

SummarySummary

�� Asset returns are not normally distributed Asset returns are not normally distributed

⇒⇒ Hence should not use tHence should not use t--stats stats

�� Skill or luck : Evidence for UKSkill or luck : Evidence for UK–– Some top funds have Some top funds have ‘‘good skillsgood skills’’, good , good performance is luck for most fundsperformance is luck for most funds

–– All bottom funds have All bottom funds have ‘‘bad skillsbad skills’’

�� Persistence : Persistence : –– Evidence is mixed Evidence is mixed

–– persistence exists mainly with poor fundspersistence exists mainly with poor funds

�� Market Timing : Not much evidenceMarket Timing : Not much evidence

THE ENDTHE END

papers can be found on : papers can be found on :

ssrn.comssrn.com