mutual fund performance : luck, skill, persistence · 2008-03-31 · skill or luck : evidence for...
TRANSCRIPT
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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))
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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
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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
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Private Pension SavingsPrivate Pension Savings
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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
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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 ’’
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Evening Standard : March Evening Standard : March
20032003
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Financial Times, Mon 29Financial Times, Mon 29thth
of Nov. 2004of Nov. 2004
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Financial Times, Mon 21Financial Times, Mon 21stst
of March 2005of March 2005
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Fund Performance : Luck or Fund Performance : Luck or
Skill ?Skill ?
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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
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Alphas : Unconditional Alphas : Unconditional FamaFama--
French 3 factor ModelFrench 3 factor Model
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Residuals of Selected Residuals of Selected
FundsFunds
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UK Mutual Fund IndustryUK Mutual Fund Industry
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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
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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
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Bootstrapped Results : Bootstrapped Results :
Best Funds Best Funds –– tt--alphasalphas
Actual t alpha 3.38Actual t alpha = 2.67
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Bootstrapped Results : Bootstrapped Results :
Worst Funds Worst Funds –– tt--alphasalphas
Actual t-alpha = -5.358pha = -5.358
Actual t-alpha = -4.180a = -5.358
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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
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Persistence of Fund Persistence of Fund
PerformancePerformance
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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).
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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
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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
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Regression Analysis Based Regression Analysis Based
Persistence AnalysisPersistence Analysis
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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)
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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.
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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…
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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
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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..
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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..
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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
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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
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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..
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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.
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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
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THE ENDTHE END
papers can be found on : papers can be found on :
ssrn.comssrn.com