Mutual funds: performance evaluation

РЭШ EFM 2004/05 2 Open-end mutual funds Active vs passive (index) funds Active vs passive (index) funds Obliged to buy/sell shares at NAV Obliged to buy/sell shares at NAV –Net Asset Value = Total Net Assets (TNA) per share Part of the fund family (run by one management company) Part of the fund family (run by one management company) Management fee: Management fee: –Asset-based: proportional to TNA –Performance-based: must be symmetric around the benchmark

РЭШ EFM 2004/05 3 MF categories (by Morningstar) Broad asset class: Broad asset class: –Domestic: equity vs bond vs money market vs hybrid –International: foreign, world (global), Europe, Pacific, etc. (Stated) investment objective (Stated) investment objective –Equity: aggressive growth, growth, growth&income, equity- income, income –Bond: government, municipal, corporate –Hybrid: balanced, asset allocation (Estimated) investment style: 3x3 matrix (Estimated) investment style: 3x3 matrix –Equity: large/mid/small-cap – value/blend/growth –Bonds: high/medium/low credit quality – short/intermediate/long duration

РЭШ EFM 2004/05 4 Benefits of investing via MF Low transaction costs Low transaction costs –Easy way to buy a diversified portfolio Customer services Customer services –Liquidity insurance –Easy transfer across funds within the family Professional management Professional management –Selecting right stocks at right time? The objective of the research: The objective of the research: –Check the validity of these claims

РЭШ EFM 2004/05 5 Research questions Why has it become one of the largest financial intermediaries? Why has it become one of the largest financial intermediaries? Why are there more mutual funds than stocks? Why are there more mutual funds than stocks? How to measure fund performance adjusted for risk? How to measure fund performance adjusted 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 managers? Which incentives does it give to fund managers? How accurately do categories divide funds? How accurately do categories divide funds?

РЭШ EFM 2004/05 6 Plan Performance evaluation Performance evaluation –Risk-adjusted performance Absolute vs relative Absolute vs relative Return-based vs portfolio-based Return-based vs portfolio-based Selection vs timing ability Selection vs timing ability Unconditional vs conditional Unconditional vs conditional –Differential performance Performance persistence Performance persistence Determinants of performance Determinants of performance –Impact of survivor bias

РЭШ EFM 2004/05 7 Plan (cont.) Determinants of fund flows Determinants of fund flows –Non-linear relation to past performance: High and low performance High and low performance Recent and distant performance Recent and distant performance Fund strategic behavior (to maximize performance and flows) Fund strategic behavior (to maximize performance and flows) –Risk-taking –Window-dressing –Allocating performance within the family –Incubator strategies

РЭШ EFM 2004/05 8 How to measure MF performance? Raw return, determined by Raw return, determined by –Risk factors –Factor exposures Timing ability: changing beta at right time Timing ability: changing beta at right time –Selection (stock-picking) ability Choosing right stocks (for same level of risk) Choosing right stocks (for same level of risk)

РЭШ EFM 2004/05 9 How to measure MF performance? Risk-adjusted return: Risk-adjusted return: –Difference between fund is return and benchmark return –Benchmark: passive portfolio with same risk as fund i How to find a right benchmark? How to find a right benchmark? –Return-based approach: estimate based on past returns –Portfolio-based approach: construct a portfolio of assets similar to those held by the fund –Relative approach: compare to performance of other funds

РЭШ EFM 2004/05 10 Factor models Regression of excess asset returns on factor returns Regression of excess asset returns on factor returns R i,t –R F,t = α i + Σ k β i,k F k,t + ε t, –Market model: RMRF –Fama-French: RMRF, SMB, HML –Carhart: RMRF, SMB, HML, MOM (1y momentum) –Elton-Gruber: RMRF, SMB, HML, excess bond index return Jensens alpha: Jensens alpha: –Shows whether fund i outperforms passive portfolio of K factors and R F

РЭШ EFM 2004/05 11 Mean-variance spanning tests Test whether adding K new assets (MFs) to N old assets leads to the shift of the MV frontier: Test whether adding K new assets (MFs) to N old assets leads to the shift of the MV frontier: –Three cases possible: spanning, intersection, shift Regression of new asset returns r (Kx1) on old asset returns R (Nx1): Regression of new asset returns r (Kx1) on old asset returns R (Nx1): r t = α + BR t + ε t –Generalized Jensens alpha Test for intersection: there exists η s.t. α-η(l N -Bl K )=0 Test for intersection: there exists η s.t. α-η(l N -Bl K )=0 Test for spanning: α=0 and Bl K =l N Test for spanning: α=0 and Bl K =l N –All additional assets can be written as portfolio of old assets

РЭШ EFM 2004/05 12 Other absolute ordinal measures Sharpe ratio: (E(R i )-R F )/σ i Sharpe ratio: (E(R i )-R F )/σ i Treynor ratio: (E(R i )-R F )/β i Treynor ratio: (E(R i )-R F )/β i Appraisal ratio: α i /σ(ε) i Appraisal ratio: α i /σ(ε) i –Called Treynor-Black ratio when alpha based on market model

РЭШ EFM 2004/05 13 Relative performance measures Use funds in the same category as a benchmark Use funds in the same category as a benchmark Ordinal measures: difference with the mean or median return in the funds category Ordinal measures: difference with the mean or median return in the funds category Cardinal measures: category ranking based on return/α/… Cardinal measures: category ranking based on return/α/… Drawbacks: Drawbacks: –There may be substantial differences in risk within the category –Survivor bias –Bad incentives to managers (as in a tournament)

РЭШ EFM 2004/05 14 How to measure performance persistence? Contingency tables: Contingency tables: –Sort funds by past and current performance E.g., 2x2 (above/below median): winner-winner, WL, LW, LL E.g., 2x2 (above/below median): winner-winner, WL, LW, LL –Check whether actual frequencies are far from those under the null Examine zero-investment portfolios formed on the basis of past performance Examine zero-investment portfolios formed on the basis of past performance –Sort funds into deciles by last-year return –Test whether top-bottom portfolio has premium unexplained by factor models Cross-sectional regressions of current performance on past performance Cross-sectional regressions of current performance on past performance

РЭШ EFM 2004/05 15 Need to control for Fund attrition Fund attrition –Survivor bias Cross-correlation in fund returns Cross-correlation in fund returns –Fewer degrees of freedom will make s.e. larger The measurement error (and mean reversion) The measurement error (and mean reversion) –If measure both current and past performance in the same way

РЭШ EFM 2004/05 16 Brown and Goetzmann (1995) "Mutual fund performance persistence" Explore MF performance persistence Explore MF performance persistence –Absolute vs relative benchmarks –Explicitly model survivor bias –Disaggregate on the annual basis

РЭШ EFM 2004/05 17 Data Common stock funds in Common stock funds in –Including dead funds –Monthly return data Table 1 Table 1 –# funds: 372 in 1976, 829 in 1988 –Total assets rose more than 4 times –MaxCap category became relatively less popular

РЭШ EFM 2004/05 18 Average performance Table 2 Table 2 –VW mean MF return is below S&P500 return by 0.4% p.a., though above index fund –Dead funds heavily underperform living funds –EW means exceed VW means

РЭШ EFM 2004/05 19 Fund disappearance Disappearance: termination or merging into another fund Disappearance: termination or merging into another fund Table 3, determinants of prob(death) Table 3, determinants of prob(death) –Lagged relative return: - –Lagged relative new money: - But insignificant in presence of past performance But insignificant in presence of past performance –Relative size: - –Expense ratio: + –Age: -

РЭШ EFM 2004/05 20 Performance persistence Contingency tables: Contingency tables: –Sort funds by performance over the last year and the current year –Winner/loser = above/below median, 2x2 matrix –Cross-product ratio: (WW*LL)/(WL*LW)=1 under the null

РЭШ EFM 2004/05 21 Bootstrapping procedure Necessary to control for fund attrition and cross-correlation: Necessary to control for fund attrition and cross-correlation: –Use de-meaned sample of fund monthly returns in –For each year, select N funds without replacement and randomize over time –Assume that poorest performers after the first year are eliminated –Repeat 100 times

РЭШ EFM 2004/05 22 Results Table 4, odds ratio test for raw returns relative to median Table 4, odds ratio test for raw returns relative to median –7 years: significant positive persistence –2 years: significant negative persistence

РЭШ EFM 2004/05 23 Controlling for differences in systematic risk Use several risk-adjusted performance measures: Use several risk-adjusted performance measures: –Jensens alpha from the market model –One-index / three-index appraisal ratio –Style-adjusted return Table 6, odds ratio test for risk-adjusted returns relative to median Table 6, odds ratio test for risk-adjusted returns relative to median –Similar results: 5-7 years +, 2 years - persistence

РЭШ EFM 2004/05 24 Absolute benchmarks Figure 1, frequencies of repeat losers and winners wrt S&P500 Figure 1, frequencies of repeat losers and winners wrt S&P500 –Repeat-losers dominate in the second half of the sample period Table 6, odds ratio test for alpha relative to 0 Table 6, odds ratio test for alpha relative to 0 –5 years +, 2 years - persistence

РЭШ EFM 2004/05 25 Investment implications Table 7, performance of last-year return octile portfolios Table 7, performance of last-year return octile portfolios –Past winners perform better than past losers Winner-loser portfolio generates significant performance Winner-loser portfolio generates significant performance –Idiosyncratic risk is the highest for past winners Winner-loser portfolio return is mostly due to bad performance of persistent losers Winner-loser portfolio return is mostly due to bad performance of persistent losers

РЭШ EFM 2004/05 26 Conclusions Past performance is the strongest predictor of fund attrition Past performance is the strongest predictor of fund attrition Clear evidence of relative performance persistence Clear evidence of relative performance persistence Performance persistence is strongly dependent on the time period Performance persistence is strongly dependent on the time period Need to find common mgt strategies explaining persistence and reversals Need to find common mgt strategies explaining persistence and reversals –Additional risk factor(s) –Conditional approach

РЭШ EFM 2004/05 27 Conclusions (cont.) Chasing the winners is a risky strategy Chasing the winners is a risky strategy Selling the losers makes sense Selling the losers makes sense –Why dont all shareholders of poorly performing funds leave? Disadvantaged clientele Disadvantaged clientele –Arbitrageurs cant short-sell losing MFs!

РЭШ EFM 2004/05 28 Carpenter and Lynch (1999 ) Survivorship bias and attrition effects in measures of performance persistence Survivorship bias and attrition effects in measures of performance persistence Simulation analysis of survivor bias in presence of heteroscedasticity in performance Simulation analysis of survivor bias in presence of heteroscedasticity in performance When attrition depends When attrition depends –only on last-year performance: spurious performance persistence magnified –on performance over several years: reversal in performance Look-ahead bias Look-ahead bias

РЭШ EFM 2004/05 29 Carhart (1997) "On persistence in mutual fund performance" Survivor-bias free sample Survivor-bias free sample Examine portfolios ranked by lagged 1-year return Examine portfolios ranked by lagged 1-year return –The four-factor model: RMRF, SMB, HML, and 1-year momentum… –Explains most of the return unexplained by CAPM… –Except for underperformance of the worst funds Fama-MacBeth cross-sectional regressions of alphas on current fund characteristics: Fama-MacBeth cross-sectional regressions of alphas on current fund characteristics: –Expense ratio, turnover, and load: negative effect

Conditional performance evaluation

РЭШ EFM 2004/05 31 Plan for today Up to now: Up to now: –Average performance Jensens alpha: selection ability Jensens alpha: selection ability –Differential performance Performance persistence Performance persistence Today: Today: –Conditional approach to performance evaluation Timing ability Timing ability Use dynamic strategies based on public info as a benchmark Use dynamic strategies based on public info as a benchmark

РЭШ EFM 2004/05 32 Problems with the unconditional approach The market model (with excess returns): The market model (with excess returns): r i,t = α i + β i r M,t + ε i,t –What if β is correlated with the market return? –If cov(β, r M )>0, the estimated α is downward- biased! How to measure timing ability? How to measure timing ability?

РЭШ EFM 2004/05 33 Market timing tests Assume that β t = β 0 + γf(R M -R F ) Assume that β t = β 0 + γf(R M -R F ) –Treynor-Mazuy: linear function, f(·)=R M -R F –Merton-Henriksson: step function, f(·)=I{R M -R F >0} –γ shows whether fund managers can time the market Typical results for an average fund Typical results for an average fund –Negative alpha: no selection ability –Negative gamma: no timing ability

РЭШ EFM 2004/05 34 Problems with measuring market timing Benchmark assets may have option-like characteristics Benchmark assets may have option-like characteristics –Gamma is positive/negative for some stocks Managers may have timing ability at higher horizon Managers may have timing ability at higher horizon –Tests using monthly data have low power of identifying market timing on a daily basis Positive covariance between beta and market return could result from using public info Positive covariance between beta and market return could result from using public info

РЭШ EFM 2004/05 35 Ferson and Schadt (1996) "Measuring Fund Strategy and Performance in Changing Economic Conditions" Evaluate MF performance using conditional approach Evaluate MF performance using conditional approach –Both selection and timing ability –Use dynamic strategies based on public info as a benchmark Consistent with SSFE Consistent with SSFE

РЭШ EFM 2004/05 36 Methodology Conditional market model: Conditional market model: r i,t+1 = α i + β i,t r M,t+1 + ε i,t+1, –where β i,t = β 0i + β 1i Z t (+ γ i f(r M,t+1 )) –Z t are instruments Estimation by OLS: Estimation by OLS: r i,t+1 = α i + (β 0i +β 1i Z t +γ i f(r M,t+1 )) r M,t+1 +ε i,t+1 Extension: a four-factor model Extension: a four-factor model –Large-cap (S&P-500) and small-cap stock returns, government and corporate bond yields

РЭШ EFM 2004/05 37 Data Monthly returns of 67 (mostly equity) funds in Monthly returns of 67 (mostly equity) funds in Instruments (lagged, mean-adjusted): Instruments (lagged, mean-adjusted): –30-day T-bill rate –Dividend yield –Term spread –Default spread –January dummy

РЭШ EFM 2004/05 38 Results Table 2, conditional vs unconditional CAPM Table 2, conditional vs unconditional CAPM –Market betas are related to conditional information 30-day T-bill rate, dividend yield, and term spread are significant 30-day T-bill rate, dividend yield, and term spread are significant –Conditional alphas are higher than the unconditional ones

РЭШ EFM 2004/05 39 Results (cont.) Table 3, cross-sectional distribution of t- stats for cond. and uncond. alphas Table 3, cross-sectional distribution of t- stats for cond. and uncond. alphas –Unconditional approach: there are more significantly negative alphas –Conditional approach: # significantly negative / positive alphas is similar –Very similar results for one-factor and four- factor models

РЭШ EFM 2004/05 40 Results (cont.) Table 4, conditional vs unconditional market timing model for naïve strategies Table 4, conditional vs unconditional market timing model for naïve strategies –Naïve strategies: Start with 65% large-cap, 13% small-cap, 20% gvt bonds, 2% corporate bonds weights Start with 65% large-cap, 13% small-cap, 20% gvt bonds, 2% corporate bonds weights Then: buy-and-hold / annual rebalancing / fixed weights Then: buy-and-hold / annual rebalancing / fixed weights –Unconditional approach: positive alpha and negative gamma for buy-and-hold strategy Evidence of model misspecification Evidence of model misspecification –Conditional approach: insignificant alpha and gamma

РЭШ EFM 2004/05 41 Results (cont.) Tables 5-6, conditional vs unconditional market timing models for actual data Tables 5-6, conditional vs unconditional market timing models for actual data –Conditional approach: the significance of alpha and gamma disappears for all categories but special (concentrating on intl investments) Table 7, cross-sectional distribution of t-stats for cond. and uncond. gammas Table 7, cross-sectional distribution of t-stats for cond. and uncond. gammas –Fewer (significantly) negative gammas under the conditional approach –More (significantly) positive gammas under the conditional approach, esp. for TM model

РЭШ EFM 2004/05 42 Interpretation of the results Dynamic strategies based on instruments contribute negatively to fund returns Dynamic strategies based on instruments contribute negatively to fund returns Is it the active policy or mechanical effects? Is it the active policy or mechanical effects? –The underlying assets may have gammas different from zero Yet, we do not observe similar (α,β,γ) patters for the buy-and- hold portfolio Yet, we do not observe similar (α,β,γ) patters for the buy-and- hold portfolio –New money flows to funds increase their cash holdings and lower betas Edelen (1999): liquidity-motivated trading lowers both alpha and gamma Edelen (1999): liquidity-motivated trading lowers both alpha and gamma

РЭШ EFM 2004/05 43 Conclusions Conditioning on public information: Conditioning on public information: –Provides additional insights about fund strategies –Allows to estimate classical performance measures more precisely The average MF performance is no longer inferior The average MF performance is no longer inferior –Both selection and timing ability

РЭШ EFM 2004/05 44 Bollen and Busse (2001) "On the timing ability of mutual fund managers" Objective: use daily returns in market timing tests Objective: use daily returns in market timing tests –Much higher power if managers time the market on a daily basis Traditional tests: Traditional tests: –40% of funds have positive gamma, 28% have negative gamma Cf: 33% +, 5% - based on monthly data Cf: 33% +, 5% - based on monthly data Compare fund gammas with those for synthetic portfolios: Compare fund gammas with those for synthetic portfolios: –1/3 of funds have positive gamma, 1/3 – negative (relative to synthetic portfolios)

РЭШ EFM 2004/05 45 Bollen and Busse (2001) "On the timing ability of mutual fund managers" Using daily returns in market timing tests Using daily returns in market timing tests –Much higher power if managers time the market on a daily basis Traditional tests: Traditional tests: –40% of funds have γ>0, 28% have γ 0, 28% have γ<0 Cf: 33% +, 5% - based on monthly data Cf: 33% +, 5% - based on monthly data Compare fund γs with those for synthetic portfolios (γ B ): Compare fund γs with those for synthetic portfolios (γ B ): –1/3 of funds have γ>γ B, 1/3 have γ γ B, 1/3 have γ<γ B

Strategic behavior

РЭШ EFM 2004/05 47 Plan for today Up to now: Up to now: –Average performance Selection vs timing ability Selection vs timing ability Unconditional vs conditional Unconditional vs conditional –Differential performance Performance persistence Performance persistence Today: Today: –Strategic behavior of fund managers Choice of risk in the annual tournaments Choice of risk in the annual tournaments

РЭШ EFM 2004/05 48 The objective function of MF manager Career concerns Career concerns –High (low) performance leads to promotion (dismissal) –High risk increases the probability of dismissal Compensation Compensation –Usually proportional to the funds size (and flows) –Convex relation between flows and performance gives strong incentives to win the MF tournament Calendar-year performance is esp important Calendar-year performance is esp important –Managers are usually evaluated at the end of the year –Investors pay more attention to calendar year performance

РЭШ EFM 2004/05 49 Chevalier and Ellison (1997) "Risk Taking by Mutual Funds as a Response to Incentives" Estimate the shape of the flow-performance relationship Estimate the shape of the flow-performance relationship –Separately for young and old funds Estimate resulting risk-taking incentives Estimate resulting risk-taking incentives Examine the actual change in riskiness of funds portfolios Examine the actual change in riskiness of funds portfolios –On the basis of portfolio holdings in September and December

РЭШ EFM 2004/05 50 Data 449 growth and growth&income funds in growth and growth&income funds in –Monthly returns –Annual TNA –Portfolio holdings in September and December About 92% of the portfolio matched to CRSP data About 92% of the portfolio matched to CRSP data Excluding index, closed, primarily institutional, merged in the current year, high expense ratio (>4%), smallest (TNA 4%), smallest (TNA<$10 mln) and youngest (age < 2y) funds

РЭШ EFM 2004/05 51 The flow-performance relationship Flow t = ΔTNA t /TNA t-1 – R t Flow t = ΔTNA t /TNA t-1 – R t –Net relative growth in funds assets Semi-parametric regression of annual flows on last-year market-adjusted returns: Semi-parametric regression of annual flows on last-year market-adjusted returns: Flow i,t+1 =Σ k γ k AgeD k f(R i,t -R M,t )+Σ k δ k AgeD k +α 1 (R i,t-1 -R M,t-1 ) +α 2 (R i,t-2 -R M,t-2 )+α 4 IndFlow i,t+1 +α 5 ln(TNA) i,t +ε i,t+1 –f(R i,t -R M,t ) is a non-parametric function estimated separately for young (2-5y) and old funds –AgeD k are dummy variables for various age categories –Funds size and growth in total TNA of equity funds are controls

РЭШ EFM 2004/05 52 Results Figures 1-2, Table 2: flow-performance relationship for young and old funds Figures 1-2, Table 2: flow-performance relationship for young and old funds –Generally convex shape Linearity is rejected, esp for old funds Linearity is rejected, esp for old funds –The sensitivity of flows to performance is higher for young funds –Flows rise with lagged performance up to 3 years, current category flows and fall with size

РЭШ EFM 2004/05 53 Estimation of risk-taking incentives Assume: Assume: –Fees are proportional to the funds assets –Flows occur at the end of the year –No agency problems between MF companies and their managers In September of year t+1, the increase in expected end-of- year flow due to a change in nonsystematic risk in the last- quarter return: In September of year t+1, the increase in expected end-of- year flow due to a change in nonsystematic risk in the last- quarter return: h k (r sep, σ, Δσ)=E[γ k (f(R sep +u)-f(R sep +v))] –After increasing nonsystematic risk by Δσ, the last-quarter return distribution changes from u to v –Take Δσ=0.5σ

РЭШ EFM 2004/05 54 Results Figure 3, risk incentives for 2y and 11y funds Figure 3, risk incentives for 2y and 11y funds –Young funds with high (low) interim performance have an incentive to decrease (increase) risk to lock up the winning position (catch up with top funds) The risk incentives are reversed at the extreme performance The risk incentives are reversed at the extreme performance –Insignificant pattern for old funds

РЭШ EFM 2004/05 55 Actual risk-taking in response to estimated risk incentives Cross-sectional regressions of within-year change in risk on risk incentive measure Cross-sectional regressions of within-year change in risk on risk incentive measure Focus on the equity portion of funds portfolios (on average, about 90% Focus on the equity portion of funds portfolios (on average, about 90% –Risk measures computed based on prior-year daily stock data

РЭШ EFM 2004/05 56 Actual risk-taking in response to estimated risk incentives Dependent variable: change between September and December in Dependent variable: change between September and December in –St deviation of the market-adjusted return: ΔSD(R i -R M ) –Unsystematic risk: ΔSD(R i -β i R M ) –Systematic risk: Δ|β i -1| Independent variables: Independent variables: –RiskIncentive: h k –Size: ln(TNA) –RiskIncentive*ln(TNA) –September risk level: to control for mean reversion

РЭШ EFM 2004/05 57 Results Table 4 Table 4 –The higher risk incentives, the higher actual change in total and unsystematic risk –This effect becomes less important for larger funds –No evidence of mean reversion

РЭШ EFM 2004/05 58 Actual risk-taking in response to interim performance Dependent variable: change between September and December in total risk Dependent variable: change between September and December in total risk Main independent variable: Main independent variable: –January-September market-adjusted return: R i,sep -R M,sep Assume that change in risk is a piecewise linear function of interim performance Assume that change in risk is a piecewise linear function of interim performance –2 fitted kink points Estimate separately for young and old funds Estimate separately for young and old funds

РЭШ EFM 2004/05 59 Results Table 5, Figure 4 Table 5, Figure 4 –Generally negative relation between actual change in total risk and interim performance –Most slopes and kink points are not significant Alternative approach to measure total risk: Alternative approach to measure total risk: –Using monthly returns: σ(Oct-Dec)-σ(Jan-Sep) Very noisy, esp for last quarter (only 3 points!) Very noisy, esp for last quarter (only 3 points!) Table 6, Figure 5 Table 6, Figure 5 –Generally positive (!) relation between actual change in total risk and interim performance

РЭШ EFM 2004/05 60 Conclusions The flow-performance relationship is convex The flow-performance relationship is convex This generates strategic risk-taking incentives during the year This generates strategic risk-taking incentives during the year Mutual funds seem to respond to these incentives Mutual funds seem to respond to these incentives The change in funds risk (measured via portfolio) is negatively related to its interim performance The change in funds risk (measured via portfolio) is negatively related to its interim performance –Though contradictory evidence based on return-based approach

РЭШ EFM 2004/05 61 Brown, Harlow, and Starks (1996) "Of tournaments and temptations: An analysis if managerial incentives in the MF industry" Contingency table approach: Contingency table approach: –Sort funds by mid-year return and within-year change in total risk Risk-adjustment ratio based on monthly returns: σ(7:12)/σ(1:6) Risk-adjustment ratio based on monthly returns: σ(7:12)/σ(1:6) –2x2 matrix: return/RAR above/below median –Each cell should have 25% of funds under the null Find 27% frequency of high-return low-RAR funds in Find 27% frequency of high-return low-RAR funds in –Support the tournament hypothesis

РЭШ EFM 2004/05 62 Busse (2001) "Another look at mutual fund tournaments" Same contingency table approach using daily and monthly data Same contingency table approach using daily and monthly data –Disaggregate: annual tournaments Control for cross-correlation and auto-correlation in fund returns Control for cross-correlation and auto-correlation in fund returns –Compute p-values from bootstrap No significant evidence for the tournament hypothesis! No significant evidence for the tournament hypothesis!

РЭШ EFM 2004/05 63 Wermers (2000) "MF performance: An empirical decomposition into stock-picking talent, style, transactions costs, and expenses " Decompose funds return into several components to analyze the value of active fund management Decompose funds return into several components to analyze the value of active fund management –Portfolio-based approach: using portfolio holdings data –Compare to return-based approach

РЭШ EFM 2004/05 64 Methodology Finding the benchmark: one of 125 portfolios Finding the benchmark: one of 125 portfolios –In June of each year t, rank stocks by size (current ME) and form 5 quintile portfolios –Subdivide each of 5 size portfolios into 5 portfolios based on BE/ME as of December of t-1 –Subdivide each of 25 size-BM portfolios into 5 portfolios based on past 12m return –From July of t to June of t+1, compute monthly VW returns of 125 portfolios

РЭШ EFM 2004/05 65 Methodology (cont.) Decomposing funds return: R = CS + CT + AS Decomposing funds return: R = CS + CT + AS –Characteristic selectivity: CS=Σ j w j,t-1 [R j,t -R t (b j,t-1 )] w j,t-1 is last-quarter weight of stock j in the funds portfolio w j,t-1 is last-quarter weight of stock j in the funds portfolio R t (b j,t-1 ) is current return on the benchmark ptf matched to stock j in quarter t-1 R t (b j,t-1 ) is current return on the benchmark ptf matched to stock j in quarter t-1 CS measures the funds return adjusted for 3 characteristics CS measures the funds return adjusted for 3 characteristics –Characteristic timing: CT=Σ j [w j,t-1 R t (b j,t-1 )-w j,t-5 R t (b j,t-5 )] CT is higher if the fund increases the factors exposure when its premium rises CT is higher if the fund increases the factors exposure when its premium rises –Average style: AS=Σ j w j,t-5 R t (b j,t-5 ) AS measures tendency to hold stocks with certain characteristics AS measures tendency to hold stocks with certain characteristics

РЭШ EFM 2004/05 66 Methodology (cont.) Comparing with return-based approach: Comparing with return-based approach: –Potentially higher power: no need to estimate factor loadings –But: may be biased due to window-dressing –But: only equity portion of funds portfolio

РЭШ EFM 2004/05 67 Data 1788 diversified equity US funds in diversified equity US funds in –CRSP: monthly returns, annual turnover, expense ratios, and TNA –CDA: quarterly portfolio holdings (only equity portion) –No survivor bias CRSP files of US stocks CRSP files of US stocks

РЭШ EFM 2004/05 68 Results Table 5, decomposition of (equity portion of) MF returns Table 5, decomposition of (equity portion of) MF returns –Gross return: 15.8% p.a. > 14.3% VW-CRSP index –CS = 0.75%, significant –CT = 0.02%, insignificant –AS = 14.8% –Expense ratio = 0.79%, up from 65 to 93 b.p. –Transactions costs = 0.8%, down from 140 to 48 b.p. –Non-equity portion of the funds portfolio: 0.4% –Net return: 13.8% < 14.3% VW-CRSP index!

РЭШ EFM 2004/05 69 Mutual funds: summary Many funds hardly follow their stated objectives Many funds hardly follow their stated objectives On average, MFs do not earn positive performance adjusted for risk and expenses On average, MFs do not earn positive performance adjusted for risk and expenses Bad performance persists Bad performance persists Money flows are concentrated among funds with best performance Money flows are concentrated among funds with best performance Poorly performing funds are not punished with large outflows Poorly performing funds are not punished with large outflows Funds try to win annual tournaments by adjusting risk Funds try to win annual tournaments by adjusting risk