Mutual funds: performance evaluation Worldwide TNA of mutual funds EFM 2006/7 2 Worldwide # mutual funds EFM 2006/7 3 Open-end mutual funds

Active vs passive (index) funds 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) Management fee: Asset-based: proportional to TNA Performance-based: must be symmetric around the benchmark EFM 2006/7 4

MF categories (by Morningstar) Broad asset class: Domestic: equity vs bond vs money market vs hybrid International: foreign, world (global), Europe, Pacific, etc. (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 Equity: large/mid/small-cap value/blend/growth Bonds: high/medium/low credit quality short/intermediate/long duration EFM 2006/7 5 TNA of US mutual funds EFM 2006/7 6 # US mutual funds EFM 2006/7

7 Benefits of investing via MF Low transaction costs Easy way to buy a diversified portfolio Customer services Liquidity insurance Easy transfer across funds within the family Professional management Selecting right stocks at right time?

The objective of the research: Check the validity of these claims EFM 2006/7 8 Research questions Why has it become one of the largest financial

intermediaries? Why are there more mutual funds than stocks? How to measure fund performance adjusted for risk? Does fund performance persist? How do investors choose between funds? Which incentives does it give to fund managers? How accurately do categories divide funds? EFM 2006/7 9 How to measure MF performance? Raw return, determined by Risk factors Factor exposures

Timing ability: changing beta at right time Selection (stock-picking) ability Choosing right stocks (for same level of risk) EFM 2006/7 10 How to measure MF performance? 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? 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 EFM 2006/7 11 Factor models Regression of excess asset returns on factor returns

Ri,tRF,t = i + ki,kFk,t + 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: Shows whether fund i outperforms passive portfolio of K factors and RF EFM 2006/7 12

Mean-variance spanning tests 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): rt = + BRt + t Generalized Jensens alpha Test for intersection: there exists s.t. -(lNBlK)=0 Test for spanning: =0 and BlK=lN

All additional assets can be written as portfolio of old assets EFM 2006/7 13 Other absolute ordinal measures Sharpe ratio: (E(Ri)-RF)/i Treynor ratio: (E(Ri)-RF)/i Appraisal ratio: i/()i Called Treynor-Black ratio when alpha based on market model EFM 2006/7

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

EFM 2006/7 15 How to measure performance persistence? Contingency tables: Sort funds by past and current performance 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 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 EFM 2006/7 16 Need to control for Fund attrition Survivor bias

Cross-correlation in fund returns Fewer degrees of freedom will make s.e. larger The measurement error (and mean reversion) If measure both current and past performance in the same way EFM 2006/7 17 Brown and Goetzmann (1995) "Mutual fund performance persistence" Explore MF performance persistence Absolute vs relative benchmarks

Explicitly model survivor bias Disaggregate on the annual basis EFM 2006/7 18 Data Common stock funds in 19761988 Including dead funds Monthly return data Table 1 # funds: 372 in 1976, 829 in 1988

Total assets rose more than 4 times MaxCap category became relatively less popular EFM 2006/7 19 Average performance 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 EFM 2006/7 20

Fund disappearance Disappearance: termination or merging into another fund Table 3, determinants of prob(death) Lagged relative return: Lagged relative new money: But insignificant in presence of past performance Relative size: Expense ratio: + Age: - EFM 2006/7 21 Performance

persistence 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 EFM 2006/7 22 Bootstrapping procedure Necessary to control for fund attrition and cross-correlation:

Use de-meaned sample of fund monthly returns in 1987-88 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 EFM 2006/7 23 Results Table 4, odds ratio test for raw returns relative to median 7 years: significant positive persistence 2 years: significant negative persistence

EFM 2006/7 24 Controlling for differences in systematic risk 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 riskadjusted returns relative to median Similar results: 5-7 years +, 2 years persistence EFM 2006/7 25 Absolute benchmarks 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 5 years +, 2 years - persistence EFM 2006/7

26 Investment implications Table 7, performance of last-year return octile portfolios Past winners perform better than past losers 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

EFM 2006/7 27 Conclusions Past performance is the strongest predictor of fund attrition Clear evidence of relative performance persistence Performance persistence is strongly dependent on the time period Need to find common mgt strategies explaining persistence and reversals Additional risk factor(s) Conditional approach

EFM 2006/7 28 Conclusions (cont.) Chasing the winners is a risky strategy Selling the losers makes sense Why dont all shareholders of poorly performing funds leave? Disadvantaged clientele Arbitrageurs cant short-sell losing MFs! EFM 2006/7

29 Carhart (1997) "On persistence in mutual fund performance" Survivor-bias free sample Examine portfolios ranked by lagged 1-year return The four-factor model: RMRF, SMB, HML, and 1year 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: Expense ratio, turnover, and load: negative effect EFM 2006/7

30 Conditional performance evaluation Plan for today Up to now: Average performance Jensens alpha: selection ability Differential performance

Performance persistence Today: Conditional approach to performance evaluation Timing ability Use dynamic strategies based on public info as a benchmark EFM 2006/7 32 Problems with the unconditional approach The market model (with excess

returns): ri,t = i + irM,t + i,t What if is correlated with the market return? If cov(, rM)>0, the estimated is downward-biased! How to measure timing ability? EFM 2006/7 33 Market timing tests Assume that t = 0 + f(Rf(RM-RF) Treynor-Mazuy: linear function, f()=RM-RF Merton-Henriksson: step function, f()=I{RM-RF>0}

f(R shows whether fund managers can time the market Typical results for an average fund Negative alpha: no selection ability Negative gamma: no timing ability EFM 2006/7 34 Problems with measuring market timing Benchmark assets may have option-like characteristics Gamma is positive/negative for some stocks

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 EFM 2006/7 35 Ferson and Schadt (1996) "Measuring Fund Strategy and Performance in Changing Economic Conditions"

Evaluate MF performance using conditional approach Both selection and timing ability Use dynamic strategies based on public info as a benchmark Consistent with SSFE EFM 2006/7 36 Methodology Conditional market model: ri,t+1 = i + i,trM,t+1 + i,t+1, where i,t = 0i + 1iZt (+ f(Rif(rM,t+1)) Zt are instruments Estimation by OLS:

ri,t+1 = i + (0i+1iZt+f(Rif(rM,t+1)) rM,t+1+i,t+1 Extension: a four-factor model Large-cap (S&P-500) and small-cap stock returns, government and corporate bond yields EFM 2006/7 37 Data Monthly returns of 67 (mostly equity) funds in 1968-1990 Instruments (lagged, mean-adjusted):

30-day T-bill rate Dividend yield Term spread Default spread January dummy EFM 2006/7 38 Results 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 Conditional alphas are higher than the unconditional ones EFM 2006/7 39 Results (cont.) 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 EFM 2006/7 40 Results (cont.) Table 4, conditional vs unconditional market timing model for nave strategies Nave strategies: Start with 65% large-cap, 13% small-cap, 20% gvt bonds, 2% corporate bonds 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 Conditional approach: insignificant alpha and gamma EFM 2006/7 41 Results (cont.) 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 tstats 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 EFM 2006/7 42 Interpretation of the results Dynamic strategies based on instruments contribute negatively to fund returns Is it the active policy or mechanical

effects? The underlying assets may have gammas different from zero Yet, we do not observe similar (,,f(R) 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 EFM 2006/7 43 Conclusions

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 Both selection and timing ability EFM 2006/7 44 Bollen and Busse (2001) "On the timing ability of mutual fund managers"

Using daily returns in market timing tests Much higher power if managers time the market on a daily basis Traditional tests: 40% of funds have f(R>0, 28% have f(R<0 Cf: 33% +, 5% - based on monthly data Compare fund f(Rs with those for synthetic portfolios (f(RB): 1/3 of funds have f(R>f(RB, 1/3 have f(R

Strategic behavior Plan for today Up to now: Average performance Selection vs timing ability Unconditional vs conditional Differential performance Performance persistence Today: Strategic behavior of fund managers

Choice of risk in the annual tournaments EFM 2006/7 47 The objective function of MF manager Career concerns High (low) performance leads to promotion (dismissal) High risk increases the probability of dismissal 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 Managers are usually evaluated at the end of the year Investors pay more attention to calendar year performance EFM 2006/7 48 Chevalier and Ellison (1997) "Risk Taking by Mutual Funds as a Response to Incentives" Estimate the shape of the flowperformance relationship Separately for young and old funds Estimate resulting risk-taking

incentives Examine the actual change in riskiness of funds portfolios On the basis of portfolio holdings in September and December EFM 2006/7 49 Data 449 growth and growth&income funds in 1982-92 Monthly returns Annual TNA

Portfolio holdings in September and December 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<$10 mln) and youngest (age < 2y) funds EFM 2006/7 50 The flow-performance relationship Flowt = TNATNAt/TNAt-1 Rt Net relative growth in funds assets

Semi-parametric regression of annual flows on last-year market-adjusted returns: Flowi,t+1=kf(RkAgeDkf(Ri,t-RM,t)+kkAgeDk+1(Ri,t-1RM,t-1) +2(Ri,t-2-RM,t2)+4IndFlowi,t+1+5ln(TNA)i,t+i,t+1 f(Ri,t-RM,t) is a non-parametric function estimated separately for young (2-5y) and old funds AgeDk are dummy variables for various age categories Funds size and growth in total TNA of equity funds are controls EFM 2006/7 51 Results Figures 1-2, Table 2: flow-performance relationship for young and old funds Generally convex shape

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 EFM 2006/7 52 Estimation of risktaking incentives 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: hk(rsep, , TNA)=E[f(Rk(f(Rsep+u)-f(Rsep+v))] After increasing nonsystematic risk by TNA, the lastquarter return distribution changes from u to v Take TNA=0.5 EFM 2006/7 53 Results 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 Insignificant pattern for old funds EFM 2006/7 54 Actual risk-taking in response to estimated risk incentives 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% Risk measures computed based on prior-year daily stock data EFM 2006/7 55 Actual risk-taking in response to estimated risk incentives Dependent variable: change between September and December in St deviation of the market-adjusted return: TNASD(Ri-RM) Unsystematic risk: TNASD(Ri-iRM)

Systematic risk: TNA|i-1| Independent variables: RiskIncentive: hk Size: ln(TNA) RiskIncentive*ln(TNA) September risk level: to control for mean reversion EFM 2006/7 56 Results

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 EFM 2006/7 57 Actual risk-taking in response to interim performance Dependent variable: change between September and December in total risk

Main independent variable: January-September market-adjusted return: Ri,sep-RM,sep Assume that change in risk is a piecewise linear function of interim performance 2 fitted kink points Estimate separately for young and old funds EFM 2006/7 58 Results

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: Using monthly returns: (Oct-Dec)-(Jan-Sep) Very noisy, esp for last quarter (only 3 points!) Table 6, Figure 5 Generally positive (!) relation between actual change in total risk and interim performance EFM 2006/7

59 Conclusions The flow-performance relationship is convex This generates strategic risk-taking incentives during the year Mutual funds seem to respond to these incentives The change in funds risk (measured via portfolio) is negatively related to its interim performance Though contradictory evidence based on returnbased approach EFM 2006/7

60 Brown, Harlow, and Starks (1996) "Of tournaments and temptations: An analysis of managerial incentives in the MF industry" Contingency table approach: Sort funds by mid-year return and within-year change in total risk Risk-adjustment ratio based on monthly returns: (7:12)/ (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 1980-1991 Support the tournament hypothesis

EFM 2006/7 61 Busse (2001) "Another look at mutual fund tournaments" Same contingency table approach using daily and monthly data Disaggregate: annual tournaments Control for cross-correlation and autocorrelation in fund returns Compute p-values from bootstrap No significant evidence for the tournament hypothesis! EFM 2006/7

62 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 Portfolio-based approach: Using portfolio holdings data EFM 2006/7

63 Methodology 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 t1 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 EFM 2006/7 64 Methodology (cont.)

Decomposing funds return: R = CS + CT + AS Characteristic selectivity: CS=jwj,t-1[Rj,t-Rt(bj,t-1)] wj,t-1 is last-quarter weight of stock j in the funds portfolio Rt(bj,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 Characteristic timing: CT=j[wj,t-1Rt(bj,t-1)-wj,t-5Rt(bj,t5)] CT is higher if the fund increases the factors exposure when its premium rises Average style: AS=jwj,t-5Rt(bj,t-5)

AS measures tendency to hold stocks with certain characteristics EFM 2006/7 65 Methodology (cont.) Comparing with return-based approach: Potentially higher power: no need to estimate factor loadings But: may be biased due to windowdressing But: only equity portion of funds portfolio EFM 2006/7 66

Data 1788 diversified equity US funds in 1975-94 CRSP: monthly returns, annual turnover, expense ratios, and TNA CDA: quarterly portfolio holdings (only equity portion) No survivor bias CRSP files of US stocks EFM 2006/7 67 Results

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! EFM 2006/7

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

EFM 2006/7 69