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Эффективные рынки

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Эффективные рынки

  1. 1. Mutual funds: performance evaluation
  2. 2. Worldwide TNA of mutual funds
  3. 3. Worldwide # mutual funds
  4. 4. Open-end mutual funds <ul><li>Active vs passive (index) funds </li></ul><ul><li>Obliged to buy/sell shares at NAV </li></ul><ul><ul><li>Net Asset Value = Total Net Assets (TNA) per share </li></ul></ul><ul><li>Part of the fund family (run by one management company) </li></ul><ul><li>Management fee: </li></ul><ul><ul><li>Asset-based: proportional to TNA </li></ul></ul><ul><ul><li>Performance-based: must be symmetric around the benchmark </li></ul></ul>
  5. 5. MF categories (by Morningstar) <ul><li>Broad asset class : </li></ul><ul><ul><li>Domestic: equity vs bond vs money market vs hybrid </li></ul></ul><ul><ul><li>International: foreign, world (global), Europe, Pacific, etc. </li></ul></ul><ul><li>(Stated) investment objective </li></ul><ul><ul><li>Equity: aggressive growth, growth, growth&income, equity-income, income </li></ul></ul><ul><ul><li>Bond: government, municipal, corporate </li></ul></ul><ul><ul><li>Hybrid: balanced, asset allocation </li></ul></ul><ul><li>(Estimated) investment style : 3x3 matrix </li></ul><ul><ul><li>Equity: large/mid/small-cap – value/blend/growth </li></ul></ul><ul><ul><li>Bonds: high/medium/low credit quality – short/intermediate/long duration </li></ul></ul>
  6. 6. TNA of US mutual funds
  7. 7. # US mutual funds
  8. 8. Benefits of investing via MF <ul><li>Low transaction costs </li></ul><ul><ul><li>Easy way to buy a diversified portfolio </li></ul></ul><ul><li>Customer services </li></ul><ul><ul><li>Liquidity insurance </li></ul></ul><ul><ul><li>Easy transfer across funds within the family </li></ul></ul><ul><li>Professional management </li></ul><ul><ul><li>Selecting right stocks at right time? </li></ul></ul><ul><li>The objective of the research: </li></ul><ul><ul><li>Check the validity of these claims </li></ul></ul>
  9. 9. Research questions <ul><li>Why has it become one of the largest financial intermediaries? </li></ul><ul><li>Why are there more mutual funds than stocks? </li></ul><ul><li>How to measure fund performance adjusted for risk? </li></ul><ul><li>Does fund performance persist? </li></ul><ul><li>How do investors choose between funds? </li></ul><ul><li>Which incentives does it give to fund managers? </li></ul><ul><li>How accurately do categories divide funds? </li></ul>
  10. 10. How to measure MF performance? <ul><li>Raw return , determined by </li></ul><ul><ul><li>Risk factors </li></ul></ul><ul><ul><li>Factor exposures </li></ul></ul><ul><ul><ul><li>Timing ability: changing beta at right time </li></ul></ul></ul><ul><ul><li>Selection (stock-picking) ability </li></ul></ul><ul><ul><ul><li>Choosing right stocks (for same level of risk) </li></ul></ul></ul>
  11. 11. How to measure MF performance? <ul><li>Risk-adjusted return : </li></ul><ul><ul><li>Difference between fund i ’s return and benchmark return </li></ul></ul><ul><ul><li>Benchmark: passive portfolio with same risk as fund i </li></ul></ul><ul><li>How to find a right benchmark? </li></ul><ul><ul><li>Return-based approach: estimate based on past returns </li></ul></ul><ul><ul><li>Portfolio-based approach: construct a portfolio of assets similar to those held by the fund </li></ul></ul><ul><ul><li>Relative approach: compare to performance of other funds </li></ul></ul>
  12. 12. Factor models <ul><li>Regression of excess asset returns on factor returns </li></ul><ul><li>R i,t –R F,t = α i + Σ k β i,k F k,t + ε t , </li></ul><ul><ul><li>Market model: RMRF </li></ul></ul><ul><ul><li>Fama-French: RMRF, SMB, HML </li></ul></ul><ul><ul><li>Carhart: RMRF, SMB, HML, MOM (1y momentum) </li></ul></ul><ul><ul><li>Elton-Gruber: RMRF, SMB, HML, excess bond index return </li></ul></ul><ul><li>Jensen’s alpha : </li></ul><ul><ul><li>Shows whether fund i outperforms passive portfolio of K factors and R F </li></ul></ul>
  13. 13. Mean-variance spanning tests <ul><li>Test whether adding K new assets (MFs) to N old assets leads to the shift of the MV frontier: </li></ul><ul><ul><li>Three cases possible: spanning, intersection, shift </li></ul></ul><ul><li>Regression of new asset returns r (Kx1) on old asset returns R (Nx1): </li></ul><ul><li>r t = α + BR t + ε t </li></ul><ul><ul><li>Generalized Jensen’s alpha </li></ul></ul><ul><li>Test for intersection: there exists η s.t. α - η ( l N -B l K )=0 </li></ul><ul><li>Test for spanning: α =0 and B l K = l N </li></ul><ul><ul><li>All additional assets can be written as portfolio of old assets </li></ul></ul>
  14. 14. Other absolute ordinal measures <ul><li>Sharpe ratio: (E(R i )-R F )/σ i </li></ul><ul><li>Treynor ratio: (E(R i )-R F )/ β i </li></ul><ul><li>Appraisal ratio: α i / σ ( ε ) i </li></ul><ul><ul><li>Called Treynor-Black ratio when alpha based on market model </li></ul></ul>
  15. 15. Relative performance measures <ul><li>Use funds in the same category as a benchmark </li></ul><ul><li>Ordinal measures: difference with the mean or median return in the fund’s category </li></ul><ul><li>Cardinal measures: category ranking based on return/ α /… </li></ul><ul><li>Drawbacks: </li></ul><ul><ul><li>There may be substantial differences in risk within the category </li></ul></ul><ul><ul><li>Survivor bias </li></ul></ul><ul><ul><li>Bad incentives to managers (as in a tournament) </li></ul></ul>
  16. 16. How to measure performance persistence? <ul><li>Contingency tables: </li></ul><ul><ul><li>Sort funds by past and current performance </li></ul></ul><ul><ul><ul><li>E.g., 2x2 (above/below median): winner-winner, WL, LW, LL </li></ul></ul></ul><ul><ul><li>Check whether actual frequencies are far from those under the null </li></ul></ul><ul><li>Examine zero-investment portfolios formed on the basis of past performance </li></ul><ul><ul><li>Sort funds into deciles by last-year return </li></ul></ul><ul><ul><li>Test whether top-bottom portfolio has premium unexplained by factor models </li></ul></ul><ul><li>Cross-sectional regressions of current performance on past performance </li></ul>
  17. 17. Need to control for <ul><li>Fund attrition </li></ul><ul><ul><li>Survivor bias </li></ul></ul><ul><li>Cross-correlation in fund returns </li></ul><ul><ul><li>Fewer degrees of freedom will make s.e. larger </li></ul></ul><ul><li>The measurement error (and mean reversion) </li></ul><ul><ul><li>If measure both current and past performance in the same way </li></ul></ul>
  18. 18. Brown and Goetzmann (1995) <ul><li>&quot;Mutual fund performance persistence &quot; </li></ul><ul><li>Explore MF performance persistence </li></ul><ul><ul><li>Absolute vs relative benchmarks </li></ul></ul><ul><ul><li>Explicitly model survivor bias </li></ul></ul><ul><ul><li>Disaggregate on the annual basis </li></ul></ul>
  19. 19. Data <ul><li>Common stock funds in 1976-1988 </li></ul><ul><ul><li>Including dead funds </li></ul></ul><ul><ul><li>Monthly return data </li></ul></ul><ul><li>Table 1 </li></ul><ul><ul><li># funds: 372 in 1976, 829 in 1988 </li></ul></ul><ul><ul><li>Total assets rose more than 4 times </li></ul></ul><ul><ul><li>MaxCap category became relatively less popular </li></ul></ul>
  20. 20. Average performance <ul><li>Table 2 </li></ul><ul><ul><li>VW mean MF return is below S&P500 return by 0.4% p.a., though above index fund </li></ul></ul><ul><ul><li>Dead funds heavily underperform living funds </li></ul></ul><ul><ul><li>EW means exceed VW means </li></ul></ul>
  21. 21. Fund disappearance <ul><li>Disappearance: termination or merging into another fund </li></ul><ul><li>Table 3, determinants of prob(death) </li></ul><ul><ul><li>Lagged relative return: - </li></ul></ul><ul><ul><li>Lagged relative new money: - </li></ul></ul><ul><ul><ul><li>But insignificant in presence of past performance </li></ul></ul></ul><ul><ul><li>Relative size: - </li></ul></ul><ul><ul><li>Expense ratio: + </li></ul></ul><ul><ul><li>Age: - </li></ul></ul>
  22. 22. Performance persistence <ul><li>Contingency tables: </li></ul><ul><ul><li>Sort funds by performance over the last year and the current year </li></ul></ul><ul><ul><li>Winner/loser = above/below median, 2x2 matrix </li></ul></ul><ul><ul><li>Cross-product ratio: (WW*LL)/(WL*LW)=1 under the null </li></ul></ul>
  23. 23. Bootstrapping procedure <ul><li>Necessary to control for fund attrition and cross-correlation: </li></ul><ul><ul><li>Use de-meaned sample of fund monthly returns in 1987-88 </li></ul></ul><ul><ul><li>For each year, select N funds without replacement and randomize over time </li></ul></ul><ul><ul><li>Assume that poorest performers after the first year are eliminated </li></ul></ul><ul><ul><li>Repeat 100 times </li></ul></ul>
  24. 24. Results <ul><li>Table 4, odds ratio test for raw returns relative to median </li></ul><ul><ul><li>7 years: significant positive persistence </li></ul></ul><ul><ul><li>2 years: significant negative persistence </li></ul></ul>
  25. 25. Controlling for differences in systematic risk <ul><li>Use several risk-adjusted performance measures: </li></ul><ul><ul><li>Jensen’s alpha from the market model </li></ul></ul><ul><ul><li>One-index / three-index appraisal ratio </li></ul></ul><ul><ul><li>Style-adjusted return </li></ul></ul><ul><li>Table 6, odds ratio test for risk-adjusted returns relative to median </li></ul><ul><ul><li>Similar results: 5-7 years +, 2 years - persistence </li></ul></ul>
  26. 26. Absolute benchmarks <ul><li>Figure 1, frequencies of repeat losers and winners wrt S&P500 </li></ul><ul><ul><li>Repeat-losers dominate in the second half of the sample period </li></ul></ul><ul><li>Table 6, odds ratio test for alpha relative to 0 </li></ul><ul><ul><li>5 years +, 2 years - persistence </li></ul></ul>
  27. 27. Investment implications <ul><li>Table 7, performance of last-year return octile portfolios </li></ul><ul><ul><li>Past winners perform better than past losers </li></ul></ul><ul><ul><ul><li>Winner-loser portfolio generates significant performance </li></ul></ul></ul><ul><ul><li>Idiosyncratic risk is the highest for past winners </li></ul></ul><ul><ul><ul><li>Winner-loser portfolio return is mostly due to bad performance of persistent losers </li></ul></ul></ul>
  28. 28. Conclusions <ul><li>Past performance is the strongest predictor of fund attrition </li></ul><ul><li>Clear evidence of relative performance persistence </li></ul><ul><li>Performance persistence is strongly dependent on the time period </li></ul><ul><li>Need to find common mgt strategies explaining persistence and reversals </li></ul><ul><ul><li>Additional risk factor(s) </li></ul></ul><ul><ul><li>Conditional approach </li></ul></ul>
  29. 29. Conclusions (cont.) <ul><li>Chasing the winners is a risky strategy </li></ul><ul><li>Selling the losers makes sense </li></ul><ul><ul><li>Why don’t all shareholders of poorly performing funds leave? </li></ul></ul><ul><ul><ul><li>Disadvantaged clientele </li></ul></ul></ul><ul><ul><li>Arbitrageurs can’t short-sell losing MFs! </li></ul></ul>
  30. 30. Carhart (1997) <ul><li>&quot; On persistence in mutual fund performance &quot; </li></ul><ul><li>Survivor-bias free sample </li></ul><ul><li>Examine portfolios ranked by lagged 1-year return </li></ul><ul><ul><li>The four-factor model: RMRF, SMB, HML, and 1-year momentum… </li></ul></ul><ul><ul><li>Explains most of the return unexplained by CAPM… </li></ul></ul><ul><ul><li>Except for underperformance of the worst funds </li></ul></ul><ul><li>Fama-MacBeth cross-sectional regressions of alphas on current fund characteristics: </li></ul><ul><ul><li>Expense ratio, turnover, and load: negative effect </li></ul></ul>
  31. 31. Conditional performance evaluation
  32. 32. Plan for today <ul><li>Up to now: </li></ul><ul><ul><li>Average performance </li></ul></ul><ul><ul><ul><li>Jensen’s alpha: selection ability </li></ul></ul></ul><ul><ul><li>Differential performance </li></ul></ul><ul><ul><ul><li>Performance persistence </li></ul></ul></ul><ul><li>Today: </li></ul><ul><ul><li>Conditional approach to performance evaluation </li></ul></ul><ul><ul><ul><li>Timing ability </li></ul></ul></ul><ul><ul><ul><li>Use dynamic strategies based on public info as a benchmark </li></ul></ul></ul>
  33. 33. Problems with the unconditional approach <ul><li>The market model (with excess returns): </li></ul><ul><li>r i,t = α i + β i r M,t + ε i,t </li></ul><ul><ul><li>What if β is correlated with the market return? </li></ul></ul><ul><ul><li>If cov(β, r M )>0, the estimated α is downward-biased! </li></ul></ul><ul><li>How to measure timing ability? </li></ul>
  34. 34. Market timing tests <ul><li>Assume that β t = β 0 + γf(R M -R F ) </li></ul><ul><ul><li>Treynor-Mazuy : linear function, f(·)=R M -R F </li></ul></ul><ul><ul><li>Merton-Henriksson : step function, f( · )=I{ R M -R F >0} </li></ul></ul><ul><ul><li>γ shows whether fund managers can time the market </li></ul></ul><ul><li>Typical results for an average fund </li></ul><ul><ul><li>Negative alpha: no selection ability </li></ul></ul><ul><ul><li>Negative gamma: no timing ability </li></ul></ul>
  35. 35. Problems with measuring market timing <ul><li>Benchmark assets may have option-like characteristics </li></ul><ul><ul><li>Gamma is positive/negative for some stocks </li></ul></ul><ul><li>Managers may have timing ability at higher horizon </li></ul><ul><ul><li>Tests using monthly data have low power of identifying market timing on a daily basis </li></ul></ul><ul><li>Positive covariance between beta and market return could result from using public info </li></ul>
  36. 36. Ferson and Schadt (1996) <ul><li>&quot;Measuring Fund Strategy and Performance in Changing Economic Conditions&quot; </li></ul><ul><li>Evaluate MF performance using conditional approach </li></ul><ul><ul><li>Both selection and timing ability </li></ul></ul><ul><ul><li>Use dynamic strategies based on public info as a benchmark </li></ul></ul><ul><ul><ul><li>Consistent with SSFE </li></ul></ul></ul>
  37. 37. Methodology <ul><li>Conditional market model: </li></ul><ul><li>r i,t+1 = α i + β i,t r M,t+1 + ε i,t+1 , </li></ul><ul><ul><li>where β i,t = β 0i + β’ 1i Z t (+ γ i f(r M,t+1 )) </li></ul></ul><ul><ul><li>Z t are instruments </li></ul></ul><ul><li>Estimation by OLS: </li></ul><ul><li>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 </li></ul><ul><li>Extension: a four-factor model </li></ul><ul><ul><li>Large-cap (S&P-500) and small-cap stock returns, government and corporate bond yields </li></ul></ul>
  38. 38. Data <ul><li>Monthly returns of 67 (mostly equity) funds in 1968-1990 </li></ul><ul><li>Instruments (lagged, mean-adjusted): </li></ul><ul><ul><li>30-day T-bill rate </li></ul></ul><ul><ul><li>Dividend yield </li></ul></ul><ul><ul><li>Term spread </li></ul></ul><ul><ul><li>Default spread </li></ul></ul><ul><ul><li>January dummy </li></ul></ul>
  39. 39. Results <ul><li>Table 2, conditional vs unconditional CAPM </li></ul><ul><ul><li>Market betas are related to conditional information </li></ul></ul><ul><ul><ul><li>30-day T-bill rate, dividend yield, and term spread are significant </li></ul></ul></ul><ul><ul><li>Conditional alphas are higher than the unconditional ones </li></ul></ul>
  40. 40. Results (cont.) <ul><li>Table 3, cross-sectional distribution of t-stats for cond. and uncond. alphas </li></ul><ul><ul><li>Unconditional approach: there are more significantly negative alphas </li></ul></ul><ul><ul><li>Conditional approach: # significantly negative / positive alphas is similar </li></ul></ul><ul><ul><li>Very similar results for one-factor and four-factor models </li></ul></ul>
  41. 41. Results (cont.) <ul><li>Table 4, conditional vs unconditional market timing model for naïve strategies </li></ul><ul><ul><li>Naïve strategies: </li></ul></ul><ul><ul><ul><li>Start with 65% large-cap, 13% small-cap, 20% gvt bonds, 2% corporate bonds weights </li></ul></ul></ul><ul><ul><ul><li>Then: buy-and-hold / annual rebalancing / fixed weights </li></ul></ul></ul><ul><ul><li>Unconditional approach: positive alpha and negative gamma for buy-and-hold strategy </li></ul></ul><ul><ul><ul><li>Evidence of model misspecification </li></ul></ul></ul><ul><ul><li>Conditional approach: insignificant alpha and gamma </li></ul></ul>
  42. 42. Results (cont.) <ul><li>Tables 5-6, conditional vs unconditional market timing models for actual data </li></ul><ul><ul><li>Conditional approach: the significance of alpha and gamma disappears for all categories but special (concentrating on intl investments) </li></ul></ul><ul><li>Table 7, cross-sectional distribution of t-stats for cond. and uncond. gammas </li></ul><ul><ul><li>Fewer (significantly) negative gammas under the conditional approach </li></ul></ul><ul><ul><li>More (significantly) positive gammas under the conditional approach, esp. for TM model </li></ul></ul>
  43. 43. Interpretation of the results <ul><li>Dynamic strategies based on instruments contribute negatively to fund returns </li></ul><ul><li>Is it the active policy or mechanical effects? </li></ul><ul><ul><li>The underlying assets may have gammas different from zero </li></ul></ul><ul><ul><ul><li>Yet, we do not observe similar (α,β,γ) patters for the buy-and-hold portfolio </li></ul></ul></ul><ul><ul><li>New money flows to funds increase their cash holdings and lower betas </li></ul></ul><ul><ul><ul><li>Edelen (1999): liquidity-motivated trading lowers both alpha and gamma </li></ul></ul></ul>
  44. 44. Conclusions <ul><li>Conditioning on public information: </li></ul><ul><ul><li>Provides additional insights about fund strategies </li></ul></ul><ul><ul><li>Allows to estimate classical performance measures more precisely </li></ul></ul><ul><li>The average MF performance is no longer inferior </li></ul><ul><ul><li>Both selection and timing ability </li></ul></ul>
  45. 45. Bollen and Busse (2001) <ul><li>&quot; On the timing ability of mutual fund managers &quot; </li></ul><ul><li>Using daily returns in market timing tests </li></ul><ul><ul><li>Much higher power if managers time the market on a daily basis </li></ul></ul><ul><li>Traditional tests: </li></ul><ul><ul><li>40% of funds have γ >0, 28% have γ <0 </li></ul></ul><ul><ul><ul><li>Cf: 33% +, 5% - based on monthly data </li></ul></ul></ul><ul><li>Compare fund γ ’s with those for synthetic portfolios ( γ B ): </li></ul><ul><ul><li>1/3 of funds have γ > γ B , 1/3 have γ < γ B </li></ul></ul>
  46. 46. Strategic behavior
  47. 47. Plan for today <ul><li>Up to now: </li></ul><ul><ul><li>Average performance </li></ul></ul><ul><ul><ul><li>Selection vs timing ability </li></ul></ul></ul><ul><ul><ul><li>Unconditional vs conditional </li></ul></ul></ul><ul><ul><li>Differential performance </li></ul></ul><ul><ul><ul><li>Performance persistence </li></ul></ul></ul><ul><li>Today: </li></ul><ul><ul><li>Strategic behavior of fund managers </li></ul></ul><ul><ul><ul><li>Choice of risk in the annual tournaments </li></ul></ul></ul>
  48. 48. The objective function of MF manager <ul><li>Career concerns </li></ul><ul><ul><li>High (low) performance leads to promotion (dismissal) </li></ul></ul><ul><ul><li>High risk increases the probability of dismissal </li></ul></ul><ul><li>Compensation </li></ul><ul><ul><li>Usually proportional to the fund’s size (and flows) </li></ul></ul><ul><ul><li>Convex relation between flows and performance gives strong incentives to win the MF tournament </li></ul></ul><ul><li>Calendar-year performance is esp important </li></ul><ul><ul><li>Managers are usually evaluated at the end of the year </li></ul></ul><ul><ul><li>Investors pay more attention to calendar year performance </li></ul></ul>
  49. 49. Chevalier and Ellison (1997) <ul><li>&quot; Risk Taking by Mutual Funds as a Response to Incentives &quot; </li></ul><ul><li>Estimate the shape of the flow-performance relationship </li></ul><ul><ul><li>Separately for young and old funds </li></ul></ul><ul><li>Estimate resulting risk-taking incentives </li></ul><ul><li>Examine the actual change in riskiness of funds’ portfolios </li></ul><ul><ul><li>On the basis of portfolio holdings in September and December </li></ul></ul>
  50. 50. Data <ul><li>449 growth and growth&income funds in 1982-92 </li></ul><ul><ul><li>Monthly returns </li></ul></ul><ul><ul><li>Annual TNA </li></ul></ul><ul><ul><li>Portfolio holdings in September and December </li></ul></ul><ul><ul><ul><li>About 92% of the portfolio matched to CRSP data </li></ul></ul></ul><ul><li>Excluding index, closed, primarily institutional, merged in the current year, high expense ratio (>4%), smallest (TNA<$10 mln) and youngest (age < 2y) funds </li></ul>
  51. 51. The flow-performance relationship <ul><li>Flow t = ΔTNA t /TNA t-1 – R t </li></ul><ul><ul><li>Net relative growth in fund’s assets </li></ul></ul><ul><li>Semi-parametric regression of annual flows on last-year market-adjusted returns: </li></ul><ul><li>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 </li></ul><ul><ul><li>f(R i,t -R M,t ) is a non-parametric function estimated separately for young (2-5y) and old funds </li></ul></ul><ul><ul><li>AgeD k are dummy variables for various age categories </li></ul></ul><ul><ul><li>Fund’s size and growth in total TNA of equity funds are controls </li></ul></ul>
  52. 52. Results <ul><li>Figures 1-2, Table 2: flow-performance relationship for young and old funds </li></ul><ul><ul><li>Generally convex shape </li></ul></ul><ul><ul><ul><li>Linearity is rejected, esp for old funds </li></ul></ul></ul><ul><ul><li>The sensitivity of flows to performance is higher for young funds </li></ul></ul><ul><ul><li>Flows rise with lagged performance up to 3 years, current category flows and fall with size </li></ul></ul>
  53. 53. Estimation of risk-taking incentives <ul><li>Assume: </li></ul><ul><ul><li>Fees are proportional to the fund’s assets </li></ul></ul><ul><ul><li>Flows occur at the end of the year </li></ul></ul><ul><ul><li>No agency problems between MF companies and their managers </li></ul></ul><ul><li>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: </li></ul><ul><li>h k (r sep , σ , Δσ )=E[ γ k (f(R sep + u )-f(R sep + v ))] </li></ul><ul><ul><li>After increasing nonsystematic risk by Δσ , the last-quarter return distribution changes from u to v </li></ul></ul><ul><ul><li>Take Δσ =0.5 σ </li></ul></ul>
  54. 54. Results <ul><li>Figure 3, risk incentives for 2y and 11y funds </li></ul><ul><ul><li>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) </li></ul></ul><ul><ul><ul><li>The risk incentives are reversed at the extreme performance </li></ul></ul></ul><ul><ul><li>Insignificant pattern for old funds </li></ul></ul>
  55. 55. Actual risk-taking in response to estimated risk incentives <ul><li>Cross-sectional regressions of within-year change in risk on risk incentive measure </li></ul><ul><li>Focus on the equity portion of funds’ portfolios (on average, about 90% </li></ul><ul><ul><li>Risk measures computed based on prior-year daily stock data </li></ul></ul>
  56. 56. Actual risk-taking in response to estimated risk incentives <ul><li>Dependent variable: change between September and December in </li></ul><ul><ul><li>St deviation of the market-adjusted return: Δ SD(R i -R M ) </li></ul></ul><ul><ul><li>Unsystematic risk: Δ SD(R i -β i R M ) </li></ul></ul><ul><ul><li>Systematic risk: Δ| β i -1| </li></ul></ul><ul><li>Independent variables: </li></ul><ul><ul><li>RiskIncentive: h k </li></ul></ul><ul><ul><li>Size: ln(TNA) </li></ul></ul><ul><ul><li>RiskIncentive*ln(TNA) </li></ul></ul><ul><ul><li>September risk level: to control for mean reversion </li></ul></ul>
  57. 57. Results <ul><li>Table 4 </li></ul><ul><ul><li>The higher risk incentives, the higher actual change in total and unsystematic risk </li></ul></ul><ul><ul><li>This effect becomes less important for larger funds </li></ul></ul><ul><ul><li>No evidence of mean reversion </li></ul></ul>
  58. 58. Actual risk-taking in response to interim performance <ul><li>Dependent variable: change between September and December in total risk </li></ul><ul><li>Main independent variable: </li></ul><ul><ul><li>January-September market-adjusted return: R i,sep -R M,sep </li></ul></ul><ul><li>Assume that change in risk is a piecewise linear function of interim performance </li></ul><ul><ul><li>2 fitted kink points </li></ul></ul><ul><li>Estimate separately for young and old funds </li></ul>
  59. 59. Results <ul><li>Table 5, Figure 4 </li></ul><ul><ul><li>Generally negative relation between actual change in total risk and interim performance </li></ul></ul><ul><ul><li>Most slopes and kink points are not significant </li></ul></ul><ul><li>Alternative approach to measure total risk: </li></ul><ul><ul><li>Using monthly returns: σ (Oct-Dec)- σ (Jan-Sep) </li></ul></ul><ul><ul><ul><li>Very noisy, esp for last quarter (only 3 points!) </li></ul></ul></ul><ul><li>Table 6, Figure 5 </li></ul><ul><ul><li>Generally positive (!) relation between actual change in total risk and interim performance </li></ul></ul>
  60. 60. Conclusions <ul><li>The flow-performance relationship is convex </li></ul><ul><li>This generates strategic risk-taking incentives during the year </li></ul><ul><li>Mutual funds seem to respond to these incentives </li></ul><ul><li>The change in fund’s risk (measured via portfolio) is negatively related to its interim performance </li></ul><ul><ul><li>Though contradictory evidence based on return-based approach </li></ul></ul>
  61. 61. Brown, Harlow, and Starks (1996) <ul><li>&quot; Of tournaments and temptations: An analysis of managerial incentives in the MF industry &quot; </li></ul><ul><li>Contingency table approach: </li></ul><ul><ul><li>Sort funds by mid-year return and within-year change in total risk </li></ul></ul><ul><ul><ul><li>Risk-adjustment ratio based on monthly returns: σ (7:12)/ σ (1:6) </li></ul></ul></ul><ul><ul><li>2x2 matrix: return/RAR above/below median </li></ul></ul><ul><ul><li>Each cell should have 25% of funds under the null </li></ul></ul><ul><li>Find 27% frequency of high-return low-RAR funds in 1980-1991 </li></ul><ul><ul><li>Support the tournament hypothesis </li></ul></ul>
  62. 62. Busse (2001) <ul><li>&quot; Another look at mutual fund tournaments &quot; </li></ul><ul><li>Same contingency table approach using daily and monthly data </li></ul><ul><ul><li>Disaggregate: annual tournaments </li></ul></ul><ul><li>Control for cross-correlation and auto-correlation in fund returns </li></ul><ul><ul><li>Compute p-values from bootstrap </li></ul></ul><ul><li>No significant evidence for the tournament hypothesis! </li></ul>
  63. 63. Wermers (2000) <ul><li>&quot; MF performance: An empirical decomposition into stock-picking talent, style, transactions costs, and expenses &quot; </li></ul><ul><li>Decompose fund’s return into several components to analyze the value of active fund management </li></ul><ul><li>Portfolio-based approach : </li></ul><ul><ul><li>Using portfolio holdings data </li></ul></ul>
  64. 64. Methodology <ul><li>Finding the benchmark: one of 125 portfolios </li></ul><ul><ul><li>In June of each year t, rank stocks by size (current ME) and form 5 quintile portfolios </li></ul></ul><ul><ul><li>Subdivide each of 5 size portfolios into 5 portfolios based on BE/ME as of December of t-1 </li></ul></ul><ul><ul><li>Subdivide each of 25 size-BM portfolios into 5 portfolios based on past 12m return </li></ul></ul><ul><ul><li>From July of t to June of t+1, compute monthly VW returns of 125 portfolios </li></ul></ul>
  65. 65. Methodology (cont.) <ul><li>Decomposing fund’s return: R = CS + CT + AS </li></ul><ul><ul><li>Characteristic selectivity: CS= Σ j w j,t-1 [R j,t -R t (b j,t-1 )] </li></ul></ul><ul><ul><ul><li>w j,t-1 is last-quarter weight of stock j in the fund’s portfolio </li></ul></ul></ul><ul><ul><ul><li>R t (b j,t-1 ) is current return on the benchmark ptf matched to stock j in quarter t-1 </li></ul></ul></ul><ul><ul><ul><li>CS measures the fund’s return adjusted for 3 characteristics </li></ul></ul></ul><ul><ul><li>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 )] </li></ul></ul><ul><ul><ul><li>CT is higher if the fund increases the factor’s exposure when its premium rises </li></ul></ul></ul><ul><ul><li>Average style: AS=Σ j w j,t-5 R t (b j,t-5 ) </li></ul></ul><ul><ul><ul><li>AS measures tendency to hold stocks with certain characteristics </li></ul></ul></ul>
  66. 66. Methodology (cont.) <ul><li>Comparing with return-based approach: </li></ul><ul><ul><li>Potentially higher power: no need to estimate factor loadings </li></ul></ul><ul><ul><li>But: may be biased due to window-dressing </li></ul></ul><ul><ul><li>But: only equity portion of fund’s portfolio </li></ul></ul>
  67. 67. Data <ul><li>1788 diversified equity US funds in 1975-94 </li></ul><ul><ul><li>CRSP: monthly returns, annual turnover, expense ratios, and TNA </li></ul></ul><ul><ul><li>CDA: quarterly portfolio holdings (only equity portion) </li></ul></ul><ul><ul><li>No survivor bias </li></ul></ul><ul><li>CRSP files of US stocks </li></ul>
  68. 68. Results <ul><li>Table 5, decomposition of (equity portion of) MF returns </li></ul><ul><ul><li>Gross return: 15.8% p.a. > 14.3% VW-CRSP index </li></ul></ul><ul><ul><li>CS = 0.75%, significant </li></ul></ul><ul><ul><li>CT = 0.02%, insignificant </li></ul></ul><ul><ul><li>AS = 14.8% </li></ul></ul><ul><ul><li>Expense ratio = 0.79%, up from 65 to 93 b.p. </li></ul></ul><ul><ul><li>Transactions costs = 0.8%, down from 140 to 48 b.p. </li></ul></ul><ul><ul><li>Non-equity portion of the fund’s portfolio: 0.4% </li></ul></ul><ul><ul><li>Net return: 13.8% < 14.3% VW-CRSP index! </li></ul></ul>
  69. 69. Mutual funds: summary <ul><li>Many funds hardly follow their stated objectives </li></ul><ul><li>On average, MFs do not earn positive performance adjusted for risk and expenses </li></ul><ul><li>Bad performance persists </li></ul><ul><li>Money flows are concentrated among funds with best performance </li></ul><ul><li>Poorly performing funds are not punished with large outflows </li></ul><ul><li>Funds try to win annual tournaments by adjusting risk </li></ul>

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