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Amihud and Goyenko

Mutual Fund’s R 2 as Predictor of Performance. PRMIA-CIRANO- Lunch Conference December 7, 2011. Amihud and Goyenko. Fund R 2 as predictor of performance. Motivation: Does selectivity enhance mutual fund performance?.

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Amihud and Goyenko

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  1. Mutual Fund’s R2 as Predictor of Performance PRMIA-CIRANO- Lunch Conference December 7, 2011 Amihud and Goyenko Fund R2 as predictor of performance

  2. Motivation: Does selectivity enhance mutual fund performance? • Cremers & Petajisto (2009): Active Share – the sum of absolute deviations of the fund’s portfolio from the benchmark portfolio – predicts alpha from a regression on the benchmark index. • Brand, Brown & Gallagher (2005) measure “active management” by a divergence index, the sum of squared deviations of the fund portfolio’s weights from the benchmark portfolio, using Australian data. The divergence index positively predicts fund performance • Daniel, Grinblatt, Titman and Wermers (1997): while securities that are picked by mutual funds outperform a characteristic-based benchmark, gains from stock picking approximately equal the funds’ average management fee. Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  3. Motivation • Kacperczyk, Sialm and Zheng (2005) find that funds exhibit better performance if they have greater industry concentration of holdings compared to the weights of these industries in a diversified portfolio • Kacperczyk and Seru (2007) find that funds whose stocks holdings are related to company-specific information different from analysts’ expectations exhibit better performance • Kacperczyk, Sialm and Zheng (2008) find that the higher return gap, the difference between the reported fund return and the return on a portfolio that invests in the previously disclosed fund holdings, predicts better subsequent performance Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  4. Motivation • These measures are hard to calculate, require a lot of data which are not readily available • Problem: Indexing vs Selectivity: if a fund puts x% in S&P500 and (1-x%) in, say, Russell 2000, (stating that its benchmark is S&P500), AS (CP, 2009) will classify it as "active" while it is not, it is just indexing • Require a well specified benchmark. CP(2009) : “Since 1998, the SEC has required each fund to report a benchmark index in its rospectus; however, this information is not part of any publicly available mutual fund database, and prior to 1998, it does not exist for all funds. These self-declared benchmarks might even lead to a bias: some funds could intentionally pick a misleading benchmark to increase their chances of beating the benchmark by a large margin, as discussed in Sensoy (2009).” • For active equity funds only! What if a fund also holds corporate bonds? (split benchmark!) Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  5. Motivation • Measuring active management by tracking error (Wermers 2003), the StdDev of S&P500-adjusted fund return. It is positively related to the contemporaneous fund alpha. But others find that tracking error does not predict performance (Cremers & Petajisto (2009)) • Omitted variable problem: for funds (not individual stocks), tracking error is a small % of the total volatility. The total volatility -- or systematic volatility -- is an omitted variable which is correlated with the tracking error Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  6. Our suggestion: • Use the fund’s R2 (from a regression on common factor) as a proxy measure of selectivity.Higher R2means greater indexation.Lower R2 means greater selectivity  better performance. Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  7. Preview of the Results • Lower R2 measures greater selectivity or active management and it significantly predicts higher fund performance. • Funds sorted into lowest-quintile lagged R2 and highest-quintile lagged alpha produce significant annual alpha of 2.4% or more • R2 also predicts performance of funds that hold corporate bonds Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  8. Methodology: Benchmark Models • Fama-French-Carhartfactors: RM-Rf, SMB, HML, UMD + Russell2000resids given the results of Cremers, Petajisto and Zitzewitz (2010) – (FFCR) • Four-factor model proposed by Cremers et al (2010) : S&P500 -Rf, Russell 2000 -S&P500, Russell 3000 value -Russell 3000 growth, and UMD – (CPZC) • Also standard four factor model (FFC) Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  9. Methodology: • R2 : calculated from semi-annual regressions of daily/weekly fund returns on the FFCR (CPZC) factor returns, contemporaneous and one-day lag (Dimson, 1979) (robustness: monthly, 24-month rolling window) • Performance measures: alpha andInfRatio = alpha/RMSE (Treynor-Black, 1973).Information Ratio gives the improvement in the Sharpe Ratio due to adding an asset (fund) to an investor’s efficient portfolio.SR2P= SR2M + [alphaA / RMSEA]2Greater InfRatio greater demand for the asset Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  10. Estimation model: • Performancey = b*TR2y-1 + control variables • TR2 = log[(√R2+c)/(1- √R2+c)] , • where c = 0.5/n, n being the sample size (Cox (1970, p. 33)). N=120 for the daily return estimation and 40 for weekly returns • Hypothesis:b < 0. Greater selectivity, or greater deviation from indexing  better performance Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  11. Control variables (all from previous half-year) (standard): *Expense ratio*Fund size (TNA) at the end of the year. (We use funds with TNA > $15m (Elton, Gruber & Blake, 1996)).*Turnover*Managerial Tenure*Age of the fund*alpha or InfRatio (skill)*Style dummies: (i) Aggressive Growth, (ii) Equity Income, (iii) Growth, (iv) Long term growth, (v) Growth and Income, (vi) Mid-Cap, (vii) Micro-Cap funds, (viii) Small cap, and (ix) Maximum Capital Gains Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  12. Sample and Data • Sample: actively-managed all-equity funds with identifiable objective. Excluded are funds with “Index” or abbreviation of common indexes in name. Funds with at least 70% holdings in common stocks • Data: 1990-2010. Earlier data are from Yale SOM’s database.CRSP data from 1999 2,460 funds, 42 periods (the test period is always 6 months), 37,198 fund-periods Required: at least 120 daily returns or 40 weekly returns in y-1 (estimation period)R2: We trim off the top and bottom 0.5%.Mean: 0.902, range: 0.270 to 0.995 Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  13. Fama-Macbeth (1973) regressions: sample 1990-2010 • FM regressions are similar to Carhart (1997) and Chen, Hong, Huang and Kubik (2004) Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  14. Daily Returns Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  15. Weekly Returns Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  16. Robustness and Economic Significance • Results for Untransformed R2 • daily returns, FFCR, coeff (R2t-1 )= ‑6.03 with t = 2.06, the weighted mean= ‑5.60 with t = 2.98 • Economic magnitudes: decline in R2 from 0.9 (the mean) to 0.8 leads to increase in alpha by an annual 0.60% (and 0.56% for the weighted mean). Using TR2 coefficient, the same decline in R 2 would raise the annualized alpha by 0.68% • If only explanatory variables are TR2t-1 Alphat-1 and style dummies (TNA>$15 mln), then coeff (TR2t-1 )= -0.775 with t = 3.12 Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  17. Robustness: • Panel regressions: style and time dummies, and standard errors are clustered by both time and fund. For Alpha equation - the coefficient of TR2 is –1.163 (t = 2.77) for the FFCR model and –1.060 (t = 2.52) for the CPZC model. • FFC model: Alpha equation- the mean coefficient of TR2t-1 is ‑0.801 (t = 2.33) and the weighted mean is ‑0.749 (t = 2.90). • Monthly returns, 24 months rolling window, 216 monthly test periods, for 1993-2010, 2,438 funds, 227,726 fund test-period months: FFC model - the mean coefficient of TR2t-1 is ‑1.077 with t = 2.23, the weighted mean coefficient is ‑0.858 with t = 3.21 • CPZC model: the mean coefficient of TR2t-1 is ‑1.328 with t = 3.52, the weighted mean is ‑1.328 with t = 4.32 Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  18. Active Share: Cremers and Petajisto (2009) • Active Share (AS), the sum of absolute deviations of the fund’s stock holdings (weights) from those of its benchmark index portfolio, predicts fund performance. More recently, Cremers, Ferreira, Matos and Starks (2011) show that AS positively predicts the performance of international mutual funds. • R2 and AS are negatively correlated (data 1990-2006 from CP) with the mean of -0.36 (ranges between ‑0.07 to -0.68). • AS measures the deviations from a single benchmark index while R2 measures deviations from multiple benchmark indexes Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  19. TR2 and TAS (weekly returns) Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  20. Industry Concentration (ICI) and Return Gap (RGap) (Kacperczyk, Sialm and Zheng, 2005, 2008) • ICI: the sum of the squared deviation between the fund’s weights in various industries and the weights of these industries in the market portfolio • Rgap: the difference between the reported fund return and the return on a portfolio that invests in the previously disclosed fund holdings gauges the effects of trades by skilled fund managers who use their informational advantage to trade individual stocks optimally. Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  21. Panel Regressions as in Kacperczyk et al. In FM regressions, Alpha equation: both TR2 and TICI are significant, the coeff are -0.905 (t = 2.12) and 0.737 (t = 2.00) respectively; both TR2 and RGAP significant , the coeff are -1.267 (t = 2.77) and 0.060 (t = 2.06) respectively. InfRatio equation: while TR2 is negative and significant, TICI and RGAP are not Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  22. Characteristics-based excess return (Daniel, Grinblatt, Titman and Wermers, 1997) "Characteristic Selectivity" (CS), is the difference between the fund return and the weighted average return on one of 125 passive portfolios of stocks that match each of the fund’s stocks on the basis of market capitalization, book-to-market and prior-year return, the weights being equal to the fund’s stock holdings “Characteristic Timing” (CT), is the weighted annual return on each of the 125 characteristics portfolios, where the weights are those of the stocks that match these characteristics Following Daniel et al. (1997), both CS return and CT return are “Carhart-adjusted” Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  23. Fama-MacBeth regressions AR(1) coefficient of the series of coefficients of TR2 in the CS regression is -0.389 with t = 2.39 Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  24. Is the R2 effect due to selectivity or to pricing of volatility? • Passive stock portfolios: Fama-French 100 portfolios sorted on size and on book-to-market (10x10) • “styles”: D-micro cap = 1 for the smallest two size decile portfolios, D‑Small cap = 1 for size portfolios 3 and 4, D‑growth = 1 for the lowest three book-to-market portfolios, and D‑value = 1 for the highest three book-to-market portfolios (zero otherwise) • Also repeated the analysis for Fama-French 48 industry portfolios which can be viewed as passive “sector” funds Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  25. Fama-French 100 portfolios Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  26. Portfolio Sorting: FFCR Alpha (sample 1990-2010, Net Returns) Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  27. Portfolio Sorting: CPZC Alpha (sample 1990-2010, Net Returns) Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  28. Determinants of R2 Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  29. Corporate bond funds: predicting performance with R2 • Funds that invest in corporate bonds more than 35% of their net asset value, which accommodates “Balanced Funds” (average holdings of corporate bonds - 69.5% across all funds) • Exclude Treasury, government or municipal bond funds • Benchmark models: • Bessembinder et al. (2008) (Fama-French+DEF+TERM) [average R2 =0.53] • Elton et al. (1995): MKT-RF, Bond Index-Rf, DEF and OPTION (Barclays GNMA index – Barclays Gov Intermediate index)[average R2 =0.46] • Sample: 2001-2010 (on average 67 funds per period) Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  30. The effect of R2 on Bond fund performance Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  31. Conclusion: Lower R 2 Higher Selectivity Better Performance Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

  32. Conclusion: • A new convenient way to predict mutual fund performance using only their return data : the R2 from a regression of the fund return on a multi-factor model that is considered a common benchmark for fund performance • The lower R2 the greater selectivity, the better the subsequent performance, after controlling for fund characteristics and past performance • the highest-alpha and lowest-R2 portfolio produces an average annual excess return of 2.4% or more (depending on the benchmark factor model) • R2 is related to fund characteristics such as fund size, expenses, manager tenure, and style. These characteristics explain nearly 50% of the cross-fund variation in R2. • R2 also predicts performance for mutual funds that hold corporate bonds Christoffersen, Goyenko, Jacobs, and Karoui Amihud and Goyenko Illiquidity Premia in the Equity Options Market Fund R2 as predictor of performance

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