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«Abstract We use the cross-section of index funds to assess the extent of skill in active mutual funds. First, we apply methods designed to ...»

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Kosowski, R., Timmermann, A., Wermers, R., White, H., 2006. Can mutual fund stars really pick stocks? new evidence from a bootstrap analysis. The Journal of Finance 61, 2551–2595.

Malkiel, B.G., 1995. Returns from investing in equity mutual funds 1971 to 1991.

The Journal of Finance 50, 549–572.

Pastor, L., Stambaugh, R., Taylor, L., 2014. Scale and Skill in Active Funds. Working Paper.

Petajisto, A., 2013. Active share and mutual fund performance. Financial Analysts Journal 69, 73–93.

Sensoy, B.A., 2009. Performance evaluation and self-designated benchmark indexes in the mutual fund industry. Journal of Financial Economics 92, 25–39.

Sirri, E., Tufano, P., 1998. Costly search and mutual fund flows. Journal of Finance 53, 1589–1622.

S&P Dow Jones Indices, 2013. S&P Indices Versus Active Funds

U.S. Scorecard (SPIVA R ) Year-End 2013. Technical Report. URL:

http://us.spindices.com/documents/spiva/spiva-us-year-end-2013.pdf.

Storey, J.D., 2002. A direct approach to false discovery rates. Journal of the Royal Statistical Society 64, 479–498.

Wermers, R., 2000. Mutual fund performance: An empirical decomposition into stock-picking talent, style, transactions costs, and expenses. The Journal of Finance 55, 1655–1703.

Table 1: Summary Statistics This table presents summary statistics for our sample. The sample contains monthly fund observations from 1995

to 2013. Risk-loadings are estimated using the Fama-French-Carhart four factor model:

–  –  –

where rit is fund i’s return in month t. Fund characteristics are winsorized at the 1/99% level and averaged over the time-series of each fund. The cross-sectional mean, median, and standard deviation of these time-series averages are reported. Active Share and Tracking Error Volatility are for the subsample matching to the Active Share data of Petajisto (2013).

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Table 5: Persistence of Gross α This table presents transition matrices for alpha estimates under the Fama-French-Carhart model. Funds are sorted into quintiles based on their estimated gross alphas from each half-decade subsample. Each row shows the transition of a fund from the lagged quintile into quintiles in the current period. Panel headers indicate the current period. The top quintile (High) contains the top-performing funds; the worst-performing funds are in the Low quintile. Beige represents transition probabilities close to random (15% - 25%). Green represents above random persistence (25%) and red represents less than random persistence (15%).

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where αi,t−1 represents the lagged return of fund i, Indexi is an indicator equal to one for index funds, Ln(T N A)i,t is the natural log of Total Net Assets under management, and ExpenseRatioi,t is the expense ratio for the fund.

The regression also includes fund and year effects. Each column presents the estimates for different returns, including excess returns and various benchmark-adjusted returns. Standard errors are clustered at the fund level, t-statistics are in brackets, and significance is represented according to: ∗p 0.10, ∗ ∗ p 0.05, ∗ ∗ ∗p 0.01.

–  –  –

where ρτ (µ) = (τ − 1(µ ≤ 0))µ for quantile τ. To test the difference in quantiles between index funds and active funds, q(Xi ) is estimated as: q(Xi ) = β0 + β1 ∗ Indexi where Indexi takes value of one if fund i is an index fund.

The first column presents estimates for the 1st percentile of the distribution, with each subsequent column presenting estimates for the 5th, 25th, 50th, 75th, 95th, and 99th percentile, respectively. Standard errors are bootstrapped, t-statistics are in brackets, and significance is represented according to: ∗p 0.10, ∗ ∗ p 0.05, ∗ ∗ ∗p 0.01.

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Table 8: Quantile Regression Estimates: Gross t-statistics This table presents quantile regression estimates from the cross-section of t-statistics of benchmark-adjusted mutual fund returns. Benchmark-adjusted returns, αi, are calculated using one of six benchmark models. Conditional

quantile estimates are found by solving:

Qτ (t(αi )|Xi ) = arg min E[ρτ (t(αi ) − q(Xi ))], q(X) where ρτ (µ) = (τ − 1(µ ≤ 0))µ for quantile τ. To test the difference in quantiles between index funds and active funds, q(Xi ) is estimated as: q(Xi ) = β0 + β1 ∗ Indexi where Indexi takes value of one if fund i is an index fund.

The first column presents estimates for the 1st percentile of the distribution, with each subsequent column presenting estimates for the 5th, 25th, 50th, 75th, 95th, and 99th percentile, respectively. Standard errors are bootstrapped, t-statistics are in brackets, and significance is represented according to: ∗p 0.10, ∗ ∗ p 0.05, ∗ ∗ ∗p 0.01.

–  –  –

Table 9: Quantile Regression Estimates: Gross Dollar Returns This table presents quantile regression estimates from the cross-section of benchmark-adjusted mutual fund dollar returns, as in Berk and van Binsbergen (2014b). Benchmark-adjusted dollar returns, di, are calculated as Ti t=1 qit−1 · αit where qit−1 is lagged real assets under management and αit is based on the various risk models.

Ti

Conditional quantile estimates are found by solving:

Qτ (di |Xi ) = arg min E[ρτ (di − q(Xi ))], q(X) where ρτ (µ) = (τ − 1(µ ≤ 0))µ for quantile τ. To test the difference in quantiles between index funds and active funds, q(Xi ) is estimated as: q(Xi ) = β0 + β1 ∗ Indexi where Indexi takes value of one if fund i is an index fund.

The first column presents estimates for the 1st percentile of the distribution, with each subsequent column presenting estimates for the 5th, 25th, 50th, 75th, 95th, and 99th percentile, respectively. Standard errors are bootstrapped, t-statistics are in brackets, and significance is represented according to: ∗p 0.10, ∗ ∗ p 0.05, ∗ ∗ ∗p 0.01.

–  –  –

Table 10: Stochastic Dominance Tests This table presents tests of second-order stochastic dominance (SD2) of index funds over active funds. The table tabulates p-values from bootstrap tests of second-order stochastic dominance tests from Barrett and Donald (2003) of the null hypothesis of second-order stochastic dominance of the index fund gross performance distribution over the active fund gross performance distribution and vice versa. The bootstrap tests each contain 1000 draws.

–  –  –

where ρτ (µ) = (τ − 1(µ ≤ 0))µ for quantile τ. To test the difference in quantiles between index funds and active funds, q(Xi ) is estimated as: q(Xi ) = β0 + β1 ∗ Indexi where Indexi takes value of one if fund i is an index fund.

The first column presents estimates for the 1st percentile of the distribution, with each subsequent column presenting estimates for the 5th, 25th, 50th, 75th, 95th, and 99th percentile, respectively. Standard errors are bootstrapped, t-statistics are in brackets, and significance is represented according to: ∗p 0.10, ∗ ∗ p 0.05, ∗ ∗ ∗p 0.01.

–  –  –

Figure 1: Cumulative distribution functions of actual and bootstrapped gross t(α) This figure plots the cumulative distribution function of t-statistics associated with the risk-adjusted return, α, for index and active funds and the associated bootstrapped “zero alpha” distributions following Fama and French (2010).

–  –  –

Figure 2: Cumulative distribution functions of gross α This figure plots the cumulative distribution function of the benchmark-adjusted return, α, for index and active funds for various benchmark adjustments.

–  –  –

(e) Cremers-Petajisto-Zitzewitz 7-Factor (f) Ferson-Schadt Figure 3: Cumulative distribution functions of gross t(α) This figure plots the cumulative distribution function of t-statistics associated with the benchmark-adjusted return, α, for index and active funds for various benchmark adjustments.

–  –  –

(e) Cremers-Petajisto-Zitzewitz 7-Factor (f) Ferson-Schadt Figure 4: Cumulative distribution functions - “Active” Active Funds vs. Index Funds This figure plots the cumulative distribution function of the benchmark-adjusted return, α, and its associated tstatistic for index and active funds using the Fama-French-Carhart model. The active fund distribution includes only funds in the top quartile of Active Share (Panel A) or Return Gap (Panel B) over the sample.

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