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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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If these most actively-managed funds are all skilled, their performance distributions should be shifted to the right; that is, they should first-order stochastically dominate the index funds. The plots of gross alphas show that the distribution of the most active actively-managed funds is wider than that of index funds, but they do not dominate the index funds. While some of the most active funds exhibit higher alpha estimates in the right tail before fees, the most active funds also underperform in the left tail. If gross alphas are scaled by idiosyncratic risk (t-statistics), the index fund distribution is still remarkably similar to that of the most active activelymanaged funds, and active funds are indistinguishable from passive funds over most of the distribution.

In terms of second-order stochastic dominance, the alphas of index funds dominate even the alphas of these most-active funds for either top quartile Active Share or Return Gap funds. The test of the null Index dominates Active has a p-value of 0.837 (0.549) for Active Share (Return Gap) while the test of the null Active dominates Index is strongly rejected with a p-value of 0.000 (0.001) for Active Share (Return Gap). Active funds look most attractive under the t-statistic distributions.

For Active Share, these results are inconclusive; we cannot reject the null of secondorder dominance in either direction. On the other hand, Active Funds dominate Index Funds using the t-statistic distributions for the active funds in the top quartile of Return Gap. We can reject the null of Index dominates Active with a p-value of 0.034.

While these results do not provide support that all high Active Share or Return Gap funds are skilled, they do suggest that a fraction of these funds outperform the index funds. These results lend credence to the use of cross-sectional sorts to help identify skill. Nonetheless, these methods are noisy enough that investors who base decisions on benchmark-adjusted returns should still prefer an investment in index funds.

5.2. S&P 500 Funds Another potential concern with our proposed skill tests utilizing the cross-section of index funds lies in the (standard) benchmark models employed. One could argue that the appropriate comparison should be within a given benchmark, e.g. S&P 500 funds, rather than across all funds. In this section, we analyze the impact of benchmark model mis-specification by testing how index funds compare to active funds when we restrict both sets to have the same benchmark. In particular, we examine the relative performance of active versus passive funds for the subset of funds that benchmark to the S&P 500. The advantage of looking at this sample is that, for this subset of funds, we ostensibly know the true benchmark.26 Therefore, we are able to abstract from standard benchmark models and just examine returns in excess of the return on the underlying S&P 500 index. With this approach, we credit active managers for skill even if they outperform the index by tilting toward well-documented strategies (e.g., value, momentum). To classify an index fund as an This assumes that active managers state the correct benchmark. Sensoy (2009) provides evidence that many active funds state benchmarks that do not match their actual style.

S&P 500 fund, we hand-checked the underlying index for all index funds. For active funds, we use the subset of actively managed funds benchmarked to the S&P 500 as identified by Cremers and Petajisto (2009).

Table 11 presents the results of quantile regressions for these two alpha groups.

In the first panel of Table 11, we see that gross alphas are consistent with what we believe to be the common prior regarding the performance of actively managed funds. The spread in alphas for the S&P 500 index funds is very small. Relative to the true benchmark, the index fund alphas are estimated at -1 basis point for 1st percentile funds to +3 basis points for the 99th percentile. This suggests that these index funds generally do what they are designed to do: track the S&P 500 index.

This also confirms that the index funds, when compared to their true benchmark exhibit little in the way of skill. It also suggests that the dispersion in index fund alphas found in Section 4 is due to benchmark model mis-specification rather than operational skill.

Some actively-managed S&P 500 funds earn much larger positive returns before fees. At the 99th percentile, the best index funds underperform the best active funds by about 55 basis points a month. However, it is also clear that the poor performing active funds are much worse than the index funds at the same points in the respective distributions. The poor performance is relatively symmetric compared to the difference between the best index funds and active funds. The worst index funds outperform the worst active S&P 500 funds by about 52 basis points.27 At the median, active funds do better by only four basis points per month.

On a t-statistic basis, the story is very different. Once we take into account the residual variance of gross excess returns, we see that skill of actively managed funds is strictly less than that of index funds, even in the tails. While active funds may be able to outperform the benchmark and the index funds, they do so by taking on substantial risk relative to the benchmark. The t-statistics are statistically significantly higher for index funds across all major points in the distribution. From Despite the smaller sample size, we continue to report the same quantiles as in the full sample analysis for comparison.

the standpoint of the t-statistics, investors would be better off choosing index funds, even before fees.

In terms of our stochastic dominance tests, S&P 500 index funds dominate S&P 500 active funds. We can reject the null that Active dominates Index (p=0.000 for either alphas or t(α)) but cannot reject the null that Index dominates Active (p=0.224 for alphas, p=0.878 for t(α)). These results indicate that any skill in the active fund space is more than outweighed by poorly-performing, unskilled funds.

If one believes that index funds should exhibit no portfolio selection skill, then the dispersion in the performance of these funds under classic benchmark models suggests either model mis-specification or operational skill. For the S&P 500 index funds, it is clear that using the true benchmark eliminates model mis-specification.

We see almost no dispersion in performance for these funds relative to the true benchmark. This suggests that the dispersion in index fund alphas found in Section 4 due to operational skill is in fact quite small, as it should show up in the S&P 500 tests as well. Unfortunately, it is well known that the stated benchmark does not necessarily correspond to the true benchmark for active funds, so it is difficult to interpret any dispersion of performance in active funds in these tests as evidence of skill.

6. Conclusion

We revisit the widely studied, yet still debated, topic of whether active mutual fund managers are skilled by comparing the distributions of index and active fund performance. Using standard measures from the literature, we first document that one would conclude that the index fund distribution contains skilled funds, contradicting their role as unskilled, passive investments. These results motivate the use of the index fund performance distribution as a set of counterfactual, unskilled funds to assess the extent of skill in the active fund distribution. We find that the topperforming index funds exhibit performance similar to the top active funds. However, for below-median funds, passive investments generally outperform actively-managed funds. In addition, we show that index funds stochastically dominate active funds in benchmark-adjusted performance, indicating that unskilled active managers more than offset any skilled active managers. On balance, we interpret our empirical findings as consistent with the view that actively-managed funds exhibit little portfolio selection skill.

Appendix A. Benchmark models

1. Market Model (Jensen, 1968)

–  –  –

The factor returns and conditioning variables are defined as follows:

• rit is fund i’s return in month t

• M KTt is the excess return of the CRSP value-weighted market return in month t

• SM Bt is the return of a portfolio long small-cap stocks and short large-cap stocks in month t

• HM Lt is the return of a portfolio long high book-to-market stocks and short low book-to-market stocks in month t

• U M Dt is the month t return of a portfolio long past winners and short past losers based on lagged returns

• Vtj is the excess return on Vanguard index j, orthogonalized to Vtnj. The Vanguard index funds are S&P 500 Index, Extended Market Index, SmallCap Index, European Stock Index, Pacific Stock Index, Value Index, Balanced Index, Emerging Markets Stock Index, Mid-Cap Index, Small-Cap Growth Index, and Small-Cap Value Index.

• S5RFt is the excess return of the S&P 500 index in month t

• RM S5t is the Russell Midcap minus S&P 500

• R2RMt is the Russell 2000 minus Russell Midcap

• S5V S5Gt is the S&P 500 Value minus S&P 500 Growth

• RM V RM Gt is the Russell Midcap Value minus Russell Midcap Growth

• R2V R2Gt is the Russell 2000 Value minus Russell 200 Growth

• zj,t−1 is the t − 1 deviation of public information variable j from its time series mean

• We use K = 4 conditioning variables: 1. The 1-month Treasury bill yield 2.

The dividend yield of NYSE/AMEX firms over the previous 12 months 3. The term spread (10-yr Treasury - 3-month Treasury yield) 4. The default spread (Yield difference between Baa and Aaa corporate bonds).

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