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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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Passive versus Active Fund Performance:

Do Index Funds Have Skill?

Alan Crane, Kevin Crotty

Jones Graduate School of Business, Rice University, Houston, TX 77005, U.S.A.


We use the cross-section of index funds to assess the extent of skill in active mutual

funds. First, we apply methods designed to disentangle skill and luck in performance

evaluation to a set of traded funds that should not exhibit skill: index funds. Surprisingly, the tests imply that index fund skill exists, is persistent, and is found in similar proportion as in active funds. Since this seems implausible, we propose a new method to control for luck in active funds using the index fund cross-section as a zero-skill distribution. Using before-fee returns, we find strong evidence that inferior active funds exist, but little evidence that the top active funds are skilled.

Second-order stochastic dominance tests indicate that the performance distribution of index funds dominates that of active funds.

$ We thank Kerry Back, Jonathan Berk, Martijn Cremers, David De Angelis, Hitesh Doshi, Nishad Kapadia, Andy Koch, Sebastien Michenaud, Dermot Murphy, Barbara Ostdiek, James Weston, and seminar/conference participants at Rice University and the 2014 Lone Star Finance Conference for helpful discussions and comments.

Email addresses: alan.d.crane@rice.edu (Alan Crane), kevin.p.crotty@rice.edu (Kevin Crotty) September 29, 2014

1. Introduction A fundamental issue in evaluating mutual fund skill is determining whether funds perform well due to skill or luck. In this paper, we apply methods used to separate skill from luck to a set of traded funds that by definition should not exhibit portfolio selection skill: index funds. Under these tests, one would conclude that index fund skill exists, is persistent, and is found in proportions similar to those found in active funds. This is surprising and disconcerting, because outperformance by index funds should be attributed to luck.1 We propose a new method to control for luck in the cross-section of fund performance. To evaluate active fund skill, we use the cross-section of index funds as a distribution of lucky fund performance. We test whether the best (and worst) active funds are skilled (or unskilled) by comparing their before-fee performance to beforefee index fund performance using quantile regressions. We find strong evidence of unskilled active managers in the left tail and little evidence of skilled managers in the highest percentiles of performance. Using stochastic dominance tests, we also test whether the aggregate amount of skill or lack thereof in active funds warrants investing in active funds versus index funds. We conclude that index funds stochastically dominate active funds in a second-order sense, indicating that a risk-averse investor should prefer a draw from the index fund distribution rather than the active fund distribution.

Comparison of active fund performance to index performance is intuitive and dates back at least to Malkiel (1995). However, our tests have only recently been feasible due to the substantial growth in the cross-section of passively managed funds.

Over the last forty years, the number of passive index funds has grown from one to over 350 (Investment Company Institute, 2013). This growth has not been confined to S&P 500 funds; index funds now track many style indices. For example, S&P Luck could be due to estimation error or to benchmark model mis-specification. Cremers, Petajisto and Zitzewitz (2013) find that benchmark indices exhibit non-zero alphas under standard benchmark models and propose alternative benchmark models. We find substantial dispersion in index fund performance even using their proposed benchmark models.

produces underlying indices for 12 different domestic equity value/growth and market capitalization combinations alone, not to mention a variety of sector-specific indices.2 Recent work on disentangling skill and luck has focused on tests using the crosssectional distribution of active fund performance. The growth in the number of index funds allows us to examine how these methods perform in a cross-section of funds that should be unskilled with respect to portfolio choice. We employ four methods from the literature.

First, we find that a large fraction of index funds outperform simulated zeroalpha distributions, similar to the results for active funds in Kosowski, Timmermann, Wermers and White (2006) and Fama and French (2010). They conclude that this outperformance is due to skill, so our results would suggest that index funds are also skilled. In fact, the index funds generally exceed the bootstrap distribution above the 40th percentile under a variety of benchmark models.

Second, we estimate the proportion of unskilled, skilled, and zero-alpha managers for the sample of index funds using the false discovery rate methodology of Barras, Scaillet and Wermers (2010). Under a standard Fama-French-Carhart four-factor model, for example, we find that 16% of index funds are classified as skilled, compared to 10% of active funds.

Our third test examines the persistence of performance, which has been used as a measure of skill (e.g., Carhart (1997)). We find that performance is persistent in index funds, even before fees.3 On average, the likelihood of an index fund remaining in the same performance quintile is about 30% from one five-year period to the next;

for active funds, the average is approximately 20%, which is what one would expect by chance.

Finally, Berk and Green (2004) argue that the observed positive relationship between past fund performance and future fund flows is due to rational learning about S&P regularly compares active fund performance to these indices in its S&P Indices Versus Active Funds (SPIVA R ) U.S. Scorecard (S&P Dow Jones Indices, 2013).

Elton, Gruber and Busse (2004) show significant persistence in S&P 500 index fund net returns.

Their findings show that much of this persistence is driven by the fees. Our results indicate a significant amount of persistence in the broader index fund space, even for gross returns.

the skill of fund managers. This suggests that the flow-performance relationship should not exist absent skill. We find that the relationship is even stronger for index funds. For example, an increase in Fama-French-Carhart abnormal performance of 10 basis points (bps) per month is associated with increased flows of 3.5 bps of assets under management for index funds. This is significantly greater than the 1.9 bps increase in assets for active funds.

Taken together, these four results would suggest that the index fund distribution has just as much “skill” as active funds, if not more. If one agrees that index funds have no portfolio selection skill, then our results imply that the the conclusions drawn about the extent of skill using existing methods are subject to benchmark misspecification or estimation error. This is consistent with the evidence documented by Cremers et al. (2013) that some underlying benchmark indices have positive alpha.4 Our work builds on this finding by showing that inferences related to skill versus luck based on the distribution of performance are affected by this issue. An alternative explanation for our findings is that index funds truly possess a significant amount of skill, possibly due to operational skills such as managing trading costs or lending shares. This possibility does not have strong support in the literature. For example, Fama and French (2010) argue that effects of trading costs and lending revenues are small for passive funds.

While these first results are troubling, they also suggest a straightforward alternative to account for luck in the spirit of both Kosowski et al. (2006) and Fama and French (2010). If the dispersion in the performance of index funds arises not due to skill, but to luck, we can use the distribution of index fund performance estimates as a benchmark distribution to assess the extent of skill for active management. In our second set of results, we test for differences between the index fund and active fund distributions.

Overall, the results of these tests are surprising. We find little evidence that active funds display greater benchmark-adjusted performance than passive funds.

We see consistent results under a host of benchmark models, including those proposed by Cremers et al. (2013) to correct for the issue of alphas for benchmark indices.

Using quantile regressions, we find that the best index funds compare favorably to the top-performing active funds, even before fees. At the 99th percentile, there is no difference between the gross alphas of active and passive funds. We do find small differences in favor of active funds consistently at the 75th percentile of approximately 5 basis points per month. However, the largest differences occur in the performance of poorly performing funds, with index funds doing significantly better. At the 1st percentile, index funds outperform active funds by approximately 40 basis points per month.

These results suggest that a random draw from the distribution of active funds carries a much larger downside compared to index funds while having at most a small advantage on the upside. While the quantile regressions are useful for comparing particular points in the distribution, they cannot speak to the aggregate performance differences between the two groups. To address this question, we test for secondorder stochastic dominance between the two distributions. We find that index funds dominate active funds. Compared to the underperformance by the worst active managers, the magnitude of any active fund skill would be insufficient to induce a risk-averse investor to choose an active fund rather than an index fund.

Previous authors have shown certain fund characteristics are correlated with skill using portfolio sorts of mutual funds. For instance, Cremers and Petajisto (2009) document that funds whose holdings deviate substantially from those of their benchmarks outperform (Active Share), and Kacperczyk, Sialm and Zheng (2008) show that funds that outperform their reported holdings also have abnormal returns (Return Gap). If we restrict our active sample to the top quartile of Active Share or Return Gap, we still conclude that index funds dominate these most-active funds in a second-order sense.

Outperformance due to luck could be due to estimation noise or model misspecification. Our results do point to some benchmark model mis-specification. In particular, for the subset of funds that are benchmarked to the S&P 500, we see little dispersion in index fund returns net of the benchmark, but a great deal of dispersion in active funds’ returns in excess of the S&P 500 return. This suggests our use of index funds as portfolios lacking any portfolio selection skill beyond that of the underlying index is justified.

Our study is the first to use the distribution of index fund returns to better understand the performance ability of active managers. Prior work studying active versus passive performance (e.g., Gruber (1996), Malkiel (1995), Ferri and Benke (2013)) has generally focused on average net returns to investors, which reflect both potential manager skill and the rent-sharing agreement between the investors and the fund. Most recently, Del Guercio and Reuter (2013) compare average active and passive net performance to study incentives induced by the fund’s distribution channel for active managers to exert effort. Berk and van Binsbergen (2014b) use Vanguard index funds in a benchmark model to estimate gross dollar performance and conclude that skill is widespread in mutual fund managers. However, index funds exhibit significant dispersion under this performance measure as well, consistent with our interpretation that the performance of active funds is similar to that of index funds.5 Unlike the prior literature, we focus on the entire distribution of performance rather than average effects. This focus on the distribution leads to our main insights that current tests for skill versus luck may be confounded by benchmark model misspecification and that the distribution of index funds can be used as a benchmark distribution to assess active fund skill.

Most broadly, our results contribute to the vast literature on the skill of actively managed mutual funds. A large number of papers conclude that active managers are skilled, while other papers conclude the opposite.6 Our results, using a new economic hurdle to assess skill, are consistent with the latter.

Our paper also contributes to the literature on the appropriate benchmark for We employ this measure in Section 4.2.3.

Examples of papers concluding at least some active skill include Grinblatt and Titman (1989), Grinblatt and Titman (1992), Grinblatt and Titman (1993), Daniel et al. (1997), Chen et al. (2000), Wermers (2000), Kosowski et al. (2006), Jiang et al. (2007), Kacperczyk et al. (2008), Cremers and Petajisto (2009), Cohen et al. (2010), Fama and French (2010), Barras et al. (2010), Berk and van Binsbergen (2014b), Cremers et al. (2013), Pastor et al. (2014), Jiang et al. (2014), Hunter et al.

(2014), and Kacperczyk et al. (2014).

Papers concluding no skill include Jensen (1968), Elton et al. (1993), Malkiel (1995), Gruber (1996), Carhart (1997), and Bollen and Busse (2001).

mutual fund performance studies. As noted by Fama and French (2010) and Berk and van Binsbergen (2014b), passive benchmark returns from standard models do not account for trading costs. Moreover, Cremers, Petajisto and Zitzewitz (2013) show that some underlying passive benchmarks exhibit alpha relative to standard models.

Both Berk and van Binsbergen (2014b) and Cremers, Petajisto and Zitzewitz (2013) propose new benchmark models using multiple indices to address these concerns and find evidence of active manager skill. While we use their proposed benchmark models (as well as others), our approach differs in that we compare the distribution of index funds to that of active funds. This is important because index funds exhibit dispersion in benchmark-adjusted returns even using these alternative benchmark models.

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