ssrn-id2295865

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Academic knowledge dissemination in the mutual fund industry: can mutual funds successfully adopt factor investing strategies?

Eduard van Gelderen a,b*, Joop Huijb,c

a Chief Investment Officer, APG Investment Management

b Associate Professor of Finance, Rotterdam School of Management

c Vice President Quant Equity Research, Robeco Investment Solutions & Research

Abstract

In this study, we investigate if investors that have adopted investment strategies based on asset pricing anomalies documented in the academic literature (i.e., the low-beta, small cap, value, momentum, short-term reversal, and long-term reversal factors) consistently earn positive abnormal returns. For this purpose we evaluate the performance of a large sample of U.S. equity mutual funds over the period 1990 to 2010. We find evidence supporting the value added of investors adopting factor investing strategies: low-beta, small cap, and value funds earn significant excess returns. We also find that these excess returns are sustainable and have not disappeared after the public dissemination of the anomalies when more asset managers have started to adopt factor investing strategies. We propose some criteria that might be helpful to determine the successful application of academic insights in the context of investment strategies. Our findings have significant implications for the role of academic research and knowledge management in the investment management industry.

JEL classification: G11; G14; G19 Keywords: intellectual capital; mutual fund performance; asset pricing anomalies; out-of-sample testing; factor investing; low-risk; small cap; value; momentum; short-term reversal; long-term reversal

Email addresses: [email protected] (E. van Gelderen) and [email protected] (J. Huij).

* We thank Simon Lansdorp, David Blitz, Pim van Vliet, Tom Steenkamp, Roderick Molenaar, Gerben de Zwart, Ronald van Dijk, and seminar participants at the 2013 Nomura Gobal Quantitative Equity conference for useful comments. We welcome comments. The usual disclaimer applies.

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Academic knowledge dissemination in the mutual fund industry: can mutual funds successfully adopt factor investing strategies?

BLIND VERSION

Abstract

In this study, we investigate if investors that have adopted investment strategies based on asset pricing anomalies documented in the academic literature (i.e., the low-beta, small cap, value, momentum, short-term reversal, and long-term reversal factors) consistently earn positive abnormal returns. For this purpose we evaluate the performance of a large sample of U.S. equity mutual funds over the period 1990 to 2010. We find evidence supporting the value added of investors adopting factor investing strategies: low-beta, small cap, and value funds earn significant excess returns. We also find that these excess returns are sustainable and have not disappeared after the public dissemination of the anomalies when more asset managers have started to adopt factor investing strategies. We propose some criteria that might be helpful to determine the successful application of academic insights in the context of investment strategies. Our findings have significant implications for the role of academic research and knowledge management in the investment management industry.

JEL classification: G11; G14; G19 Keywords: intellectual capital; mutual fund performance; asset pricing anomalies; out-of-sample testing; factor investing; low-risk; small cap; value; momentum; short-term reversal; long-term reversal

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Introduction While the investment management industry is generally considered to be a knowledge-based industry, surprisingly little has been documented about the effectiveness and the value added of incorporating academic insights by investment managers into their investment strategies. To the best of our knowledge, no study has been conducted on the value added of innovative investment strategies that incorporate new academic insights. In consequence, we have no clear understanding of how many investment managers have incorporated academic insights into their investment strategies; what the value added is of incorporating these insights into investment strategies; in which cases application of these insights is successful; or what criteria might be helpful to determine the successful application of these insights.

At the same time, the relevance of an in-depth study on the differential performance of adaptors of academic knowledge in the investment management industry seems to be high and its implications are expected to be significant. Expenditures on research and development in the investment management industry are substantial and many investment managers claim to have incorporated insights from academic studies. For example, after the publication of the results of the study of Fama and French (1993) (who document that strategies that invest in small cap stocks and value stocks earn positive excess returns), many investment managers claim that they have adopted investment styles based on the Fama-French small cap and value factors. Interestingly, there is currently no solid empirical evidence indicating that investment managers that have adopted investment styles based on factors that originate from academic research show sustainable better performance. There are a few studies that evaluate the performance of specific investment vehicles such as value funds, but there is no all-encompassing study that investigates the more general research question whether the adopters of academic knowledge gain excess returns, or under which circumstances application of this knowledge is successful. The aim of this study is to fill this gap in the literature.

When we consider the application of academic insights into investment strategies in this study, we restrict ourselves to strategies that incorporate factors that have been documented in academic studies to have predictive power for stock returns above and beyond market betas. Such strategies are often referred to as factor investing strategies. We do not consider the application of academic knowledge in a broad context such as the application of insights from

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option pricing theory in the context of risk management. The underlying reason for us to specifically focus on factor investing strategies is that the application of such strategies can

reliably be measured through regression-based techniques like return-based style analysis a la Sharpe and our aim is to perform a large-scale empirical study.

In the first part of the paper we evaluate the monthly performance for a large sample of

U.S. equity mutual funds over the period 1990 to 2010 and use a regression-based method to indicate if the funds follow factor investing strategies based on the low-beta, small cap, value, momentum, short-term reversal, and long-term reversal anomalies. We find that a significant number of funds (i.e., roughly 20 to 30 percent) have adapted small cap and value investment strategies. Only a small number of funds (1 to 6 percent) follow low-beta, momentum, and short-term and long-term reversal strategies.

Subsequently, we investigate if the funds that have adopted the factor investing strategies exhibit superior returns. We find evidence supporting the value added of funds adopting low-beta, small cap, and value strategies. We also find that the excess returns earned by these funds are sustainable and have not disappeared after the public dissemination of the anomalies: not only during the first decade of our sample we find a positive relation between fund performance and the adoption of factor investing strategies, but we also find this positive relation to be present over the second decade in our sample. However, we do not find consistent evidence supporting value added for funds adopting momentum and reversal strategies. For funds engaging in momentum strategies we find mixed evidence of positive excess returns, and for funds engaging in short-term reversal strategies we even find evidence of negative excess returns.

The outperformances of funds adopting low-beta, small cap, and value strategies are not only significant from a statistical point of view, but are also economically highly significant. In terms of one-factor alpha against the market index, small cap and value funds deliver average alphas of 56 and 119 basis points per annum, respectively, after costs. And the returns of low-beta funds are indistinguishable from the market return, while these funds exhibit significantly lower levels of risk. In terms of success ratio (i.e., the probability of outperforming in the long run), we also find large differences between factor investing funds and the other funds in our sample: only 20 percent of the funds not engaging in factor investing yield outperformance in the long run. For funds engaging in factor investing this figure is substantially more favorable

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ranging up to 61 and 67 percent for small cap and value funds, respectively. All in all, we conclude that there can be large value added of funds incorporating academic knowledge in their investment processes by engaging in factor investing. However, the incorporation of academic knowledge does not appear to always result in adding value.

We hypothesize that the extent to which academic knowledge can successfully be adopted by mutual funds in their investment strategies depends on how strong the empirical evidence supporting the underlying anomaly is. Regarding both the momentum and short-term reversal anomalies, there are also several studies that challenge that strategies based on these anomalies actually earn positive excess return. Specifically, these studies argue that trading frictions (like transaction costs) might prevent profitable execution of these strategies. Also, the evidence supporting the existence of the long-term reversal anomaly is substantially weaker than the evidence supporting the low-risk, small cap, and value anomalies. Based on our results we argue that it is less likely that new academic knowledge can successfully be adopted in the investment management industry if the empirical evidence on which the knowledge is based exhibits significant ambiguities.

Overall, our findings have important implications for the role of academic research and knowledge management in the investment management industry. First of all, our results indicate that investors that have adopted investment strategies based on asset pricing anomalies documented in the academic literature can earn consistent excess returns. Our results thereby provide a case to justify expenditures on research and development in the investment management industry. Our results also indicate that the excess returns earned by funds that have engaged in factor investing strategies are sustainable and do not disappear after the public dissemination of the anomalies. This result implies that investors do not have to worry that the value added of incorporating new knowledge is only short-lived and that mispricings are quickly arbitraged away once more investors adopt the knowledge. This implication is inconsistent with the conventional wisdom that financial markets quickly adapt and that investors should continuously search for the newest knowledge which they can only exploit over a short period of time (this line of reasoning is often referred to as the Adaptive Market Hypothesis of Lo, 2004). In fact, our empirical results point in the opposite direction: we find that factor strategies for which there is little documentation in the academic literature do not earn excess returns. Our

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results therefore support a more conservative approach to incorporating academic insights into investment processes and indicate that it is important that empirical evidence has withstand a significant number of attempts of falsification before investment strategies are engineered that incorporate this knowledge.

Perhaps an even more important implication relates to the way academic research is conducted in the stream of literature on empirical finance. Typically, the characteristic of knowledge that is considered to be the most important by the academic community when a study is considered for publication in an academic journal is the extent to which the knowledge is new. Consequently, little credit is typically given to studies that validate (or attempt to falsify) existing knowledge. However, our results indicate that attempts to falsify existing knowledge provide an important contribution to the successful incorporation of academic knowledge into investment processes. We therefore argue that falsification of existing knowledge should deserve more credits in the academic community because it plays an important role in applying the knowledge.

The remainder of this paper is organized as follows. Section 2 describes the development of the academic literature of empirical asset pricing during the 1990s. Section 3 describes the data and methodology we use in our study. Section 4 presents our empirical results. Section 5 concludes.

2. Academic literature, choice of factors, and some considerations

Up to the 1980s, the academic literature on asset pricing was theoretical and deductive in nature. Testing the theories empirically was often difficult due to the lack of solid and reliable databases. However, at the end of the the 1980s large and reliable databases became readily available and technological developments (e.g., improvements in computational power) started to offer favorable conditions for conducting empirical research to test asset pricing theories like the CAPM. A large number of empirical studies followed that tested the CAPM. Perhaps the most important contribution of this empirical stream of literature to our knowledge on asset pricing is that multiple factors can be identified which have predictive power for stock returns above and beyond stock market betas. The most important factor that have been documented in our opinion and the ones that are included in our study are: the (1) low-risk factor [see, amongst others,

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Black (1993); and Haugen & Baker (1991), (2) the small cap factor [see, amongst others, Banz (1981); Reinganum (1981); and Fama & French (1992)], (4) the value factor [see, amongst others, Fama & French (1992); Lakonishok, Shleifer, and Vishny (1994)], (4) the momentum factor [see, amongst others, Jegadeesh & Titman (1993); and Chan, Jegadeesh & Lakonishok (1996)], (5) the short-term reversal factor [see, amongst others, Lehmann (1990); Jegadeesh (1990); and Lo & Mackinlay (1990)], and (6) the long-term reversal factor [see, amongst others, De Bondt & Thaler (1985)].

However, while (most of) the results of the abovementioned anomalies have been confirmed by other studies, there are also several studies that postulate some important considerations regarding the practical applicability of the results of these studies. These studies in particular express their concerns regarding the real-life applicability of momentum and short-term reversal strategies. In the light of the goal of our study, we believe it is important not only to discuss positive evidence for factors predicting stock returns, but also to discuss important considerations that have been put forward in the literature.

Specifically, several studies point out that momentum and short-term reversal strategies are concentrated in small cap stocks that typically exhibit large trading and require frequent portfolio rebalancing . As a consequence of these features of the strategies, several studies argue that the excess returns of momentum and short-term reversal strategies may be offset by the trading costs associated with the strategies costs [see, e.g. Ball, Kothari & Wasley (1995), Jegadeesh & Titman (1995), Conrad, Gultekin & Kaul (1997), Lesmond, Schill & Zhou (2004), Korajczyk & Sadka (2006), Avramov, Chordia and Goyal (2006), and De Groot, Huij & Zhou (2012)].

There is also a stream of literature that argues that momentum strategies are associated with very high levels of risk making it difficult to implement in a real-life investment strategy [see, e.g., and Grundy & Martin (2001), Chordia, T. and L. Shivakumar (2002), and Avramov, Chordia, Gergana, & Philipov (2007)].

Also when we consider the long-term reversal anomaly we note that the evidence supporting the existence of the anomaly is substantially weaker than the evidence supporting the

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existence of the low-risk, small cap, and value anomalies. For example, Fama and French (1996) show that the long-term reversal anomaly is largely encompassed by the value anomaly.

Finally, the Adaptive Market Hypothesis of Lo (2004) postulates that factors documented in academic studies to predict stock returns might lose their predictive power after the public dissemination of the factors because professional arbitrageurs like hedge funds might arbitrage away the premiums associated with the factors. For example, if many investors would engage in a small cap/value strategy, the excess returns of the strategies would eventually disappear because the increased demand for small cap/value stocks drives their prices up, and expected returns down. However, this theory has not been confirmed by empirical studies.

When evaluating the value added of investment managers engaging in factor investing, the considerations that have been put forward regarding some of the factors might be helpful to better understand in which cases the value added might be absent.

3. Data and methodology

This bring us to describing the data and methodology we use in our empirical analyses to test for the value added of investment managers incorporating insights from the academic literature on factor investing.

3.1 Mutual fund return data

For our empirical analyses we obtain return data on U.S. equity funds from the Morningstar database. Our database covers monthly returns for 6,814 U.S. equity funds over the period January 1990 to December 2010. Next, we estimate the single factor model below for all funds in our database that have at least 36 consecutive return observations:

(1) titfm,tiitfti rrrr ,,,1,, )( ++=

where tir , is the return of fund i in month t, tfr , is the risk-free return in month t, tftm rr ,, is the

Market-Rf factor of French (2012), which represents the return of the value-weighted CRSP universe in excess of the risk-free return, i and i,1 are parameters to be estimated, and ti , is

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the residual return of fund i in month t. We now select all funds that have a R-squared value for the single factor model specification above 60 percent. This brings our sample to 4,026 funds.

For the first year in our sample, we have 7,809 monthly return observations available. This number steadily increases to 42,621 observations in the final year of our sample.

3.2 Asset pricing anomalies return series

We obtain return data for the low-risk, small cap, value, momentum, short-term reversal, and long-term reversal anomalies from the webpage of French (2012) over the period January 1990 to December 2010. Table 1 shows the descriptive statistics for these return series.

[INSERT TABLE 1 ABOUT HERE]

Table 1 shows average factor returns and standard deviations over our sample period. Additionally, Table 1 shows the returns and standard deviations for the first and second half of our sample period. Consistent with the results of the aforementioned studies, we observe large premiums associated with the factors: over our sample period we observe a small cap premium of 20 basis points per month, a value premium of 33 basis points, a momentum premium of 60 basis points, a short-term reversal premium of 25 basis points, and a long-term reversal premium of 43 basis points. When we consider the subsample results, we observe that there is quite some variability in the magnitude of the premiums over time. For example, while the SMB factor earns a return of 7.50 percent per annum over the most recent half of our sample, the factor yields a negative return of -3.15 percent per annum over the first half of our sample period. In the following analyses we investigate how many investment funds have adapted investment strategies based on these factors, and if these funds earn consistent excess returns.

3.3 Fund classification

To indicate if mutual funds have adopted investment strategies based on the asset pricing anomalies mentioned earlier, we apply a return-based approach throughout our empirical analyses to indicate if mutual funds have adopted investment strategies based on the asset pricing anomalies mentioned earlier. More specifically, for each fund we estimate the six-factor model below for their entire return history:

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(2) titi

tiitititftmiitfti

LTR

STRWMLHMLSMBrrrr

,,6

,5,4,3,2,,,1,, )(

+

++++++=

where tftm rr ,, , tSMB , tHML , tWML , tSTR ,and tLTR are the returns on factor-mimicking

portfolios for the market, small cap, value, momentum, short-term reversal, and long-term

reversal factors in month t, respectively, i , i,1 , i,2 , i,3 i,4 , i,5 , and i,6 are parameters to be estimated, and ti , is the residual return of fund i in month t.

Next we apply two approaches to indicate if mutual fund follow investment strategies that are correlated with the return series of for the small cap, value, momentum, short-term reversal, and long-term reversal anomalies. The main difference between the two approaches is that the first approach measures if a funds exposure to a specific asset pricing anomaly is statistically significant, while the second approach measures if the exposure is economically significant. With the first approach, we indicate that a fund has statistically significant exposure to a specific style if the t-statistic of the beta of the fund to the style is larger than 2. For example, if a funds t-statistic of its SMB beta is larger than 2, that fund is classified as a fund that follows an investment strategy that incorporates the small cap anomaly. And if a funds t-statistic of its HML beta is larger than 2, that fund is classified as a value fund. With the second approach, we indicate that a fund has economically significant exposure to a specific style if the beta of the fund to the style is larger than 0.25. For example, if a funds SMB beta is larger than 0.25, that fund is classified as a small cap fund. And if a funds HML beta is larger than 0.25, that fund is classified as a value fund. We indicate that a fund follows a low-beta style if its market beta is smaller than 0.80. Because our methodology only requires fund return data that are readily available, our sample basically covers all funds that existed during our sample period. Therefore, the effects that selection bias and survivorship bias described in Brown et al. (1992) could have on the results of this study are likely to be insignificant. The results of our classification methods are presented in Table 2.


We first consider how many funds follow a low-beta investment style. Not surprisingly, the average fund beta is equal to one. However, even though there is quite some dispersion in fund

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betas, it appears that only a small portion of all funds follows a low-beta strategy: only 6 percent of the funds in our sample exhibit a market beta lower than 0.8.

More funds appear to follow small cap and value factor investing strategies. Depending on whether we consider the statistical significance of the factor exposures or the economic magnitude of the exposures, we find that between roughly 20 to 30 percent of the funds follow small cap and value investment strategies. When we consider the number of funds in our sample that have statistically significant exposures to the small cap and value factors, we find that 38 percent of the funds follow small cap investment strategies, and 33 percent of the funds follow value investment strategies. When we consider the number of funds in our sample that have economically significant exposures to the factors, we find that that 31 percent of the funds follow small cap investment strategies, and 19 percent of the funds follow value investment strategies. So basically, irrespective of whether statistical of economic significance is considered, it appears that a substantial number of mutual funds engage in small cap and value investment strategies.

Next, we consider how many funds follow momentum strategies. While we find that 25 percent of the funds do exhibit statistical significant exposure to the momentum factor, only a very small number of funds (i.e., 2 percent) have economically significant exposure to the factor. Apparently, just a small number of funds engage in momentum strategies with high conviction. We find similar results for the number of funds engaging in short- and long-term reversal strategies: while some funds do have statistically significant exposure to the factors, only a very small number of funds appear to really engage in reversal strategies (i.e., 1 to 2 percent of the funds in our sample).

To obtain more insights into the magnitudes of the funds factor exposures, we list the average factor exposures for the funds in our sample classified as low-beta, small cap, value, momentum, short-term, and long-term reversal funds. The results are listed in Table 3.


While the funds factor exposures are similar irrespective if we classify funds based on the statistical or economic significance of their factor exposures, we observe that the fund factor exposures are more pronounced if funds are classified based on the economic magnitude of their factor exposures. For example, while the average WML exposure of momentum funds is 0.13 if funds are classified based on the statistical significance of their exposures, this WML exposure is

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0.32 if funds are classified based on the economic magnitude of their exposures. This result is consistent with our earlier finding that while a significant number of funds have a statistical exposure to momentum and reversal factors, only a small number of funds follow these types of strategies with high conviction. Another notable observation is that it appears that both value and momentum funds typically have significant exposure to small caps. To disentangle the effects of funds having multiple factor exposures at the same time, we additionally perform multivariate regression analyses in the subsequent section.

When we consider the results in this section all together, we conclude that a substantial number of mutual funds are engaging in factor investing strategies. However, most of the funds that engage in factor investing appear to follow small cap and value strategies. Funds that engage in low-beta, momentum, and reversal strategies appear to be quite scarce.

3.4 Fund styles and outperformance

Now we have discussed how we measure if funds engage in factor investing, we now continue and discuss how we measure if these funds exhibit differential performance.

To measure fund outperformance, we take the intercept from the single factor model in Equation (1). This intercept, known as Jensens (1969) alpha, reflects a funds return that is not due to its sensitivity to returns of the market portfolio (i.e., beta).

To ensure that our results are not driven by a few outliers, we normalize and winsorize fund alphas:

(3)

=

iiAlphaz ,2max,2min_

where is the average fund alpha obtained from the global market model and is the cross-

sectional standard deviation.

Next, we run the following regression to investigate if funds that engage in factor investing exhibit differential performance:

(4) i

i

REVERSALLONGbREVERSALSHORTbMOMENTUMbVALUEbCAPSMALLbBETALOWbaAlphaz

++

+++++=

__

___

65

4321

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where LOW_BETA is an indicator variable that equals one if a funds is classified as a fund engaging in low-beta factor investing and zero otherwise; SMALL_CAP is an indicator variable that equals one if a funds is classified as a fund engaging in small cap factor investing; VALUE is an indicator variable that equals one if a funds is classified as a fund engaging in value factor investing; MOMENTUM is an indicator variable that equals one if a funds is classified as a fund engaging in momentum factor investing; SHORT_REVERSAL is an indicator variable that equals one if a funds is classified as a fund engaging in short-term reversal factor investing; and LONG_REVERSAL is an indicator variable that equals one if a funds is classified as a fund engaging in long-term reversal factor investing. We run the regressions for fund classifications based on both statistical and economic significance.

4. Empirical analyses

Proceeding further, we move to our empirical analyses. In our first analysis we regress fund performance (z_Alpha) on the indicator variables that indicate if the funds engage in factor investing. In this first analysis our fund classification is based on statistical significance of the funds factor exposures. Besides the multi-factor regression in Equation (4), we also run single-factor regressions for each indicator variable. Running both single- and multi-factor regressions helps us to detect if there are any interaction effects. The results of our first analysis are presented in Table 4.


When we consider the results in Table 4 of Regressions 1, 2, 3, and 4, we observe that both funds engaging in low-beta, small cap, value, and momentum strategies earn significant excess returns. Low-beta funds earn alphas that on average are 0.22 standard deviations above the cross-sectional mean; small-cap funds earn alphas that are 0.54 standard deviations above the mean; value fund earn alphas that are 0.50 standard deviations above the mean; and momentum funds earn alphas that are 0.07 standard deviations above the mean. For funds engaging in low-beta, small cap, and value strategies the differential performances are statistically highly significant (e.g., the t-statistics of the coefficient estimates are 4.12, 19.61, and 18.20, respectively, for the low-beta, small cap, and value funds). For funds that have adopted momentum strategies the results are also statistically significant (with a t-statistic of 2.27), but the excess returns are less

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pronounced than for the funds engaging in low-beta, small cap, and value strategies. Moreover, the differential excess performance of 0.07 standard deviations is also economically very small compared to the numbers observed for low-beta, small cap, and value funds. We are therefore hesitant to say that momentum funds earn excess returns based on these results.

When we consider the results of Regressions 5, and 6, we observe that funds that have adopted short-term reversal, and long-term reversal strategies have also not been successful in earning excess returns. In fact, these funds have significantly underperformed the average fund: both the coefficient estimates for their differential performance and the associated t-statistics indicate significant underperformance.

When we consider the results for the multi-factor regression (Regression 7), our conclusions remain unchanged: funds engaging in low-beta, small cap, and value strategies have earned excess returns, while we find no positive differential performance for momentum and reversal (both short-term and long-term) funds. It does appear that some portion of the outperformance of value funds can be attributed to these funds typically also having some exposure to small cap stocks.

We follow-up these empirical analyses by basing our fund classification on the magnitude of their exposures. The results of these analyses are presented in Table 5.


Interestingly, although we did observe some differences in the number of funds engaging in factor investing strategies in our earlier analyses when fund classifications are based on either the statistical significance of fund exposures or the economic magnitude, the results in Table 5 are very similar to the results in Table 4: for low-risk, small cap, and value funds we observe significant positive excess returns, while we find no positive differential performance for momentum and reversal funds. In fact, for funds engaging in short-term reversal strategies our results consistently indicate negative differential performance.

Up to this point, we conclude that there is evidence supporting the value added of funds adopting factor investing strategies in some cases. In our follow-up analyses, we investigate if this value added has been sustainable and economically significant. We finalize our analyses by making a first attempt in setting up a framework that might be helpful to determine the

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successful application of academic insights in the context of investment strategies and explain why some factor investing strategies are successfully implemented and others not.

To investigate if the excess returns earned by funds that engage in factor investing have been sustainable and have not disappeared after the public dissemination of the anomalies we perform a subsample analyses and repeat our regressions analyses for the second half of our sample period. Because we did not observe material differences between our results when we classify funds on the statistical or economic magnitude of their factor exposures, we base our fund classification through the remainder of this study based on the economic magnitude of the funds factor exposures. The regression results for the second half of our sample period are presented in Table 6.


Interestingly, it appears that our results become even stronger when we consider the second half of our sample period: while low-beta, small cap, and value fund outperformance is 0.24, 0.61, and 0.59 standard deviations above average fund performance over our entire sample period, these figures are 0.30, 0.93, and 0.88 standard deviations over the second half of our sample period, respectively. These results are inconsistent with the Adaptive Market Hypothesis which states that financial markets quickly adapt and that investors should continuously search for the newest knowledge which they can only exploit over a short period of time, and indicate that investors do not have to worry that the value added of incorporating new knowledge is only short-lived and that mispricings are quickly arbitraged away once more investors adopt the knowledge.

Continuing our analyses, we address the economic significance of the excess returns that are earned by funds engaging in factor investing. In our previous analysis we compared the performance of factor investing funds relative to the performance of funds that do not engage in factor investing. While we found that factor investing funds do better than no-factor investing funds, it is still an open question if factor investing funds outperform passive benchmark indexes. In other words, it is unclear how factor investing funds do in a comparison vis--vis passively managed index funds and if they earn positive alphas relative to the market benchmark. To

investigate this issue we take fund alphas ( iAlpha ) resulting from Regression (1) and regress the alphas on the indicator variables that indicate if the funds engage in factor investing:

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(5) i

i

REVERSALLONGbREVERSALSHORTbMOMENTUMbVALUEbCAPSMALLbBETALOWbaAlpha

++

+++++=

__

__

65

4321

As mentioned earlier, we base our fund classification on the economic magnitude of the funds factor exposures. The regression results of this analysis are presented in Table 7.


When we consider the differential alphas for low-beta, small cap, and value funds, we observe that these funds earn significantly larger alphas than the other funds. Low-beta funds have a differential alpha of 91 basis points per annum (with a t-statistic of 3.94), small cap funds have a differential alpha of 211 basis points per annum (with a t-statistic of 18.11), and value funds even have a differential alpha of 259 basis points per annum (with a t-statistic of 19.00). The alphas of small cap and value funds are even significantly larger than zero at 56 and 119 basis points per annum, respectively. On the other hand, factor investing funds engaging in momentum and reversal strategies do not display positive differential alphas. In fact, funds engaging in short-term reversal strategies even appear to earn a highly negative differential alpha of 453 basis points per annum (with a t-statistic of -6.53).

Another way to gauge the economic significance of funds incorporating factor investing insights into their investment strategies is to consider the funds success ratios versus other funds. We therefore construct a dummy variable that indicates if a fund has a positive alpha (one if true and zero if false) and regress this dummy variable on the indicator variables that indicate if the funds engage in factor investing:

(6) i

i

REVERSALLONGbREVERSALSHORTbMOMENTUMbVALUEbCAPSMALLbBETALOWbaSUCCES

++

+++++=

__

__

65

4321

The results of this regression analysis are presented in Table 8.


When we consider Table 8 we observe both low-beta, small cap, and value factor investing funds have a significantly larger probability to yield outperformance than the average fund as the coefficient estimates for LOW_BETA, SMALL_CAP, and VALUE are significantly positive. For funds engaging in momentum or reversal strategies we do not find a positive differential success

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ratio. Besides average success ratios, we continue our analysis and consider the distributions of the alphas for various groups of funds. To this end we construct a histogram that shows how fund alphas vary across a range of performance buckets. The results of this analysis are shown in Table 9.


In the first panel of Table 9 the distribution of fund alphas is shown for our entire sample. Consistent with most studies in the stream of literature of fund performance evaluation we find that the majority of funds (i.e., 64 percent) underperform the market benchmark in the long run. Only 36 percent of the funds deliver long-run outperformance. The largest number of funds delivers a long-run alpha between minus one and zero percent per annum, and only 17 percent of the funds earn an excess return larger than two percent per annum.

In the second panel we show the distribution of fund alphas for funds that do not engage in factor investing. This group of funds is basically our control group for evaluating the performance of factor investing funds. Strikingly, it appears that only a very small group of funds that do not engage in factor investing are able to earn positive alphas. 80 percent of these funds earn negative alphas, with the largest number of funds earning an alpha between minus two and minus three percent per annum. Only half of the funds earning positive excess returns earn an alpha smaller than one percent per annum, and only five percent of the funds earn an alpha larger than two percent per annum. Apparently, factor investing funds do significantly better than their non-factor investing counterparts. We continue our empirical analyses by evaluating the alpha distributions for low-beta, small cap, value, momentum, and reversal funds separately.

In the third panel the alpha distribution is shown for low-beta funds. Interestingly, we observe that the probability that low-beta funds earn a negative alpha is substantially smaller than for our control group: while 80 percent of the non-factor investing funds underperform the market index in the long run, this figure is 53 percent for low-beta funds. For small cap, value, and momentum funds we also observe substantially smaller probabilities on underperformance of 39 percent, 34 percent, and 63 percent, respectively. Also the probabilities of yielding a large outperformance is substantially larger for factor investing funds: while only one percent of the non-factor investing funds earns an alpha of more than five percent per annum, this figure is

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seven, 11, 12 and seven percent for low-beta, small cap, value, and momentum funds, respectively. For both short-term and long-term reversal funds, however, there is no evidence of outperformance. While the alpha distribution of long-term reversal funds is somewhat more favorable than for our control group of no-factor investing funds, almost all short-term reversal funds in our sample (i.e., 96 percent) appear to deliver negative alphas.

When we consider all empirical results in this section together we can conclude the following: there is compelling evidence supporting the value added of incorporating academic insights in the form of factor investing for mutual funds. In particular, low-beta, small cap, and value funds appear to deliver economically and significantly better returns than no-factor investing funds. For funds engaging in momentum strategies we find mixed evidence. While the majority of these funds earn positive excess returns, there are also quite a few of these funds earning highly negative alphas. Long-term reversal funds do not seems to earn differential returns. And for short-term reversal funds the results even seem to indicate that these funds destroy value.

Apparently, the incorporation of new knowledge does not appear to always result in adding value for investment fund. We hypothesize that the extent to which new academic knowledge can successfully be adopted by mutual funds in their investment strategies depends on how strong the empirical evidence supporting the results is. While numerous studies document momentum and reversal patterns in the data, there are also a number of studies that argue that trading frictions might prevent profitable execution of these strategies. We therefore postulate that it is less likely that new academic knowledge can successfully be adopted in the investment management industry if the empirical evidence on which the knowledge is based exhibits significant ambiguities.

This brings us to the final question we address in this section: to what extent does incorporation of a certain academic insight generates value-added above and beyond the value generated by another insight? For example, if a fund already engages in a small cap investment strategy, how would the probability of the fund yielding outperformance change if the fund would additionally engage in a value strategy? To investigate this research question we proceed the following way: first, for all funds we construct counter variables that indicate to how many factors the funds are exposed. Like in our previous analyses, we indicate that a fund is exposed

19

to a certain factor if its loadings are larger than 0.25. So, for example, a fund that has a market beta of one; a loading on SMB of 0.30; a loading of 0.30 on HML and zero exposure to the other factor would be classified as a fund with exposure to two factors. Now, we regress (winsorized) alphas and success ratios on the indicator variables. For example, for winsorized alphas we run the following regression:

(7) ii FACbFACbFACbaAlphaz ++++= _3_2_1_ 321

where 1_FAC, 2_FAC, and 3_FAC are dummy variables that indicate if a fund is exposed to one, two, or three factors, respectively. We have no fund in our sample that is exposed to more than three factors. The results of the analyses are presented in Table 10.


When we consider the results in Table 10 we can see that for both (winsorized) alphas and success ratios we have significant loadings on all indicator variables. More specifically, in all cases the loading on 2_FAC is larger than the loading on 1_FAC, and the loading on 3_FAC in turn is larger than the loading on 2_FAC. Put it differently, the more strategies a fund is exposed to, the higher its alpha and success ratio. For instance, no-factor investing funds have an average alpha of -189 basis points and a success ratio of 20 percent. For comparison, funds that are exposed to one factor have an average alpha of -26 (= -189 + 163) basis points per annum and a success ratio of 51 (= 20 + 31) percent; funds that are exposed to two factor have an average alpha of 145 basis points and a success ratio of 68 percent; and funds that are exposed to three factors have an average alpha of 164 basis points and a success ratio of 78 percent. Hence, our results clearly indicate that incorporation of a certain academic insight can have incremental value above and beyond the value-added of another insight.

5. Follow-up empirical analyses

We plan to perform the following follow-up empirical analyses: results using Sharpe as performance measure; results using multi-factor alpha as performance measure (to analyze shortfall differences for the different strategies); results using alternative RBSA settings (0.15 and 0.35 as cut-off points for fund classification).

20

6. Summary In this study we perform an in-depth study on the differential performance of adaptors of academic knowledge in the investment management industry. In particular, we investigate if investors that have adopted investment strategies based on asset pricing anomalies documented in the academic literature (i.e., the low-beta, small cap, value, momentum, short-term reversal, and long-term reversal anomalies) earn consistent excess returns. For this purpose we evaluate the performance for a large sample of U.S. equity mutual funds over the period 1990 to 2010 and use a regression-based method to indicate if the funds follow factor investing strategies based on the low-beta, small cap, value, momentum, short-term reversal, and long-term reversal anomalies. We find evidence supporting the value added of funds adopting low-beta, small cap, and value strategies. We also find that the excess returns earned by these funds are sustainable and have not disappeared after the public dissemination of the anomalies: not only during the first decade of our sample we find a positive relation between fund performance and the adoption of factor investing strategies, but we also find this positive relation to be present over the second decade in our sample. To illustrate the large performance differential between factor investing funds and the other funds, we would like to point towards the distribution of fund alphas of value funds and no-factor investing funds in Figure 1 (the analysis underlying this figure is in detail discussed in Section 4 of the paper).

[INSERT FIGURE 1 ABOUT HERE]

As can be clearly shown from this figure, the alpha distribution of value funds is much more favorable than that of funds that do not engage in factor investing strategies. The results for low-beta and small-cap funds are also much more favorable than for no-factor investing funds.

On the other hand, we do not find consistent evidence supporting value added for funds adopting momentum and reversal strategies. For funds engaging in momentum strategies we find mixed evidence of positive excess returns, and for funds engaging in short-term reversal strategies we even find evidence of negative excess returns. We conclude that there can be large value added of funds incorporating academic knowledge in their investment processes by engaging in factor investing. However, the incorporation of new knowledge does not appear to

21

always result in adding value. We hypothesize that the extent to which academic knowledge can successfully be adopted by mutual funds in their investment strategies depends on how strong the empirical evidence supporting the results is. It is less likely that academic knowledge can successfully be adopted in the investment management industry if the empirical evidence on which the knowledge is based exhibits significant ambiguities.

Our findings have important implications for the role of academic research and knowledge management in the investment management industry. In the first place, our results provide a case to justify expenditures on research and development in the investment management industry. Our results also indicate that the excess returns earned by funds that have engaged in factor investing strategies are sustainable and do not disappear after the public dissemination of the anomalies. This result implies that investors do not have to worry that the value added of incorporating new knowledge is only short-lived and that mispricings are quickly arbitraged away once more investors adopt the knowledge. Our results therefore support a more conservative approach to incorporating academic insights into investment processes and indicate that it is important that empirical evidence has withstand a significant number of attempts of falsification before investment strategies are engineered that incorporate this knowledge.

Finally, our results indicate that attempts to falsify existing knowledge provide an important contribution to the successful incorporation of academic knowledge into investment processes. We therefore argue that falsification of existing knowledge should deserve more credits in the academic community because it plays an important role in applying the knowledge.

22

References Avramov, D., T. Chordia, J. Gergana, and A. Philipov, 2007, Momentum and Credit Rating, Journal of Finance, 62:2503-2520.

Avramov, D., T. Chordia and A. Goyal, 2006. Liquidity and Autocorrelations in Individual Stock Rreturns, Journal of Finance, 61, 2365-2394. Ball, R., S. P. Kothari, and C. Wasley, 1995. Can We Implement Research on Stock Trading Rules?, Journal of Portfolio Management, 21, 54-63.

Banz, R.W., 1981, The Relationship between Return and Market Value of Common Stocks, Journal of Financial Economics, 9:3-18.

Black, F., 1993, Beta and Return, Journal of Portfolio Management, 20:8-18.

Chan, L.K.C., Jegadeesh, N. & Lakonishok, J., 1996, Momentum Strategies, Journal of Finance, 51:1681-1713.

Chordia, T. and L. Shivakumar, 2002, Momentum, Business Cycle and Time-Varying Expected Returns, Journal of Finance, 57:985-1019.

Conrad, J. S., M. Gultekin, and G. Kaul, 1997, Profitability of Short-Term Contrarian Strategies: Implications for Market Efficiency, Journal of Business and Economic Statistics, 15:379-386.

De Bondt, W.F.M., & R. Thaler, 1985, Does the Stock Market Overreact?, Journal of Finance, 15:793-805.

De Groot, W., J. Huij, and W. Zhou, 2012. Another Look at Trading Costs and Reversal Profits, Journal of Banking and Finance, 36:371-382.

Fama, E. F., and K. R. French, 1992, The Cross-Section of Expected Stock Returns, Journal of Finance, 47:427-465.

Fama, E. F., and K. R. French, 1993. Common Risk Factors in the Returns on Stocks and Bonds, Journal of Financial Economics, 33:3-56.

23

Fama, E.F., and K.R. French, 1996, Multifactor Explanations of Asset Pricing Anomalies, Journal of Finance, 51:55-84.

French, K.R., 2012, Fama and French Factors, from the website

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

Grundy, B.D. and S. Martin, 2001, Understanding the Nature of the Risks and the Source of the Rewards to Momentum Investing, Review of Financial Studies, 14:29-78.

Haugen, R.A., and N.L. Baker, 1991, The Efficient Market Inefficiency of Capitalization-Weighted Stock Portfolios, Journal of Portfolio Management, 17:35-40.

Jegadeesh, N., 1990, Evidence of Predictable Behavior of Security Returns, Journal of Finance, 45:881-898.

Jegadeesh, N., and S. Titman, 1993, Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency, Journal of Finance, 48:65-91.

Jegadeesh, N. and S. Titman, 1995. Short-Horizon Return Reversals and the Bid-Ask Spread, Journal of Financial Intermediation, 4:116-132.

Korajczyk, R., and R. Sadka, 2006, Are Momentum Profits Robust to Trading Costs? Journal of Finance, 59:1039-1082.

Lakonishok, J., A. Shleifer, and R.W. Vishny, 1994, Contrarian Investment, Extrapolation, and Risk, Journal of Finance, 49:1541-1578.

Lehmann, B. N., (1990). Fads, Martingales, and Market Efficiency, Quarterly Journal of Economics, 105:1-28.

Lesmond, D.A., M.J. Schill, and C. Zhou, 2004, The Illusory Nature of Momentum Profits, Journal of Financial Economics, 71:349-380.

Lo, A.W., 2004. The Adaptive Markets Hypothesis: Market Efficiency from an Evolutionary Perspective, Journal of Portfolio Management, 30:15-29.

24

Lo, A. W., and A. C. MacKinlay, (1990). When are Contrarian Profits Due to Stock Market Overreaction?, Review of Financial Studies, 3:175-205.

Reinganum, M.R., 1981, Misspecification of Capital Asset Pricing: Empirical Anomalies based

on Earnings' Yields and Market Values, Journal of Financial Economics, 9:19-46.

25

Table 1. Returns for the market, small cap, value, momentum, short-term, and long-term reversal factors

We obtain return data for the market (RMRF), small cap (SMB), value (HML), momentum (WML), short-term reversal (STR), and long-term reversal anomalies (LTR) from the webpage of French (2012) over the period January 1990 to December 2010. Table 1 shows average factor returns for our entire sample period and the first and second half.

RMRF SMB HML WML STR LTR

Full sample periodAverage 5.85 2.46 3.94 7.24 3.04 5.15StDev 15.53 12.17 11.58 18.53 13.13 8.69

1st half of sample periodAverage 11.86 -3.15 1.43 10.67 3.04 4.56StDev 13.54 9.42 8.80 10.17 7.49 7.32

2nd half of sample periodAverage 1.12 7.50 6.26 3.45 3.22 6.08StDev 16.95 13.96 13.48 23.52 16.47 9.81

26

Table 2. Summary statistics of data sample

To indicate if mutual funds have adopted factor investing strategies, we apply a return-based approach and estimate the six-factor model below for their entire return history:

titi

tiitititftmiitfti

LTR

STRWMLHMLSMBrrrr

,,6

,5,4,3,2,,,1,, )(

+

++++++=

where tSMB , tHML , tWML , tSTR ,and tLTR are the returns on factor-mimicking portfolios for the low-risk, small cal, value, momentum, short-term reversal, and long-term reversal anomalies in month t, respectively, i , i,1 , i,2 , i,3 i,4 , i,5 , and i,6 are parameters to be estimated, and ti , is the residual return of fund i in month t. We apply two approaches to indicate if mutual fund follow investment strategies that are correlated with the return series of for the small cap, value, momentum, short-term reversal, and long-term reversal anomalies. With the first approach, we indicate that a fund has statistically significant exposure to a specific style if the t-statistic of the beta of the fund to the style is larger than 2. With the second approach, we indicate that a fund has economically significant exposure to a specific style if the beta of the fund to the style is larger than 0.25. We indicate that a fund follows a low-beta style if its market beta is smaller than 0.80. Table 2 shows the number of funds in our sample that the two approaches classify as factor investing funds.

Average fund beta

% of funds with statistically significant exposure

% of funds with economically

significant exposure

Market factor 1.00 6% 6%SMB factor 0.13 38% 31%HML factor 0.02 33% 19%WML factor 0.01 25% 2%STR factor 0.01 7% 1%LTR factor 0.01 10% 2%

27

TABLE 3. Fund factor exposures

We form groups of funds for our alternative classification schemes and compute average factor exposures for each group. The results of this analysis are presented in Table 3.

funds with CAPM beta

= 2

funds with HML-T >= 2

funds with WML-T >=

2

funds with STR-T >= 2

funds with LTR-T >= 2

RMRF 0.73 1.03 0.94 1.05 0.91 0.96SMB 0.07 0.49 0.19 0.26 0.07 -0.12HML 0.15 0.05 0.30 -0.07 0.07 0.00WML -0.03 0.04 -0.02 0.13 -0.03 -0.04STR 0.03 -0.03 0.00 -0.04 0.13 0.00LTR -0.03 -0.11 -0.06 -0.10 -0.06 0.16RSQ 0.85 0.89 0.90 0.90 0.89 0.94

funds with CAPM beta

= 0.25

funds with HML beta >= 0.25

funds with WML beta

>= 0.25

funds with STR beta >=

0.25

funds with LTR beta >=

0.25

RMRF 0.73 1.05 0.94 1.19 1.07 1.06SMB 0.07 0.56 0.26 0.37 0.04 0.02HML 0.15 0.05 0.40 -0.17 0.02 -0.12WML -0.03 0.04 -0.04 0.32 0.00 -0.09STR 0.03 -0.03 0.01 -0.05 0.31 0.00LTR -0.03 -0.12 -0.09 -0.15 -0.18 0.35RSQ 0.85 0.89 0.89 0.88 0.84 0.90

28

Table 4. Fund (statistical) factor exposures and outperformance We run the following regression to investigate if funds that engage in factor investing exhibit differential performance:

ii REVERSALLONGbREVERSALSHORTbMOMENTUMbVALUEbCAPSMALLbBETALOWbaAlphaz +++++++= _____ 654321where LOW_BETA is an indicator variable that equals one if a funds is classified as a fund engaging in low-beta factor investing and zero otherwise; SMALL_CAP is an indicator variable that equals one if a funds is classified as a fund engaging in small cap factor investing; VALUE is an indicator variable that equals one if a funds is classified as a fund engaging in value factor investing; MOMENTUM is an indicator variable that equals one if a funds is classified as a fund engaging in momentum factor investing; SHORT_REVERSAL is an indicator variable that equals one if a funds is classified as a fund engaging in short-term reversal factor investing; and LONG_REVERSAL is an indicator variable that equals one if a funds is classified as a fund engaging in long-term reversal factor investing. We indicate that a fund follows a specific style if the t-statistic of the beta of the fund to the style is larger than 2. iAlphaz _ is the winsorized alpha of fund i. The regression results are presented in Table 4.

29

Table 4. Fund (statistical) factor exposures and outperformance (CONTINUED)

Regression 1 Regression 2 Regression 3 Regression 4 Regression 5 Regression 6 Regression 7

Intercept -0.01 -0.23 -0.19 -0.01 0.02 0.02 -0.38t-statistic -0.69 -13.60 -11.79 -0.85 1.22 1.59 -18.03

LOW_BETA 0.24 - - - - - 0.22t-statistic 4.07 - - - - - 4.12

SMALL_CAP - 0.61 - - - - 0.54t-statistic - 22.53 - - - - 19.61

VALUE - - 0.59 - - - 0.50t-statistic - - 20.98 - - - 18.20

MOMENTUM - - - 0.07 - - 0.02t-statistic - - - 2.27 - - 0.68

SHORT_ REVERSAL - - - - -0.18 -0.18t-statistic - - - - -3.34 -3.66

LONG_REVERSAL - - - - - -0.19 0.05t-statistic - - - - - -4.02 1.23

30

Table 5. Fund (economical) factor exposures and outperformance We run the following regression to investigate if funds that engage in factor investing exhibit differential performance:

ii REVERSALLONGbREVERSALSHORTbMOMENTUMbVALUEbCAPSMALLbBETALOWbaAlphaz +++++++= _____ 654321where LOW_BETA is an indicator variable that equals one if a funds is classified as a fund engaging in low-beta factor investing and zero otherwise; SMALL_CAP is an indicator variable that equals one if a funds is classified as a fund engaging in small cap factor investing; VALUE is an indicator variable that equals one if a funds is classified as a fund engaging in value factor investing; MOMENTUM is an indicator variable that equals one if a funds is classified as a fund engaging in momentum factor investing; SHORT_REVERSAL is an indicator variable that equals one if a funds is classified as a fund engaging in short-term reversal factor investing; and LONG_REVERSAL is an indicator variable that equals one if a funds is classified as a fund engaging in long-term reversal factor investing. We indicate that a fund follows a specific style if the beta of the fund to the style is larger than 0.25.

iAlphaz _ is the winsorized alpha of fund i. The regression results are presented in Table 5.

31

Table 5. Fund (economical) factor exposures and outperformance (CONTINUED)


Intercept -0.01 -0.18 -0.13 0.01 0.01 0.01 -0.27t-statistic -0.69 -11.00 -8.54 0.43 0.78 0.56 -15.92




MOMENTUM - - - -0.07 - - -0.11t-statistic - - - -0.72 - - -1.22

SHORT_ REVERSAL - - - - -0.98 - -0.89t-statistic - - - - -5.62 - -5.59

LONG_REVERSAL - - - - - -0.17 -0.09t-statistic - - - - - -1.66 -0.98

32

Table 6. Fund factor exposures and outperformance over the second part of the sample time period

We run the same regression as for the analysis in Table 5, but now for the second subperiod of our sample. The results are presented in Table 6.


Intercept -0.02 -0.29 -0.18 -0.01 0.00 0.00 -0.40t-statistic -1.58 -18.38 -11.60 -0.43 0.03 -0.14 -25.21




MOMENTUM - - - 0.05 - - -0.08t-statistic - - - 0.47 - - -0.94



33

Table 7. Economic significance of fund factor exposures and outperformance

We run a similar regression as for the analysis in Table 5, but now take absolute fund alphas as explanatory variable: ii REVERSALLONGbREVERSALSHORTbMOMENTUMbVALUEbCAPSMALLbBETALOWbaAlpha +++++++= ____ 654321

The results are presented in Table 7.


Intercept -0.97 -1.56 -1.40 -0.90 -0.88 -0.90 -1.89t-statistic -16.81 -24.15 -23.61 -15.98 -15.82 -16.00 -28.11




MOMENTUM - - - -0.39 - - -0.47t-statistic - - - -1.03 - - -1.33



34

TABLE 8. Success ratios and fund factor exposures

We run a similar regression as for the analysis in Table 5, but now take fund success ratios as explanatory variable: ii REVERSALLONGbREVERSALSHORTbMOMENTUMbVALUEbCAPSMALLbBETALOWbaSUCCES +++++++= ____ 654321

The results are presented in Table 8.


Intercept 0.36 0.26 0.30 0.36 0.37 0.37 0.21t-statistic 45.72 30.08 36.66 47.50 48.25 47.68 23.30




MOMENTUM - - - 0.01 - - -0.03t-statistic - - - 0.20 - - -0.57


LONG_REVERSAL - - - - - -0.04 0.00t-statistic - - - - - -0.74 0.01

35

TABLE 9. Distributions of success ratios

We construct histograms that show how one-factor fund alphas vary across a range of performance buckets for various groups of funds. The results of this analysis are shown in Table 9.

s

m

a

l

l

e

r

t

h

a

n

-

5

%

-

5

t

o

-

4

%

-

4

t

o

-

3

%

-

3

t

o

-

2

%

-

2

t

o

-

1

%

-

1

t

o

0

%

0

t

o

1

%

1

t

o

2

%

2

t

o

3

%

3

t

o

4

%

4

t

o

5

%

l

a

r

g

e

r

t

h

a

n

5

%

All Funds 9% 6% 9% 12% 13% 14% 11% 8% 5% 5% 3% 4%

64% 36%No exposures 10% 7% 13% 17% 17% 16% 10% 5% 2% 1% 1% 1%

80% 20%LOW-BETA 7% 4% 6% 7% 17% 12% 13% 11% 6% 6% 5% 7%

53% 47%SMALL CAP 9% 4% 4% 5% 7% 10% 11% 12% 9% 10% 7% 11%

39% 61%VALUE 5% 1% 2% 6% 7% 13% 12% 16% 10% 10% 6% 12%

34% 66%MOMENTUM 16% 8% 6% 8% 16% 9% 7% 11% 3% 6% 3% 7%

63% 38%SHORT_REVERSAL 38% 19% 12% 12% 12% 4% 0% 0% 0% 0% 0% 4%

96% 4%LONG_REVERSAL 18% 10% 9% 18% 8% 6% 6% 5% 6% 4% 3% 9%

68% 33%

36

TABLE 10. Multiple factor exposures and outperformance

We run a similar regression as for the analysis in Table 5, but now regress (winsorized) fund alphas and success ratios on the number of factors to which the funds are exposed. For example, for winsorized fund alphas we run the following regression:

ii FACbFACbFACbaAlphaz ++++= _3_2_1_ 321 . The results of this analysis are shown in Table 10.

# z_Alpha Alpha Succes

Intercept 2146 -0.27 -1.89 0.20t-statistic - -15.03 -26.26 20.67

1_FAC 1360 0.46 1.63 0.31t-statistic - 16.06 14.06 19.87

2_FAC 484 0.91 3.34 0.48t-statistic - 21.75 19.88 21.66

3_FAC 36 0.98 3.53 0.58t-statistic - 6.99 6.29 7.77

37

FIGURE 1. Distribution of alphas for value funds versus no-factor investing funds

We construct a histogram that shows how one-factor fund alphas vary across a range of performance buckets for value funds versus no-factor investing funds. The results of this analysis are shown in Figure 1.

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