On the robustness of persistence in mutual fund performance

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North American Journal of Economics and Finance

On the robustness of persistence in mutual fund performance夽

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Juan Carlos Matallín-Sáez a,∗, Amparo Soler-Domínguez a, Emili Tortosa-Ausina b

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Universitat Jaume I, Spain Universitat Jaume I and Ivie, Spain

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a r t i c l e

i n f o

a b s t r a c t

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Article history: Received 23 December 2014 Received in revised form 5 January 2016 Accepted 6 January 2016 Available online xxx

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Keywords: Mutual fund Performance Persistence Robustness

This paper analyzes persistence in US equity mutual fund performance over the period 1990–2015. We apply commonly used measures of persistence, which we test using a set of simulated passive funds. In the first stage we apply contingency tables and transition matrices in accordance with previous literature. Results show how these methodologies are biased towards finding evidence of persistence too easily. In the second stage, we take a recursive portfolio approach, which assesses the performance of investing by following recommendations based on past performance. Results show the importance of both estimating persistence by distinguishing among fund style groups, and considering the cross-sectional significance of recursive portfolios. In general, our results support evidence of persistence in mutual fund performance, especially for the case of the best mutual funds. However, this evidence does not hold for the most recent subperiod, 2008–2015. Empirical evidence of persistence is conditioned by the sample period, a result that could explain the inconclusive results found in the literature. © 2016 Elsevier Inc. All rights reserved.

夽 This study is part of the research projects P1·1B2012-07 and P1·1B2014-17 supported by the Universitat Jaume I, the Spanish Ministerio de Economía y Competitividad (project ECO2014-55221-P) and Generalitat Valenciana (PROMETEOII/2014/046 and ACOMP/2014/283). We thank Manuel J. Rocha-Armada, José L. Sarto-Marzal and Katja Ahoniemi for their comments. We are especially grateful to two anonymous referees whose comments have contributed to the overall improvement of the article. The usual disclaimer applies. ∗ Corresponding author at: Department of Finance and Accounting, Universitat Jaume I, Campus del Riu Sec, 12071 Castelló

de la Plana, Spain. Tel.: +34 964387147; fax: +34 964728565. E-mail address: [email protected] (J.C. Matallín-Sáez). http://dx.doi.org/10.1016/j.najef.2016.01.002 1062-9408/© 2016 Elsevier Inc. All rights reserved.

Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

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1. Introduction

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For decades, the development of mutual fund industries has motivated a large body of literature that attempts to further understanding mutual fund performance, an important issue for both investors and managers because of its undeniable impact on wealth. In this important field of research, the question of whether mutual fund managers are skilled enough to beat the market is still under debate. However, while the issue of past performance is important, that of whether it might arise in the future is of even greater concern. Indeed, both individual and institutional investors have an interest in performance methods that can help them to select the funds that will provide the best future results. In this context, the objective of the present study is to analyze the performance and persistence of a sample of 17,775 US multi-share mutual funds from 1990 to 2015, with particular interest in testing the robustness of the persistence methodologies commonly considered in the literature. Firstly, to assess performance we use several linear models with different risk factors: Jensen’s (1968) one-factor model, Fama and French’s (1993) three-factor model, Carhart’s (1997) four-factor model, Fama and French’s (2015) five-factor model, and Cremers et al.’s (2013) seven-factor model. We opted for multifactor models because they mitigate the bias due to the omission of factors or benchmarks related to the classes of assets in which the mutual funds invest (Elton, Gruber, & Blake, 1996; Matallín-Sáez, 2006; Pastor & Stambaugh, 2002; Sharpe, 1992). Multifactor models have been widely used in the literature, in studies such as Kosowski, Timmermann, Wermers, and White (2006), Busse, Goyal, and Wahal (2010) or Fama and French (2010), among others. Concerning the evidence for mutual fund performance in the literature, some studies conclude that, in aggregate terms, it is impossible for funds to beat the market, while others find that a certain number of funds outperform, thereby justifying active management. Our results show that in aggregate, abnormal performance estimated with net returns is negative. As in studies by Carhart (1997), Wermers (2000), Fama and French (2010), among others, performance improves when it is estimated with gross returns. In short, although there are differences at the individual level and for the subperiod analyzed, in aggregate and after considering management and operational expenses, mutual funds do not add value for final investors. The second objective of the paper is to analyze the persistence of mutual fund performance. The evidence on this issue in the financial literature is not conclusive. Studies by Gruber (1996), Chen, Jegadeesh, and Wermers (2000) and Cohen, Coval, and Pástor (2005), Bollen and Busse (2005), Cremers and Petajisto (2009) find evidence of persistence. However some researchers point to underlying factors that could drive persistence. Carhart’s (1997) influential paper shows how persistence could be caused by managers’ costs and the momentum effect, rather than managers’ ability. Gottesman and Morey (2007) attribute persistence to the expense ratio and more recently, in the same vein, Fama and French (2010) identify costs as the source of persistence. To estimate performance, we therefore include a momentum factor to capture any source of persistence from momentum behavior in the stocks in which the fund invests. We also estimate performance and persistence with gross returns. In this way, we avoid mutual fund performance persistence being driven by persistence in mutual fund expenses. Another significant aspect regarding the evidence found in the literature is the methodology used to measure persistence. Our main contribution to this literature is to test for the robustness of different methodologies to measure mutual fund performance persistence. To meet this aim, for all the mutual funds in the sample we generate a counterpart passive fund that mimics its style. The procedure of using passive and simulated funds has been applied in some studies on mutual funds, such as Hendricks, Patel, and Zeckhauser (1993) and Bollen and Busse (2001), among others. Therefore, as by definition passive funds do not have any value added by managers, abnormal performance should be zero and persistence will not exist. The first methodologies analyzed are contingency tables and transition matrices. The application of statistical measures such as contingency tables by Brown, Goetzmann, Ibbotson, and Ross (1992), Goetzmann and Ibbotson (1994), Brown and Goetzmann (1995), Malkiel (1995), Kahn and Rudd (1995), Allen and Tan (1999), Lunde, Timmermann, and Blake (1999), Droms and Walker (2001), Silva, Cortez, and Armada (2005), Babalos, Caporale, Kostakis, and Philippas (2008) and Elyasiani and Jia (2011), has reinforced the persistence evidence mainly over short time horizons. Evidence of persistence is also Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

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found when the transition probability matrix approach is used, as in Brown, Draper, and McKenzie (1997) and Malkiel (1995). However Cuthbertson, Nitzsche, and O’Sullivan (2010) point out some limitations of contingency tables, such as the fact that they are not easy for investors to interpret, and they take advantage of aggregate information presented as predictability whether or not this predictability is significant. Furthermore, Cortez, Paxson, and Armada (1999) pointed out how results from contingency tables for small mutual fund samples should be interpreted with caution. When we apply contingency tables and transition matrices to measure mutual fund persistence, the results indicate generalized evidence supporting persistence. However, when we also apply these methodologies to the set of passive funds the results are very similar, that is, evidence of persistence in the performance of passive funds is found even though there is no active management. Therefore, these methodologies seem to be biased towards finding evidence to support mutual fund performance persistence. Secondly, another methodology applied in the literature on performance persistence measurement is the recursive portfolio approach proposed by Grinblatt and Titman (1993), Hendricks et al. (1993) and Carhart (1997). This approach assesses persistence by estimating the performance of recursive portfolios that follow investment recommendations according to the past performance of mutual funds. If there is persistence one would expect that investing in the worst (best) mutual funds in the past would result in worse (better) performance in the future. More recently, Bollen and Busse (2005), Cohen et al. (2005), Busse and Irvine (2006), Kacperczyk, Sialm, and Zheng (2008), Busse et al. (2010), Fama and French (2010) and Benos and Jochec (2011) also apply a similar approach in different markets. However, Hendricks et al. (1993) and Brown and Goetzmann (1995) find that common investment strategies adopted by managers, but not captured by benchmarks or risk adjustment, could cause evidence of persistence. In this line, our second contribution focuses on showing that artificial evidence of performance persistence could be found if abnormal performance between stock classes is persistent over time. First, our results reveal the importance of estimating persistence by considering a separate analysis for groups of mutual funds according to their style. When persistence is analyzed for all mutual fund styles, evidence of persistence might be due not to persistence in the value added by active management, but rather to the behavior of the underlying classes of stock in which the mutual fund invests. Second, we are concerned about the significance of abnormal performance of the recursive portfolios that invest according to dynamic strategies based on mutual funds’ past performance. Usually, if this abnormal performance is significant and negative (positive) for strategies that invest in the worst (best) past mutual funds, evidence of persistence is found. However, it is necessary to correctly identify whether this abnormal performance is due precisely to a dynamic investment strategy based on past performance, or whether it is obtained per se by simply investing in a particular style group of mutual funds. With this aim, we contribute to the literature by proposing a cross-sectional test to control for significance of the recursive portfolios. Specifically, we generate synthetic portfolios in the same way as recursive portfolios, but with the difference that now the dynamic investment strategy is not based on the mutual funds’ past performance, but that the mutual funds invested in are selected randomly. We then estimate the abnormal performance of these synthetic portfolios. Thus, for all recursive portfolios, we generate a set with a higher number of synthetic portfolios whose abnormal performances define a cross-sectional distribution with which to test significance. If there is persistence in the added value from managers, a recursive portfolio that invests in the worst (best) mutual funds should show a negative (positive) abnormal performance significantly different from that obtained by a random strategy that invests in the mutual funds without any criteria. Next, we apply the recursive portfolio methodology to the sample of US mutual funds. Robustness is also tested by comparing with the set of simulated passive funds. Finally, when controlling for the cross-sectional significance of the abnormal performance, our results show evidence of persistence, especially for the performance of the best mutual funds. However, when the analysis is carried out for different subperiods, the evidence of persistence does not holds for all them. Thus, for the 1990–2007 subperiod persistence is found, and is more significant for the case of funds that add positive value for investors; however, for the 2008–2015 subperiod we find no evidence of persistence. Indeed, in this most recent subperiod some evidence of reversal persistence is even found: investing in past losers results in better future performance than investing in past winners. This evidence is found Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

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for simulated passive funds and groups of mutual funds with low active management such as index funds. This is due to a contrarian effect in the classes of stock in which funds invest. This result could explain the modest reversion also found by Busse et al. (2010) in the persistence of mutual fund performance. In sum, the existence of mutual fund persistence seems to be conditioned by the sample period considered, a result that could explain the varied and inconclusive evidence found in the literature. The remainder of the paper is organized as follows: Section 2 proposes the methodological framework. In Section 3, the US market and US mutual fund data is described. Section 4 contains the empirical results for both performance and persistence, and finally Section 5 concludes.

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2. Performance methodology

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To add value to a particular portfolio, a mutual fund manager can implement a set of strategies Sj, for j = 1, . . ., J. These strategies may vary widely, however. Some examples of different strategies may include investing in the risk free asset; investing in the stock market index; investing in microcap stocks; or exploiting an arbitrage opportunity. Therefore, the return of a given portfolio p can be expressed as: Rp,t =



ESj,t /Ap,t−1

(1)

j 141 142 143 144

145

where ESj,t are the earnings obtained by following the Sj strategy, and Ap,t−1 is the value of the assets in which portfolio p invests at the beginning of the period (t − 1). Computing the return for a given strategy RSj,t as the quotient of ESj,t and Ap,t−1 , the return of the portfolio at time t may be expressed as the sum of the returns of the strategies, namely Rp,t =



RSj,t

(2)

j 146 147 148

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In the literature it is frequently the case that performance measures compare mutual fund returns with a set of factors, or benchmarks, in the context of a linear model. Likewise, the strategies may be assessed by a model such as RSj,t = aSj +



ˇSj,i Fi,t + Sj,t

(3)

i 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168

where aSj measures the value added by following strategy Sj to the performance measure defined by factors Fi,t , for i = 1, . . ., N, and Sj,t is the error term of the model. For instance, in the CAPM, only two factors Fi,t would be considered in Eq. (3), namely, the return of the risk free asset rf,t (assuming that ˇSj,f is equal to one), and the excess return of the market rm,t . Therefore, strategies will be assessed by means of RSj,t = aSj + rf,t + ˇSj,m rm,t + Sj,t

(4)

Let us suppose there is a given fund with a particular strategy, Sf, which consists of investing in the risk free asset. Then, when it is assessed by means of Eq. (4), and assuming cov(rf,t ; rm,t ) = 0, the abnormal performance aSf will be equal to zero since RSf,t = rf,t . In other words, this strategy does not add any value when Eq. (4) is used to measure performance. Also, it is well-known that a strategy on the Capital Market Line of the CAPM which combines the investment in the stock market and the risk free asset will show an abnormal performance equal to zero in (4). Another example is a strategy based on arbitrage, which we refer to as Sb. If it is uncorrelated with respect to rm,t , then the performance obtained when applying Eq. (4) will be computed directly as aSb = E(RSb,t − rf,t ). In general, the last result will be expected for any strategy uncorrelated with the market factor. Analogously, if a strategy Sj shows any level of dependence, part of the RSj,t is captured by the factor, but another part will be priced by aSj . Therefore, a strategy based on investing in small cap stocks may yield a performance different from zero when Eq.(4) is applied. However if a factor for small stocks is Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

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considered in Eq. (3), it is very possible that the strategy will be correlated with the new factor, and then the performance aSj will be closer to zero. At the mutual fund portfolio level, by substituting Eq. (3) into (2) we can obtain the following expression: Rp,t =



aSj +

j 174

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 j

ˇSj,i Fi,t +

i



Sj,t

(5)

j

And, if we compare Eq. (5) with the following expression: Rp,t = ˛p +



ˇp,i Fi,t + εp,t

(6)

i 176

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we will obtain the following three expressions: ˛p =



aSj

(7)

j

178

ˇp,i =



ˇSj,i

(8)

Sj,t

(9)

j

179

εp,t =

 j

180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211

Therefore, the alpha or abnormal performance of a p mutual fund, ˛p , can be expressed as the sum of the performance aSj of the strategies implemented by the mutual fund manager. If a manager aims to achieve a positive performance, strategies with a positive performance must be implemented. In this task, the strategy will be, up to a certain level, uncorrelated with factors. On this question, Sharpe (1991, 1992) indicated that in order to beat the market or benchmark, a mutual fund will be differentiated from the benchmark, and then the residual variance of a model like that represented by Eq. (6) will measure the level of active management of the mutual fund. However, as noted above the relationship between management skills and abnormal performance may not be bi-univocal. In fact, as Berk and Green (2004) point out, no alpha does not imply no skill or, as Savov (2009) concludes, even negative alpha does not imply no skill. Therefore, according to our model it is possible that managers will follow a passive strategy, such as buy and hold, but that in Eq. (4) a value of performance aSj will be obtained because, for instance, they invest in a class of stocks that is not perfectly correlated with the factors, or benchmarks in Eq. (3). One solution might be to include relevant factors or benchmarks to ensure that all asset classes are considered in the performance model in order to avoid omitted benchmark bias (Elton, Gruber, Das, & Hlavka, 1993; Matallín-Sáez, 2006; Pastor & Stambaugh, 2002). In this vein, the most recent literature on mutual fund performance has applied multifactor models as particular cases of expression (6). Then we measure mutual fund performance with a set of different linear models for which the number of factors is increasing. The first, named the 1F model, is the CAPM with one factor only—the excess market return rm,t . The second, referred to here as the 3F model, is the Fama and French (1993) three factor model, which considers an additional two factors, namely, the return of small stocks minus the return of big stocks rsmb,t , and the difference of the return between higher and lower bookto-market ratio stocks rhml,t . Next, the 4F model in which the momentum factor is added, the return of past winners minus past losers rwml,t proposed by Carhart (1997). This model has been widely applied in the recent mutual fund literature, by Kosowski et al. (2006), Kacperczyk and Seru (2007), Fama and French (2010), Busse et al. (2010), Huij and Derwall (2011), among others. The 5F model is from Fama and French (2015) and incorporates two additional factors into the the 3F model: (i) rrmw,t , corresponding to the difference between the returns on diversified portfolios of stocks with robust and weak profitability; and (ii) rcma,t , corresponding to the difference between the returns on diversified portfolios of the stocks of low and high investment firms—referred to here as conservative and aggressive firms. Finally, we consider the 7F model by Cremers et al. (2013) who, based on the 4F model, replaces HML and SMB factors with five other factors: (i) mid minus big; (ii) rmmb,t ; (iii) small Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

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minus mid rsmm,t ; (iv) big high book-to-market ratio minus big low book-to-market ratio, rbhml,t ; and, similarly, small high minus small low, rshml,t , and mid high minus mid low, rmhml,t . As these factors are representative of US stock markets, the omitted benchmark bias is a priori lower when considering models with a higher number of factors. However, it is important to point out that, even so, a passive strategy, with low correlation with factors, could yield non-zero performance. This is especially relevant in the case of some classes of stocks which, during the sample period, perform differently from others. Thus, for instance, if aSvalue > aSgrowth in Eq. (3), i.e. if value stocks show better performance than growth stocks, then value style mutual funds will perform better than growth style funds, even though managers have not undertaken any particular active management in either case. Analogously, “artificial” evidence of persistence could be found in the case where performance between stock classes is persistent over time. For this reason, we consider different groups of mutual funds to estimate persistence. But, even so, it is possible that in Eq. (3) some other passive management strategy will obtain non-zero performance that persists over time. We therefore test for the robustness of the persistence measurement with a nonparametric approach in which performance and persistence results are benchmarked to the performance and persistence of simulated passive funds. This approach of building portfolios by mimicking style, or simulating strategies, has been documented in previous literature such as Bollen and Busse (2001), Bollen and Busse (2005), or Benos and Jochec (2011), among others. The simulated funds are constructed following Sharpe (1992) methodology. In this approach, the passive management of a fund is identified by the weight invested in each asset class. Therefore, the set of weights will define the style of the fund. In contrast, the deviations from the style in each period are identified as the active management. Therefore, for each p fund in the sample we construct a simulated fund Sp that replicates its style. This procedure guarantees that the simulated funds will be diversified in the same way as the mutual funds are.1 To form simulated funds, we applied the methodology proposed by Sharpe (1992) finding the weight ωSp,b invested in each benchmark b (for b = 1 to B benchmarks) that solve the following linear programming problem, T 

Minimize

ε2Sp,t

t=1

s.t. 238

(10)

ωSp,b ≥ 0, B 

ωSp,b = 1.

b=1 239

(i.e. subject to conditions of non-negativity and convexity), taking also into account that: rSp,t =

240

B 

ωSp,b rb,t

(11)

b=1 241 242 243 244 245 246

and εSp,t = rp,t − rSp,t

(12)

The mutual fund performance literature is usually concerned with analyzing whether managers add value from the investor’s perspective (Bär, Kempf, & Ruenzi, 2011). To this end, net returns are used in performance models from Eq. (6). Net returns are computed by comparing the NAV (the net asset value of the fund) on particular dates, and considering any distributed gain. The NAV is net

1 We also considered the possibility of totally random simulated funds, but these investments were highly variable in different classes of stocks. As a result, although they were passively managed funds, some performance and persistence were evidenced by the implicit effect of the performance and persistence of certain classes of stocks. For this reason we constructed simulated funds that replicate the style of each fund.

Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

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of expenses, and for this reason it is a good proxy for the investor’s return without accounting for subscription and redemption costs. However, we also show results using gross returns, since this is especially relevant for measuring persistence. In fact, if cross-sectional performance is explained, up to a significant level, by expenses, artificial evidence of persistence may be found if the differences in the expenses across the mutual funds are persistent over time.2 We compute gross returns by adding expenses to net returns.

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3. Data

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3.1. Mutual fund and factors’ data

247 248 249 250 251

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We analyze the performance persistence of a large number of US domestic equity mutual funds for an extended period of time. Such a large sample allows us to draw inferences about the performance of the fund industry in general. In this way a sufficiently high number of funds can be included to analyze persistence in each different fund group. We use daily mutual fund return data, which are available from 1990; our study therefore covers more than 25 years—specifically, the sample period runs from January 1990 to June 2015. To assess the performance of mutual funds in the industry and to avoid survivorship bias, both new and non-survivor mutual funds were considered. Previous research provides evidence on the effect of survivorship bias, especially when nonsurvivors are underperforming funds, as pointed out by Brown and Goetzmann (1995), Elton et al. (1996) and Deaves (2004). But, as our main objective is to analyze persistence, the inclusion of funds with limited data has several effects: (i) the low number of observations limits the measurement of persistence robustness; (ii) there may be a bias if the mutual fund’s performance is correlated with the period for which data are available (for instance, the performance could differ depending on the economic cycle); and (iii) in consequence, comparing funds with different periods of existence could add some noise to the estimations. Therefore, the sample used for the persistence analysis contains all US domestic equity mutual funds with at least one and a half years over the sample period. As we measure the persistence between natural semesters, this way we ensure that each fund in the sample has at least two full semesters in which to estimate the performance. Specifically, we initially considered 17,775 multi-share mutual funds from the Morningstar database. Of these the final sample contained only the 15,059 multi-share funds that met the requisite of having complete data for at least one and a half years. Following standard procedure, multiple share classes are aggregated as one single unit, or mutual fund. The final sample consisted of 4,467 mutual funds. In order to increase the robustness of the empirical results, the sample period was split into three subperiods, coinciding with moments of pre- and post-financial crises. The first period runs from 1990 to 1997 and consists of 1,278 mutual funds; the second from 1998 to 2007 with 3425 funds; and the third, from 2008 to 2015, with 2994 funds. In the previous section we pointed out how in expression (3) we can find passive strategies that will provide non-zero performance, and how they are linked to the behavior of the different classes of stocks. To ameliorate the severity of this issue, mutual funds are grouped according to their investment style as defined by the Morningstar Style Box. Previous studies, such as Teo and Woo (2004) have also demonstrated the suitability of using the Style Box. These categories are useful to show performance results, but are also necessary to measure mutual fund persistence. If we evaluate the persistence for all funds as a whole, i.e. without grouping by style, it is likely that most of the persistence that we might find would not be attributable to managers, but to the persistence of the stock style classes in which the fund invests. Panel A of Table 1 shows some descriptive statistics of the mutual funds sample, and the varied behavior across the mutual fund style groups is noteworthy. This highlights the need to perform the persistence analysis within each group. For Table 1 and for the rest of the

2 This issue is especially important for the case of fixed income or cash mutual funds. Given that the return of the underlying asset does not show very much volatility and active management is lower, the main factor explaining performance is expenses. Although our sample is made up of equity funds and the impact of expenses is lower in cross-sectional terms, we show all the persistence results for gross returns.

Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

Mid Blend

Mid Value

Large Growth

Large Blend

Large Value

Index

All

72 1.53% 17.27% 12.11%

40 1.40% 19.09% 10.70%

124 1.63% 17.42% 15.04%

67 1.41% 16.88% 12.18%

43 1.65% 15.47% 11.06%

267 1.39% 18.04% 14.43%

280 1.30% 17.01% 12.15%

195 1.32% 17.83% 10.74%

62 0.52% 18.26% 13.02%

1,278 1.38% 17.48% 12.96%

346 1.56% 9.40% 22.61%

226 1.49% 9.17% 18.37%

144 1.47% 7.87% 16.80%

350 1.50% 8.69% 22.78%

149 1.48% 9.40% 18.29%

131 1.32% 8.41% 16.60%

702 1.37% 4.89% 20.77%

659 1.27% 6.02% 17.22%

511 1.33% 7.50% 16.68%

207 0.67% 5.25% 19.61%

3,425 1.34% 7.10% 19.21%

290 1.47% 7.39% 27.24%

255 1.47% 9.02% 26.47%

140 1.39% 8.99% 26.57%

292 1.38% 5.54% 26.06%

148 1.33% 7.43% 24.71%

145 1.25% 8.77% 24.98%

588 1.24% 5.75% 23.84%

527 1.15% 5.86% 22.81%

442 1.18% 5.17% 24.28%

167 0.54% 7.68% 24.77%

2,994 1.25% 6.59% 24.77%

435 1.53% 8.69% 24.03%

319 1.40% 9.46% 21.95%

208 1.43% 8.20% 21.04%

435 1.47% 7.92% 23.38%

220 1.38% 8.24% 20.85%

197 1.35% 8.92% 20.37%

870 1.34% 6.36% 21.75%

878 1.24% 6.85% 18.76%

651 1.27% 7.70% 19.45%

254 0.62% 7.09% 21.25%

4,467 1.31% 7.59% 21.06%

Mkt-RF

SMB

10.92% 11.66%

−1.12% 7.16%

4.27% 18.21%

HML

RMW

CMA

WML

MMB

SMM

BHML

SHML

MidHML

3.31% 6.38%

6.29% 3.88%

1.82% 5.11%

10.61% 6.43%

−0.80% 4.97%

−1.18% 4.47%

0.25% 11.61%

11.04% 7.91%

2.64% 9.69%

4.82% 0.09%

3.31% 9.95%

4.43% 10.54%

3.97% 9.16%

4.98% 8.68%

11.72% 14.15%

1.88% 7.04%

0.80% 7.04%

0.77% 15.30%

9.11% 12.02%

3.54% 16.95%

3.49% 0.11%

9.53% 22.51%

3.47% 9.94%

−0.58% 10.58%

3.27% 5.73%

1.46% 4.79%

−2.11% 17.93%

3.60% 5.58%

−0.73% 7.38%

−1.00% 15.56%

1.86% 10.64%

−0.54% 12.26%

0.26% 0.04%

7.91% 17.92%

1.96% 9.16%

2.61% 9.44%

4.50% 6.87%

2.95% 6.66%

7.31% 13.63%

1.54% 6.02%

−0.27% 6.45%

0.09% 14.33%

7.59% 10.46%

2.06% 13.64%

2.96% 0.14%

RF

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128 1.54% 17.07% 15.27%

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PANEL B: Factors Sub-Sample 1990–1997 Annualized mean return Annualized s.d. Sub-Sample 1998–2007 Annualized mean return Annualized s.d. Sub-Sample 2008–06/2015 Annualized mean return Annualized s.d. Sample 1990–06/2015 Annualized mean return Annualized s.d.

Mid Growth

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PANEL A: Mutual funds Sub-Sample 1990–1997 # funds Average of expense ratio Average of annualized net return Average of annualized s.d. Sub-Sample 1998–2007 # funds Average of expense ratio Average of annualized net return Average of annualized s.d. Sub-Sample 2008–06/2015 # funds Average of expense ratio Average of annualized net return Average of annualized s.d. Sample 1990–06/2015 # funds Average of expense ratio Average of annualized net return Average of annualized s.d.

Small Value

ECOFIN 569 1–40

Small Blend

Small Growth

8

Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

Table 1 Summary statistics for the mutual funds, factors, and benchmarks in the sample. The sample runs from January 1990 to June 2015. Panel A shows the number of mutual funds, average expense ratio, average annualized net return and average annualized standard deviation (s.d.). Mutual funds are classified according to Morningstar Style box. Panel B shows the annualized mean of return and risk (measured by s.d.) for factors used in the performance models. Panel C shows this same data for benchmarks used to estimate simulated funds in model (10)–(12).

Russell 1000 Value

Russell 2000

Russell 2000 Growth

Russell 2000 Value

Russell 2500

Russell 2500 Growth

Russell 2500 Value

Russell 3000

Russell 3000 Growth

Russell 3000 Value

16.12% 12.06%

16.36% 13.87%

16.02% 11.78%

14.18% 10.89%

12.68% 17.37%

16.46% 12.87%

15.54% 12.63%

14.34% 17.15%

16.73% 12.32%

15.91% 11.80%

16.04% 14.33%

16.08% 11.99%

7.65% 18.05%

6.11% 21.69%

8.75% 16.31%

9.03% 20.81%

7.33% 24.87%

10.26% 17.66%

10.47% 19.10%

9.53% 24.89%

10.50% 15.83%

7.67% 18.05%

6.12% 21.69%

8.78% 16.20%

9.54% 22.65%

10.39% 21.54%

8.72% 24.33%

12.03% 28.45%

12.86% 27.96%

11.25% 29.33%

12.04% 26.33%

12.57% 26.05%

11.60% 26.98%

9.69% 22.97%

10.54% 21.90%

8.88% 24.57%

10.88% 18.00%

10.60% 19.52%

11.03% 17.93%

11.53% 21.08%

10.64% 23.80%

12.50% 20.66%

12.53% 19.91%

11.94% 23.11%

12.79% 18.96%

10.86% 18.06%

10.54% 19.74%

11.11% 18.03%

Russell Micro Cap

Russell Micro Cap Growth

Russell Micro Cap Value

Russell Mid Cap

Russell Mid Cap Growth

Russell Mid Cap Value

Russell Small Cap Complete

Russell Small Cap Complete Growth

Russell Small Cap Complete Value

Russell Top 200

Russell Top 200 Growth

Russell Top 200 Value

16.05% 13.71%

15.63% 15.70%

16.33% 12.81%

15.66% 14.35%

14.74% 17.27%

16.71% 12.37%

16.38% 12.98%

16.91% 14.39%

15.94% 12.34%

PANEL C: Benchmarks (contd.) Sub-Sample 1990–1997 Annualized mean return Annualized s.d. Sub-Sample 1998–2007 9.34% Annualized mean return Annualized s.d. 17.59% Sub-Sample 2008–06/2015 Annualized mean return 11.10% 27.73% Annualized s.d. Sample 1990–06/2015 Annualized mean return 10.22% 23.22% Annualized s.d.

2.95% 20.20%

14.79% 17.16%

11.10% 18.01%

10.55% 25.38%

10.88% 15.19%

9.47% 21.50%

9.48% 27.68%

9.42% 16.39%

6.63% 18.45%

5.19% 21.35%

7.95% 17.23%

12.11% 27.59%

10.39% 28.43%

11.41% 24.94%

11.36% 24.88%

11.48% 25.44%

11.90% 26.30%

12.69% 26.06%

11.15% 27.09%

8.86% 21.95%

10.15% 20.49%

7.68% 24.14%

7.53% 24.18%

12.59% 23.48%

12.75% 19.20%

12.39% 22.61%

12.77% 18.22%

12.14% 21.19%

12.08% 24.35%

12.23% 19.20%

10.36% 18.10%

10.34% 19.15%

10.39% 18.31%

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Russell 1000 Growth

G Model

ECOFIN 569 1–40

PANEL C: Benchmarks Sub-Sample 1990–1997 Annualized mean return Annualized s.d. Sub-Sample 1998–2007 Annualized mean return Annualized s.d. Sub-Sample 2008–06/2015 Annualized mean return Annualized s.d. Sample 1990–06/2015 Annualized mean return Annualized s.d.

Russell 1000

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Table 1 (Continued)

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article, mutual funds’ daily net returns are computed by comparing the NAV of the fund for daily dates and considering any distributed gain. Gross returns are subsequently estimated by adding daily fund expenses. First, Panel A of Table 1 shows that the largest groups are those corresponding to Large styles; in fact 53.70% of the 4467 funds in the sample belong to these groups. This is important information because any results or conclusions drawn about these groups of funds have implications for most of the assets managed in the sample. Also notable is that, on average, Large and Index funds, are cheaper, and in general show lower return and risk. In contrast, Mid and Small style groups, are more expensive, and achieve higher levels of return and risk. Second, we look at the data for the mutual funds in Panel A of Table 1 based on the characteristics of growth, blend and value. Note that, in general, the number of funds of the group decrease as we move from growth funds to blend and value funds (within each set of Small, Mid and Large funds, respectively). This pattern is monotonically repeated for expenses, thus growth funds are more expensive than blend and value funds. In contrast, in general, growth style funds are riskier than blend and value funds. The above descriptive data tell us something about the characteristics of the mutual fund sample. However, a proper performance model must be applied to assess management. To apply different versions of model (6) we use the daily data of the returns of the three and five Fama and French factors, the Carhart momentum factor, and the five additional factors from Cremers et al. (2013). This data—together with the data for the risk free asset, the one-month Treasury bill rate, to compute excess returns for mutual funds—was taken from French’s website.3 Panel B of Table 1 shows the annualized mean of daily return and risk (measured by the standard deviation of the returns) for these data. In addition to the differences between the funds due to style, there are also relevant differences depending on the sample subperiod considered. During the 1990–1997 subperiods, the funds present a better risk-return combination than in other subperiods. The data in the last column of Panel A (Table 1), corresponding to all funds, shows that on an annualized basis the average return was 17.48% and the average risk 12.96%, whereas in the period 1998–2007 results worsened (7.10% and 19.21% respectively), and deteriorated even further in the period 2008–2015 (6.59% and 24.77%). These values provide an initial overview of the best (worst) fund performance in the first (last) sample subperiod. This result is corroborated by observing the values for the market factor (first column to the left of Panel B, Table 1) and the risk-free asset (RF) (last column on the right of Panel B, Table 1). It therefore seems that although mutual fund risk is slightly higher than market risk, the difference between fund and market excess return is positive for the first subperiod (17.48% −4.82 % −10.92 % =1.74 %) and negative both for the second (7.10% −3.49 % −4.27 % =0.66 %) and especially for the last subperiod (6.59% −0.26 % −9.53 % = −3.20 %). As we will show below, these changes in the mutual funds’ behavior imply that the period analyzed will determine the evidence on performance persistence.

328

3.2. Simulated funds’ estimation

292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326

329 330 331 332 333 334 335 336 337 338 339

Finally, we apply linear programming problem (10)–(12) to estimate the simulated mutual funds. To this end, we need to compute the returns, rb,t , of each benchmark b. We use 24 Russell indexes for the US stock market as data for the benchmarks. These indexes represent a wide variety of stock style classes, which is very useful for developing simulated funds that replicate the style or investment objectives of the funds in the sample. Following Sharpe’s (1992) methodology, the objective is obtaining a passive management fund which correctly replicates the style of the fund. We should consider that mutual funds usually have highly diversified portfolios which invest in assets with different characteristics. Using a sufficiently high number of indexes guarantees that all asset classes are considered in the estimation procedure in order to avoid omitted benchmark bias (Elton et al., 1993; Matallín-Sáez, 2006; Pastor & Stambaugh, 2002). In addition, using a high number of indexes enables the optimization procedure to more easily achieve the combination of asset classes which best represents the style of

3

See http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data library.html.

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the fund. Panel C of Table 1 shows the annualized mean of daily return and risk (measured by standard deviation of the returns) for these data. For each fund in our sample, Eqs. (10)–(12) are estimated four times, i.e., once for the full sample and once for each of the three subperiods. The objective is to find an artificial passive management fund for which a given investor might have invested during the sample period so that it replicates the asset allocation or average style of the mutual fund under analysis. Table 2 shows some statistics corresponding to the estimation of Eqs. (10)–(12). Specifically, we report the average values, for each group of funds, of the number of benchmarks as a function of their weights, wSp,b , in the simulated fund. Table 2 also reports information on the average weight, the average of the maximum weights, and the up to the 3rd and 5th highest weights. Simulated funds offer a diversified investment among the benchmarks, for which the average weight for the entire sample period ranges between 20.69% and 27.16%. In addition, and also on average, between 96.42% and 98.73% of their portfolios are diversified among at least five benchmarks.

353

4. Results

354

4.1. Performance

340 341 342 343 344 345 346 347 348 349 350 351

355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389

From Eq. (6) five linear models are applied to measure the performance of the mutual funds. Table 3 shows a summary of the results: Panel A when performance is estimated from mutual fund net returns and Panel B for gross returns. Annualized performance from daily alpha is reported. In each panel, results are grouped by style type and the average is reported. From net returns, the last row of Panel A shows an average performance for all funds and the whole sample with negative values that range from −1.38% for the 1F model to −1.81% for the 7F model. We observe differences according to both the model used and the fund style. In general, applying the 1F model (CAPM) yields better performance than the other models, especially for small funds. This result is not surprising if we consider that this model omits risk factors whose relevance is wellknown and recognized by the literature. In general, the models yielding more similar performances are models 3F, 4F and 7F. As we anticipated in the data section, differences in performance are also evident depending on the sample subperiod considered. A look at the rows corresponding to the average for all funds shows that the performance corresponding to the last period (2008–2015) is much worse than that corresponding to the two previous subperiods and, of these two, the performance corresponding to 1990–1997 is slightly better than that corresponding to the middle subperiod. This evidence is robust with respect to the model applied, since in almost all cases this result is maintained. Consequently, over time it appears that managers’ ability to add value (in net terms) has deteriorated. In this regard, a particularly remarkable case is that of Growth funds for the 7F model which in the 1990–1997 subperiod and within each group (Small, Mid and Large) achieve the best performance (2.20%, 1.89% and −0.12%, respectively), whereas in the last subperiod (2008–2015) they achieve the worst performance (−3.91%, −4.46% and −2.96%, respectively. However, if performance is estimated with gross returns, as reported in Panel B, abnormal performance improves. The last row in Panel B shows how average performance for all funds and the whole sample range from −0.26% for the 1F model to −0.69% for the 7F model. In short, as documented widely in the literature, mutual fund expenses erode performance and, in aggregate, managers do not provide added value for final investors, as Sharpe’s (1991) theoretical proposal indicated. In fact, the distance of the mean performance from gross returns and that from net returns in Table 3 is close to the mean of the expense ratio (1.31%) in Table 1. The report for the Index funds is worth additional mention. Regardless of whether we consider net or gross returns, or the subperiod analyzed, and for virtually all models applied performance takes either non-significant or negative values. This result sheds light on the efficient-market hypothesis debate. Index funds offer an investment alternative for less sophisticated investors because they are cheaper than other fund styles (see expense ratio data in Table 1), and the inefficiencies of stock selection can be avoided, but negative performance remains across subperiods. This result shows Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

Average of the number of benchmarks with wSp,b > 5%

Average of the number of benchmarks with wSp,b > 10%

Average of weight for values wSp,b > 1%

Average of maximum weights

Average of the sum Average of the sum of the 3 highest of the 5 highest weights weights

4.03 5.35 6.33 4.02 5.97 7.47 4.68 6.40 7.08 3.97

2.90 3.44 3.93 3.06 4.07 5.12 3.37 4.18 4.41 2.97

2.07 2.46 2.58 2.33 2.87 3.21 2.60 2.94 2.93 2.47

34.84% 22.58% 16.61% 33.16% 20.50% 14.37% 27.65% 19.11% 15.84% 36.45%

67.50% 59.02% 52.57% 62.08% 50.15% 42.42% 54.24% 45.69% 47.87% 58.41%

92.43% 87.22% 82.43% 93.48% 83.26% 75.71% 90.33% 81.51% 78.64% 91.98%

97.97% 96.76% 95.28% 97.72% 94.54% 89.73% 96.86% 93.08% 92.02% 97.44%

4.73 5.11 4.88 4.53 5.30 4.85 4.84 5.29 4.61 4.35

3.68 3.86 3.60 3.63 4.00 3.72 3.86 4.14 3.68 3.39

2.93 3.06 2.73 2.78 3.05 2.76 3.02 3.14 2.95 2.57

24.36% 21.79% 22.98% 25.73% 21.62% 23.25% 23.31% 20.99% 23.93% 25.41%

50.66% 48.60% 52.94% 53.55% 48.73% 54.35% 48.87% 46.66% 48.72% 56.84%

89.39% 87.56% 90.33% 89.93% 86.42% 89.09% 87.98% 85.05% 89.81% 92.10%

98.33% 97.94% 98.48% 98.31% 96.91% 98.20% 98.11% 96.63% 98.73% 98.63%

4.37 5.30 4.74 4.04 4.99 4.79

3.62 4.34 3.89 3.39 4.16 3.91

2.94 3.38 3.14 2.83 3.38 3.08

25.27% 21.55% 23.63% 28.33% 23.86% 22.80%

51.09% 44.58% 50.19% 52.88% 45.88% 51.13%

90.82% 83.10% 87.79% 92.39% 84.49% 87.76%

99.25% 96.60% 98.40% 98.99% 97.34% 98.57%

ARTICLE IN PRESS

Sub-Sample 1990–1997 Small Growth 4.71 Small Blend 6.25 6.93 Small Value 4.52 Mid Growth 6.76 Mid Blend 8.19 Mid Value Large Growth 5.25 Large Blend 7.35 Large Value 7.92 Index 5.23 Sub-Sample 1998–2007 Small Growth 5.10 5.64 Small Blend 5.37 Small Value 4.82 Mid Growth 5.85 Mid Blend 5.40 Mid Value Large Growth 5.24 5.79 Large Blend 4.99 Large Value 5.43 Index Sub-Sample 2008–06/2015 Small Growth 4.55 5.62 Small Blend 4.94 Small Value 4.28 Mid Growth 5.21 Mid Blend Mid Value 5.08

Average of the number of benchmarks with wSp,b > 1%

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Average of the number of benchmarks with wSp,b >0%

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Style

ECOFIN 569 1–40

12

Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

Table 2 Summary statistics for the simulated mutual fund estimation. For any mutual fund a counterpart simulated fund is estimated solving the model (10)–(12) using daily gross returns from March 2001 to May 2011. The table reports a summary of the statistics of the estimates.

Large Growth 4.44 5.46 Large Blend 4.60 Large Value 6.18 Index Sample 1990–06/2015 Small Growth 4.85 5.92 Small Blend 5.57 Small Value 4.71 Mid Growth 5.80 Mid Blend Mid Value 5.66 Large Growth 4.81 5.60 Large Blend 4.90 Large Value 5.13 Index

Average of the number of benchmarks with wSp,b > 1%

Average of the number of benchmarks with wSp,b > 5%

Average of the number of benchmarks with wSp,b > 10%

Average of weight for values wSp,b > 1%

Average of maximum weights

Average of the sum Average of the sum of the 3 highest of the 5 highest weights weights

4.16 5.13 4.33 5.41

3.41 4.21 3.52 4.04

2.74 3.33 2.89 3.29

27.61% 23.78% 26.22% 23.66%

55.14% 44.90% 52.00% 44.40%

91.88% 83.91% 91.22% 83.91%

98.67% 96.26% 98.93% 95.64%

4.58 5.42 5.19 4.41 5.51 5.21 4.48 5.15 4.54 4.30

3.60 4.08 3.77 3.61 4.31 3.97 3.59 3.93 3.58 3.15

2.82 3.05 2.80 2.91 3.20 3.01 2.82 3.01 2.78 2.39

25.58% 21.34% 22.09% 25.86% 20.69% 21.45% 25.03% 22.17% 24.44% 27.16%

52.92% 47.83% 52.51% 51.86% 46.19% 49.99% 53.23% 50.14% 53.23% 60.74%

90.23% 85.40% 87.72% 90.28% 83.79% 86.10% 90.53% 86.37% 90.48% 92.51%

98.58% 96.73% 97.60% 98.45% 96.42% 97.18% 98.73% 96.97% 98.63% 98.70%

ARTICLE IN PRESS

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Style

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Table 2 (Continued)

p-value

3F model

p-value

5F model

p-value

7F model

p-value

(0.207) (0.543) (0.027) (0.685) (0.328) (0.191) (0.290) (0.000) (0.000) (0.138) (0.002)

−1.41% 0.36% 2.51% −0.53% −0.91% −1.07% −0.53% −1.05% −1.12% −0.48% −0.71%

(0.011) (0.630) (0.014) (0.313) (0.152) (0.311) (0.073) (0.000) (0.000) (0.249) (0.000)

2.23% 1.20% 1.66% 3.20% 0.95% −0.84% 1.66% −1.04% −1.33% −0.73% 0.56%

(0.000) (0.059) (0.103) (0.000) (0.148) (0.403) (0.000) (0.001) (0.000) (0.124) (0.000)

2.20% 0.89% 1.52% 1.89% 0.30% −0.80% −0.12% −1.34% −0.61% −0.77% 0.04%

(0.000) (0.201) (0.113) (0.000) (0.624) (0.391) (0.697) (0.000) (0.003) (0.014) (0.768)

(0.027) (0.000) (0.000) (0.010) (0.720) (0.015) (0.002) (0.000) (0.001) (0.027) (0.000)

−0.87% −1.13% −1.56% 0.12% −0.08% −0.60% −0.85% −1.52% −1.09% −0.47% −0.90%

(0.004) (0.001) (0.002) (0.671) (0.799) (0.259) (0.000) (0.000) (0.035) (0.137) (0.000)

0.74% −1.47% −2.64% 2.92% 0.30% −1.48% 0.34% −2.09% −2.69% −0.69% −0.65%

(0.023) (0.000) (0.000) (0.000) (0.400) (0.012) (0.102) (0.000) (0.000) (0.103) (0.000)

−0.26% −1.31% −1.98% 0.14% −0.08% −0.51% −1.33% −1.50% −0.47% −0.96% −0.89%

(0.412) (0.000) (0.000) (0.619) (0.817) (0.359) (0.000) (0.000) (0.387) (0.000) (0.000)

(0.000) (0.000) (0.000) (0.000) (0.000) (0.046) (0.000) (0.000) (0.000) (0.000) (0.000)

−3.85% −2.19% −1.73% −3.29% −2.63% −0.92% −2.64% −2.18% −2.45% −1.57% −2.49%

(0.000) (0.000) (0.000) (0.000) (0.000) (0.017) (0.000) (0.000) (0.000) (0.000) (0.000)

−2.32% −2.03% −1.79% −2.01% −2.03% −0.43% −2.06% −2.29% −2.47% −1.75% −2.07%

(0.000) (0.000) (0.000) (0.000) (0.000) (0.175) (0.000) (0.000) (0.000) (0.000) (0.000)

−3.91% −2.43% −2.04% −4.46% −3.75% −2.06% −2.96% −2.34% −2.60% −1.71% −2.87%

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

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4F model

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PANEL A: Performance estimated with mutual fund net returns Sub-Sample 1990–1997 Small Growth −1.49% (0.027) −0.69% 2.53% (0.003) 0.45% Small Blend 5.65% (0.000) 2.33% Small Value −1.63% (0.012) 0.21% Mid Growth Mid Blend 0.49% (0.483) −0.60% Mid Value 1.22% (0.295) −1.39% −2.14% (0.000) 0.31% Large Growth −0.64% (0.030) −0.99% Large Blend 1.15% (0.000) −1.41% Large Value −0.57% (0.196) −0.64% Index −0.36% (0.029) −0.43% All Sub-Sample 1998–2007 0.93% (0.010) −0.70% Small Growth Small Blend 1.31% (0.005) −1.51% Small Value −0.08% (0.918) −2.50% Mid Growth 1.05% (0.001) 0.79% Mid Blend 1.24% (0.003) −0.13% Mid Value 0.30% (0.713) −1.36% Large Growth −1.92% (0.000) −0.59% Large Blend −1.13% (0.000) −1.68% Large Value 0.28% (0.623) −1.76% Index −0.44% (0.112) −0.70% All −0.25% (0.055) −1.00% Sub-Sample 2008–06/2015 Small Growth −1.80% (0.000) −3.85% Small Blend −1.00% (0.008) −2.20% −0.47% (0.323) −1.65% Small Value Mid Growth −2.27% (0.000) −3.31% Mid Blend −1.94% (0.001) −2.54% −0.36% (0.280) −0.69% Mid Value −2.41% (0.000) −2.74% Large Growth Large Blend −2.29% (0.000) −2.17% −2.78% (0.000) −2.30% Large Value −1.37% (0.000) −1.55% Index −1.98% (0.000) −2.47% All

p-value

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1F model

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Table 3 Mutual fund performance. This table reports a summary of the results of estimating mutual fund performance (ap ) using daily returns by means of different models. In each panel, results are grouped by style type and the average of the all funds is reported and the corresponding p-value, is the critical value corresponding to the t-statistic. Panel A shows performance when is estimated from mutual fund net returns and Panel B for gross returns.

1F model

p-value

3F model

p-value

4F model

p-value

5F model

p-value

7F model

p-value

(0.000) (0.573) (0.055) (0.000) (0.011) (0.149) (0.000) (0.000) (0.078) (0.000) (0.000)

−2.26% −1.77% −2.39% −1.39% −1.96% −1.61% −1.35% −2.19% −1.81% −1.07% −1.78%

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

−2.46% −1.60% −1.85% −1.64% −1.92% −1.21% −1.50% −2.09% −1.46% −0.91% −1.72%

(0.000) (0.000) (0.000) (0.000) (0.000) (0.003) (0.000) (0.000) (0.000) (0.001) (0.000)

−0.67% −1.89% −2.85% 0.75% −1.61% −1.69% −0.45% −2.60% −2.75% −1.14% −1.48%

(0.018) (0.000) (0.000) (0.002) (0.000) (0.000) (0.111) (0.000) (0.000) (0.002) (0.000)

−1.71% −1.76% −2.30% −1.79% −2.32% −1.65% −1.92% −2.19% −1.13% −1.33% −1.81%

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.010) (0.000) (0.000)

(0.360) (0.016) (0.002) (0.006) (0.475) (0.795) (0.000) (0.754) (0.025) (0.581) (0.000)

−0.23% 1.57% 3.59% 0.64% 0.12% 0.05% 0.48% −0.15% −0.20% −0.07% 0.28%

(0.670) (0.026) (0.001) (0.210) (0.847) (0.964) (0.096) (0.595) (0.346) (0.863) (0.041)

3.41% 2.41% 2.73% 4.37% 1.98% 0.28% 2.67% −0.14% −0.41% −0.32% 1.55%

(0.000) (0.000) (0.010) (0.000) (0.004) (0.776) (0.000) (0.638) (0.072) (0.489) (0.000)

3.37% 2.09% 2.59% 3.07% 1.33% 0.32% 0.89% −0.43% 0.31% −0.36% 1.04%

(0.000) (0.002) (0.010) (0.000) (0.037) (0.732) (0.004) (0.117) (0.135) (0.211) (0.000)

(0.032) (0.503) (0.017) (0.000) (0.002) (0.662) (0.005) (0.000) (0.218) (0.582) (0.270)

0.50% 0.17% −0.34% 1.35% 1.15% 0.52% 0.28% −0.50% 0.03% 0.05% 0.22%

(0.099) (0.598) (0.505) (0.000) (0.000) (0.329) (0.132) (0.000) (0.960) (0.869) (0.040)

2.11% −0.17% −1.42% 4.15% 1.53% −0.37% 1.47% −1.07% −1.57% −0.16% 0.47%

(0.000) (0.584) (0.005) (0.000) (0.000) (0.533) (0.000) (0.000) (0.004) (0.695) (0.000)

1.12% −0.02% −0.76% 1.37% 1.16% 0.61% −0.20% −0.48% 0.64% −0.43% 0.23%

(0.000) (0.959) (0.145) (0.000) (0.001) (0.272) (0.298) (0.001) (0.238) (0.055) (0.039)

PANEL B: Performance estimated with mutual fund gross returns Sub-Sample 1990–1997 −0.32% (0.632) 0.49% Small Growth Small Blend 3.74% (0.000) 1.66% Small Value 6.72% (0.000) 3.40% Mid Growth −0.45% (0.468) 1.38% Mid Blend 1.52% (0.030) 0.43% Mid Value 2.34% (0.048) −0.27% Large Growth −1.13% (0.001) 1.31% Large Blend 0.26% (0.367) −0.09% Large Value 2.07% (0.000) −0.49% Index −0.16% (0.706) −0.23% All 0.63% (0.000) 0.57% Sub-Sample 1998–2007 Small Growth 2.30% (0.000) 0.67% Small Blend 2.61% (0.000) −0.21% Small Value 1.14% (0.151) −1.28% Mid Growth 2.28% (0.000) 2.02% Mid Blend 2.47% (0.000) 1.11% Mid Value 1.42% (0.089) −0.24% Large Growth −0.79% (0.000) 0.54% Large Blend −0.11% (0.506) −0.66% Large Value 1.40% (0.015) −0.64% 0.09% (0.747) −0.17% Index 0.88% (0.000) 0.12% All

ARTICLE IN PRESS

Sample 1990–06/2015 -1.14% Small Growth −0.20% Small Blend −1.04% Small Value Mid Growth −1.23% Mid Blend −1.08% −0.71% Mid Value Large Growth −2.23% −1.98% Large Blend −0.80% Large Value Index −1.05% All −1.38%

G Model

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Table 3 (Continued)

3F model

p-value

4F model

p-value

5F model

p-value

7F model

p-value

(0.238) (0.290) (0.076) (0.003) (0.212) (0.013) (0.000) (0.000) (0.000) (0.010) (0.000)

−2.44% −0.80% −0.35% −1.99% −1.31% 0.50% −1.57% −1.09% −1.19% −1.03% −1.29%

(0.000) (0.031) (0.367) (0.000) (0.023) (0.143) (0.000) (0.000) (0.000) (0.001) (0.000)

−2.43% −0.80% −0.43% −1.98% −1.40% 0.27% −1.46% −1.10% −1.33% −1.05% −1.31%

(0.000) (0.030) (0.274) (0.000) (0.021) (0.477) (0.000) (0.000) (0.000) (0.000) (0.000)

−0.91% −0.64% −0.49% −0.70% −0.80% 0.76% −0.88% −1.20% −1.35% −1.23% −0.89%

(0.005) (0.064) (0.199) (0.014) (0.143) (0.018) (0.000) (0.000) (0.000) (0.000) (0.000)

−2.49% −1.03% −0.74% −3.14% −2.53% −0.87% −1.79% −1.25% −1.48% −1.19% −1.69%

(0.000) (0.006) (0.072) (0.000) (0.000) (0.031) (0.000) (0.000) (0.000) (0.000) (0.000)

(0.507) (0.003) (0.741) (0.965) (0.878) (0.369) (0.000) (0.000) (0.523) (0.024) (0.018)

−0.92% −0.52% −1.17% −0.16% −0.81% −0.46% −0.22% −1.16% −0.73% −0.56% −0.67%

(0.001) (0.086) (0.005) (0.491) (0.055) (0.276) (0.448) (0.000) (0.081) (0.039) (0.000)

−1.11% −0.35% −0.63% −0.42% −0.77% −0.06% −0.37% −1.06% −0.38% −0.40% −0.60%

(0.000) (0.247) (0.107) (0.064) (0.073) (0.879) (0.195) (0.000) (0.363) (0.144) (0.000)

0.68% −0.64% −1.63% 1.97% −0.46% −0.54% 0.68% −1.57% −1.67% −0.63% −0.37%

(0.016) (0.026) (0.000) (0.000) (0.276) (0.201) (0.015) (0.000) (0.000) (0.073) (0.001)

−0.37% −0.50% −1.08% −0.57% −1.17% −0.50% −0.79% −1.16% −0.05% −0.82% −0.69%

(0.173) (0.102) (0.005) (0.008) (0.008) (0.204) (0.007) (0.000) (0.907) (0.000) (0.000)

ARTICLE IN PRESS

p-value

G Model

1F model

Sub-Sample 2008–06/2015 −0.39% Small Growth Small Blend 0.40% 0.83% Small Value −0.95% Mid Growth −0.71% Mid Blend 0.83% Mid Value −1.23% Large Growth −1.21% Large Blend −1.66% Large Value Index −0.85% −0.80% All Sample 1990–06/2015 0.21% Small Growth 1.05% Small Blend 0.18% Small Value −0.01% Mid Growth Mid Blend 0.07% 0.44% Mid Value −1.10% Large Growth −0.95% Large Blend 0.29% Large Value Index −0.54% −0.26% All

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Style

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Table 3 (Continued)

G Model

ARTICLE IN PRESS

ECOFIN 569 1–40

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426

the perverse asymmetric behavior of Index funds: they are unable to achieve positive performance because they are unable to beat the market, but negative values may be achieved due to expenses and the impact of mimicking index rules in the context of a multifactor model like that in expression (6) for performance measurement. The differences in performance between each mutual fund style group indicated above highlight the relevance of estimating persistence for each group. Thus, if we analyze the persistence for all funds, we can find that persistence is not due to the fact that the value added by managers is persistent, but because the performance of the underlying type of stocks for any group of funds is persistent. As stated in the methodology section, we will compare the performance and persistence results of the sample funds with those of passively managed funds that mimic their style. The style of each mutual fund is estimated by applying expression (10)–(12), which gives a simulated fund for each real mutual fund. Since we are interested in measuring persistence before considering expenses, this procedure is carried out for gross returns. Table 4 presents the results of applying model from expression (6) to the simulated mutual funds’ daily returns. As Cremers et al. (2013) pointed out, it is possible to find non-zero alphas even for benchmarks, and in general for passive portfolios. However, the dimension corresponding to these alphas is generally lower than that for mutual funds in Table 3. Analyzing the differences obtained when applying different performance models we observe that for all funds and for the whole sample period (last row of Table 4) the best performance (0.37%) is achieved using the 1F model (i.e., the CAPM), followed by the 5F model (0.05%), and for the other three models it takes negative values (−0.21% for the 3F model, −0.03% for the 4F model, and −0.07% for the 7F model. This pattern (i.e., the performance is better with the 1F and 5F models than with the 3F, 4F and 7F models) is, in general, repeated for the analyzed subperiods. Given that theoretically the performance of passive portfolios should be zero, these values tell us about the bias of the performance model. The omitted factors in the 1F model contribute to improve the performance of the mutual funds. According to the last row of Table 4, the lowest alpha in absolute terms and, therefore, close to zero is −0.03% for the 4F model. Therefore, and in order to save space, in the next sections dealing with the analysis of persistence we only report results when performance is measured via the 4F model. However, in order to make the study more robust, we will also show results using the model with the highest number of factors—namely, model 7F. In summary, the results show very slight evidence of performance. Even when performance is calculated from gross returns, it takes a negative value close to zero. When it is calculated from net returns, performance actually worsens. This result is largely due to the expenses incurred by the fund. In general, having compared performance with that of the simulated funds, we can conclude that the relevance of the differences in performance is due to mutual fund styles, and the effect of the model applied and the subperiod analyzed. For this reason in the next section we analyze persistence within each group of funds and for different sample subperiods.

427

4.2. Persistence

390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425

428 429 430 431 432 433

434 435 436 437 438 439 440

As stated throughout the paper, the evidence on mutual fund performance persistence in the existing literature is inconclusive. This section aims to add further evidence to this literature. We have applied two methodologies. The first one is based on contingency tables as in Brown and Goetzmann (1995), Silva et al. (2005) and Elyasiani and Jia (2011), among others. The second of the applied methodologies analyzes persistence by assessing the performance of investment strategies based on past performance. 4.2.1. Measuring persistence by contingency tables and transition probability matrices The two-way contingency tables rank funds as winners (losers) depending on whether the fund performance is above (below) the median relative performance of the group. The analysis considers semi-annual periods. We define as WW (winner-winner) the number of funds that are winners in both the current and the subsequent period. The inverse criterion is used to identify LL (loser-loser) funds. LW and WL correspond to funds with performance reversals. We then compare the number of cases observed with the theoretical values under the null hypothesis of absence of independence. Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

3F model

p-value

4F model

p-value

5F model

p-value

7F model

p-value

(0.000) (0.236) (0.057) (0.003) (0.715) (0.011) (0.000) (0.007) (0.000) (0.003) (0.003)

−2.72% −1.30% −1.62% −0.93% −1.08% −1.00% 0.36% 0.06% −1.08% 0.22% −0.64%

(0.000) (0.000) (0.000) (0.001) (0.000) (0.000) (0.001) (0.589) (0.000) (0.208) (0.000)

−2.83% −1.38% −1.65% −1.00% −1.14% −1.00% 0.29% 0.05% −1.07% 0.21% −0.68%

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.009) (0.647) (0.000) (0.251) (0.000)

−0.75% −0.59% −1.44% 0.71% −0.20% −0.76% 0.68% −0.05% −1.01% 0.04% −0.14%

(0.000) (0.003) (0.000) (0.002) (0.300) (0.000) (0.000) (0.673) (0.000) (0.790) (0.008)

−0.41% −0.73% −1.56% 0.55% −0.25% −0.59% 0.16% −0.08% −0.46% 0.12% −0.16%

(0.000) (0.000) (0.000) (0.002) (0.093) (0.002) (0.035) (0.402) (0.000) (0.410) (0.000)

(0.000) (0.000) (0.109) (0.000) (0.000) (0.000) (0.377) (0.000) (0.000) (0.000) (0.000)

−0.99% −1.17% −1.66% 1.35% 0.41% −0.14% 0.77% 0.00% −0.51% −0.01% −0.02%

(0.000) (0.000) (0.000) (0.000) (0.000) (0.313) (0.000) (0.949) (0.000) (0.924) (0.541)

−0.86% −0.70% −0.92% 1.26% 0.59% 0.28% 0.98% 0.36% 0.01% 0.26% 0.28%

(0.000) (0.000) (0.000) (0.000) (0.000) (0.008) (0.000) (0.000) (0.818) (0.028) (0.000)

0.32% −1.02% −1.81% 3.12% 0.72% −0.33% 1.53% −0.34% −1.32% 0.05% 0.28%

(0.002) (0.000) (0.000) (0.000) (0.000) (0.025) (0.000) (0.000) (0.000) (0.835) (0.000)

−0.53% −0.75% −1.14% 1.20% 0.70% 0.42% 0.49% 0.38% 0.61% 0.04% 0.28%

(0.000) (0.000) (0.000) (0.000) (0.000) (0.001) (0.000) (0.000) (0.000) (0.653) (0.000)

ARTICLE IN PRESS

Sub-Sample 1990–1997 −2.54% Small Growth 0.44% Small Blend Small Value 0.76% −1.19% Mid Growth 0.09% Mid Blend Mid Value 1.07% −0.88% Large Growth Large Blend 0.36% 0.77% Large Value Index 0.48% All −0.25% Sub-Sample 1998–2007 0.71% Small Growth 1.66% Small Blend 0.80% Small Value 2.03% Mid Growth 2.03% Mid Blend 1.68% Mid Value −0.07% Large Growth 0.81% Large Blend 1.69% Large Value 0.66% Index 1.01% All

p-value

G Model

1F model

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Table 4 Simulated funds performance. This table reports a summary of the results of estimating simulated fund performance (ap ) using daily returns by means of different models. In each panel, results are grouped by style type and the average of the all funds is reported and the corresponding p-value, is the critical probability from t-statistic test. Simulated funds were estimated using gross mutual funds returns in model (10)–(12).

1F model

3F model

p-value

4F model

p-value

5F model

p-value

7F model

p-value

(0.000) (0.000) (0.031) (0.000) (0.000) (0.000) (0.000) (0.001) (0.000) (0.406) (0.000)

−0.72% −0.74% −0.78% 0.15% 0.25% 0.37% 0.49% 0.15% −0.22% −0.17% −0.04%

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.005) (0.001)

−0.77% −0.75% −0.76% 0.00% 0.18% 0.30% 0.47% 0.14% −0.22% −0.15% −0.08%

(0.000) (0.000) (0.000) (0.891) (0.000) (0.000) (0.000) (0.000) (0.000) (0.014) (0.000)

0.58% −0.37% −0.88% 1.11% 0.62% 0.42% 0.65% −0.01% −0.51% −0.28% 0.17%

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.552) (0.000) (0.000) (0.000)

−0.59% −0.71% −0.70% −0.62% −0.45% −0.40% 0.38% 0.17% −0.22% −0.16% −0.19%

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.073) (0.000)

(0.274) (0.000) (0.549) (0.000) (0.000) (0.000) (0.133) (0.000) (0.000) (0.032) (0.000)

−1.38% −0.92% −1.25% 0.35% 0.06% −0.15% 0.43% 0.00% −0.46% −0.01% −0.21%

(0.000) (0.000) (0.000) (0.000) (0.441) (0.124) (0.000) (0.979) (0.000) (0.903) (0.000)

−1.30% −0.73% −0.93% 0.44% 0.17% 0.07% 0.61% 0.20% −0.20% 0.13% −0.03%

(0.000) (0.000) (0.000) (0.000) (0.009) (0.375) (0.000) (0.000) (0.000) (0.146) (0.087)

0.06% −0.75% −1.49% 2.03% 0.35% −0.35% 1.06% −0.29% −1.21% −0.01% 0.05%

(0.464) (0.000) (0.000) (0.000) (0.000) (0.001) (0.000) (0.000) (0.000) (0.950) (0.071)

−0.76% −0.72% −1.02% 0.27% −0.02% −0.17% 0.19% 0.16% 0.15% −0.06% −0.07%

(0.000) (0.000) (0.000) (0.000) (0.719) (0.020) (0.000) (0.000) (0.000) (0.332) (0.000)

ARTICLE IN PRESS

Sub-Sample 2008–06/2015 1.12% Small Growth Small Blend 0.44% 0.49% Small Value 1.15% Mid Growth Mid Blend 0.90% 0.75% Mid Value Large Growth 0.82% Large Blend 0.09% Large Value −0.60% Index −0.08% All 0.45% Sample 1990–06/2015 Small Growth −0.16% 0.66% Small Blend 0.17% Small Value 0.83% Mid Growth 1.04% Mid Blend 0.81% Mid Value −0.08% Large Growth 0.35% Large Blend 0.62% Large Value 0.29% Index 0.37% All

p-value

G Model

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Table 4 (Continued)

G Model ECOFIN 569 1–40 20 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467

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The non-parametric CPR (Cross Product Ratio) test by Agarwal and Naik (2000) is then applied, where the Z-Statistic tests the null hypothesis of absence of persistence for all funds in the group (Z total). However, the evidence of persistence could be non-symmetrical. It is therefore also pertinent to isolate the persistence of the winner funds from that of the loser funds. For instance, evidence from previous research suggests that persistence is only revealed in the worst mutual funds. Statistics are therefore computed to analyze only winners’ persistence (Z WW) and losers’ persistence (Z LL). Table 5 shows the results—in Panel A, when performance is estimated by means of the 4F model, and in Panel B with the 7F model. Results are very similar for both panels. In general, the 2 test rejects the null hypothesis of independence between winners and losers in each pair of consecutive periods. From these results, and considering the distribution of the values of the categories WW, LL, WL and LW, we can infer strong positive persistence for most of the funds, mainly for those styles that include a higher number of funds, because this test is directly proportionate to the subsample size. Regarding the time period analyzed, the evidence on persistence is lower for the 2008–2015 subperiod than for the previous ones. Recall that it is in this subperiod when funds achieve the worst performance. We also perform an analysis of five groups and the transition between them over two periods. Specifically, mutual funds are ranked by performance to form quintiles from Q1 (worst) to Q5 (best) in each period. The results are shown in the last columns on the left of panels of Table 5. For virtually all the categories of mutual funds we find significant evidence of persistence. To test for the robustness of the methodologies applied above, we analyze the persistence of the simulated mutual funds. In Table 6, Panel A and Panel B show the results when the performance of the simulated funds was estimated with 4F and 7F models, respectively. Given that, by definition, simulated funds are passive portfolios, significant evidence of persistence will not be expected. However, both panels in fact reveal persistence in many cases. In other words, methodologies based on contingency tables and transition probability matrices allow for the existence of persistence all too easily. This raises serious doubts about the results in Table 5. The previous evidence of persistence, therefore, may not in fact be due to fund manager activity, but rather, to the use of a methodology with questionable robustness. 4.2.2. Measuring persistence by portfolios based on past performance In this section we assess persistence by analyzing the performance of portfolios that invest according to the mutual funds’ past performance. This so-called recursive portfolio approach was initially proposed in the literature by Carhart (1997) and is one of the most commonly used methods in the literature, as in Bollen and Busse (2005) and subsequent papers, including Kosowski et al. (2006), Busse et al. (2010) and Fama and French (2010), who have also proposed variations to this approach, in some cases related to the statistical significance of the alphas. We have already highlighted the importance of estimating the persistence between each group of funds in terms of the funds’ style. For instance, Table 3 shows that the Small Growth type mutual funds achieve the worst performance with the 4F model; if we analyze the persistence of all mutual funds, we can find persistence for the worst funds, not because of poor management, but because investing in small growth stocks was an Sj strategy that showed negative performance aSj in Eq. (3) for the sample period. Then, when the persistence for any type of fund is analyzed, the number of funds in each group is smaller and, for this reason, we use quintiles instead of deciles, following Carhart (1997) to differentiate from worst to best mutual funds. In order to develop a homogeneous analysis, we follow the same window period as in the previous approaches; that is, we analyze whether there is persistence between two consecutive six-month periods. We first estimate the performance of the mutual funds by means of models 4F and 7F for the first semester of the sample period. Next, for each style group, we rank mutual funds in increasing order according to the performance they achieved in the period, to form quintiles. Then, for each style group, at the beginning of the next semester we form five equally weighted portfolios according to quintile past performance. Hence, the first portfolio, Q1, invests in the worst performing funds in the previous semester and, conversely, the last portfolio, Q5, invests in the previous best funds. The same pattern is followed for the other quintiles. This procedure is repeated at the beginning of each semester, so that each portfolio represents a dynamic investment strategy that rebalances selected funds according to their previous performance. We therefore compute the daily return of 50 Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

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Table 5 Performance persistence using winner-loser and transition matrix approaches. This table reports the persistence results obtained by following the contingency table and transition matrix methodology. In each semester, past performance is estimated by means of (6) using daily gross returns. Panel A shows the results when performance was estimated from model 4F and Panel B from 7F model. The two-way contingency tables rank funds as winners (losers) depending on whether the fund performance is above (below) the median relative performance of the group. The number of funds that are winners in both the current and the subsequent period is defined as WW (winner-winner). The inverse criterion is used to identify LL (loser-loser) funds. LW and W L correspond to funds with performance reversals. Then we compared the number of cases observed with the theoretical values under the null hypothesis of independence, i.e. absence of persistence in the group. The 2 tests, the Z-statistic tests (according to separate WW and LL analyses) and Z total tests with their respective p-values are reported. Style

Transition matrix

Contingency table 

2

p-value

Z total

p-value

PANEL A: Performance estimated by means of model 4F Sub-Sample 1990–1997 42.19 (0.000) 2.80 (0.003) Small Growth 13.43 (0.000) 1.58 (0.056) Small Blend 3.65 (0.056) 0.83 (0.204) Small Value Mid Growth 37.55 (0.000) 2.64 (0.004) 1.14 (0.285) 0.46 (0.321) Mid Blend Mid Value 1.23 (0.110) 8.05 (0.005) 27.87 (0.000) 2.29 (0.011) Large Growth 28.37 (0.000) 2.31 (0.011) Large Blend 24.57 (0.000) 2.15 (0.016) Large Value 4.58 (0.032) 0.93 (0.177) Index Sub-Sample 1998–2007 Small Growth 76.19 (0.000) 3.78 (0.000) 32.89 (0.000) 2.49 (0.006) Small Blend Small Value 1.26 (0.104) 8.41 (0.004) 65.33 (0.000) 3.50 (0.000) Mid Growth 13.51 (0.000) 1.59 (0.055) Mid Blend 20.76 (0.000) 1.97 (0.024) Mid Value 113.51 (0.000) 4.62 (0.000) Large Growth 68.19 (0.000) 3.58 (0.000) Large Blend 27.72 (0.000) 2.28 (0.011) Large Value 0.32 (0.569) −0.25 (0.598) Index Sub-Sample 2008–06/2015 3.96 (0.046) 0.86 (0.194) Small Growth 3.62 (0.057) 0.83 (0.204) Small Blend 0.02 (0.892) −0.06 (0.524) Small Value 11.97 (0.001) 1.50 (0.067) Mid Growth 1.86 (0.173) 0.59 (0.277) Mid Blend 0.63 (0.429) 0.34 (0.366) Mid Value 0.67 (0.412) 0.36 (0.361) Large Growth Large Blend 11.66 (0.001) 1.48 (0.069) 5.18 (0.023) 0.99 (0.162) Large Value 22.09 (0.000) −2.04 (0.979) Index Sample 1990–06/2015 121.73 (0.000) 4.78 (0.000) Small Growth 52.88 (0.000) 3.15 (0.001) Small Blend 9.76 (0.002) 1.36 (0.088) Small Value 110.21 (0.000) 4.55 (0.000) Mid Growth 15.80 (0.000) 1.73 (0.042) Mid Blend 17.27 (0.000) 1.80 (0.036) Mid Value 101.20 (0.000) 4.36 (0.000) Large Growth Large Blend 106.21 (0.000) 4.47 (0.000) 38.75 (0.000) 2.70 (0.003) Large Value 9.91 (0.002) −1.37 (0.914) Index

p-value

2

p-value

3.39 2.10 1.07 3.41 0.74 1.69 2.83 2.72 2.65 0.89

(0.000) (0.018) (0.143) (0.000) (0.229) (0.046) (0.002) (0.003) (0.004) (0.186)

66.77 36.25 28.97 86.60 39.70 26.34 118.98 165.60 71.89 105.92

(0.000) (0.003) (0.024) (0.000) (0.001) (0.049) (0.000) (0.000) (0.000) (0.000)

(0.000) (0.004) (0.099) (0.000) (0.039) (0.015) (0.000) (0.000) (0.005) (0.653)

4.59 3.07 1.61 4.02 1.92 2.38 5.46 4.37 2.72 −0.18

(0.000) (0.001) (0.053) (0.000) (0.028) (0.009) (0.000) (0.000) (0.003) (0.570)

230.88 138.69 74.16 185.54 58.50 77.93 325.55 406.06 152.48 350.08

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

0.95 0.75 −0.16 1.55 0.49 0.26 0.32 1.60 1.06 −2.43

(0.170) (0.225) (0.565) (0.061) (0.310) (0.396) (0.376) (0.055) (0.145) (0.993)

1.04 1.15 0.03 1.91 0.87 0.53 0.50 1.82 1.22 −2.27

(0.150) (0.125) (0.489) (0.028) (0.193) (0.299) (0.307) (0.035) (0.112) (0.988)

60.09 62.96 54.61 52.23 45.53 27.71 74.85 153.33 70.45 353.87

(0.000) (0.000) (0.000) (0.000) (0.000) (0.034) (0.000) (0.000) (0.000) (0.000)

5.18 3.25 1.29 5.03 1.80 1.77 4.85 4.91 3.03 −1.72

(0.000) (0.001) (0.099) (0.000) (0.036) (0.038) (0.000) (0.000) (0.001) (0.957)

5.85 4.02 1.84 5.47 2.18 2.38 5.21 5.40 3.19 −1.43

(0.000) (0.000) (0.033) (0.000) (0.015) (0.009) (0.000) (0.000) (0.001) (0.924)

321.11 209.87 119.90 276.83 126.63 95.94 429.18 707.65 236.15 741.79

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

ZWW

p-value

3.11 1.57 0.84 2.71 0.33 1.15 2.45 2.60 2.31 1.25

(0.001) (0.058) (0.200) (0.003) (0.372) (0.124) (0.007) (0.005) (0.011) (0.106)

4.13 2.66 1.29 4.07 1.76 2.18 5.19 3.88 2.55 −0.39

ZLL

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Table 5 (Continued) Style

Contingency table 2

p-value

Transition matrix Z total

p-value

PANEL B: Performance estimated by means of model 7F Sub-Sample 1990–1997 Small Growth 15.93 (0.000) 1.73 (0.042) 4.79 (0.029) 0.95 (0.171) Small Blend 7.55 (0.006) 1.19 (0.117) Small Value 23.23 (0.000) 2.08 (0.019) Mid Growth 1.15 (0.283) 0.47 (0.321) Mid Blend (0.203) 3.68 (0.055) 0.83 Mid Value 7.30 (0.007) 1.17 (0.120) Large Growth 16.97 (0.000) 1.79 (0.037) Large Blend 13.82 (0.000) 1.61 (0.053) Large Value 1.59 (0.056) 13.53 (0.000) Index Sub-Sample 1998–2007 Small Growth 39.10 (0.000) 2.71 (0.003) 24.29 (0.000) 2.14 (0.016) Small Blend Small Value 11.02 (0.001) 1.44 (0.075) 59.88 (0.000) 3.35 (0.000) Mid Growth Mid Blend 1.79 (0.037) 17.06 (0.000) 37.93 (0.000) 2.66 (0.004) Mid Value 4.20 (0.000) 93.70 (0.000) Large Growth 60.97 (0.000) 3.39 (0.000) Large Blend 20.47 (0.000) 1.96 (0.025) Large Value 0.47 (0.492) 0.30 (0.383) Index Sub-Sample 2008–06/2015 14.97 (0.000) 1.68 (0.047) Small Growth 2.04 (0.153) 0.62 (0.268) Small Blend 1.93 (0.165) 0.60 (0.273) Small Value 20.92 (0.000) 1.98 (0.024) Mid Growth 15.40 (0.000) 1.70 (0.044) Mid Blend 25.26 (0.000) 2.18 (0.015) Mid Value 8.29 (0.004) 1.25 (0.106) Large Growth 50.76 (0.000) 3.09 (0.001) Large Blend 25.26 (0.000) 2.18 (0.015) Large Value Index 0.01 (0.905) 0.05 (0.479) Sample 1990–06/2015 Small Growth 95.93 (0.000) 4.25 (0.000) Small Blend 40.26 (0.000) 2.75 (0.003) Small Value 27.15 (0.000) 2.26 (0.012) Mid Growth 114.35 (0.000) 4.63 (0.000) 33.39 (0.000) 2.51 (0.006) Mid Blend Mid Value 43.00 (0.000) 2.84 (0.002) 106.94 (0.000) 4.49 (0.000) Large Growth 137.76 (0.000) 5.09 (0.000) Large Blend Large Value 58.10 (0.000) 3.31 (0.000) 6.77 (0.009) 1.13 (0.129) Index

494 495 496 497 498 499 500 501 502 503 504

p-value

2

p-value

2.30 1.45 1.42 2.79 0.84 1.35 1.65 2.25 1.91 1.66

(0.011) (0.073) (0.077) (0.003) (0.201) (0.088) (0.050) (0.012) (0.028) (0.049)

71.31 20.93 30.86 37.26 33.19 31.98 97.42 106.76 55.51 121.80

(0.000) (0.181) (0.014) (0.002) (0.007) (0.010) (0.000) (0.000) (0.000) (0.000)

(0.002) (0.015) (0.065) (0.000) (0.030) (0.002) (0.000) (0.000) (0.013) (0.369)

3.32 2.76 1.80 3.83 2.25 3.34 4.88 4.08 2.31 0.35

(0.000) (0.003) (0.036) (0.000) (0.012) (0.000) (0.000) (0.000) (0.011) (0.362)

189.81 137.93 75.88 165.53 71.93 88.26 350.09 422.97 107.38 317.39

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

1.84 0.54 0.55 2.11 1.80 2.38 1.42 3.46 2.38 0.02

(0.033) (0.296) (0.293) (0.018) (0.036) (0.009) (0.077) (0.000) (0.009) (0.490)

2.03 0.89 0.84 2.47 2.12 2.65 1.46 3.66 2.65 0.10

(0.021) (0.186) (0.199) (0.007) (0.017) (0.004) (0.073) (0.000) (0.004) (0.462)

79.56 77.24 90.79 73.06 58.60 104.48 90.04 220.71 104.48 273.19

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

4.51 2.71 2.33 5.10 2.57 2.79 5.05 5.59 3.74 1.24

(0.000) (0.003) (0.010) (0.000) (0.005) (0.003) (0.000) (0.000) (0.000) (0.107)

5.28 3.63 2.88 5.59 3.21 3.77 5.29 6.15 3.88 1.36

(0.000) (0.000) (0.002) (0.000) (0.001) (0.000) (0.000) (0.000) (0.000) (0.087)

380.11 237.65 170.71 258.43 147.62 95.70 513.93 767.49 209.04 682.49

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

ZWW

p-value

1.69 0.74 1.32 2.02 0.23 0.58 1.06 1.87 1.81 2.02

(0.045) (0.228) (0.093) (0.022) (0.408) (0.282) (0.145) (0.031) (0.035) (0.022)

2.93 2.17 1.52 3.91 1.88 2.81 4.80 3.72 2.22 0.33

ZLL

portfolios (5 for each of the 10 styles) and then we estimate the performance of the portfolio, also using models 4F and 7F. We hypothesize that if there is persistence in mutual fund performance, a portfolio with investments based on a poor (good) past performance will show a negative (positive) performance. Fig. 1 shows the abnormal performance of these portfolios based on mutual funds’ past performance when it is estimated by means of the 4F model. For all styles of mutual funds, the performance improves from Q1 portfolios (that invest in past worst funds) to Q5 portfolios (that invest in past best funds); this pattern may be observed especially in Small Growth funds. For other styles, the slope, although less steep, is still positive so that Q5 performance is better than that of Q1. In sum, in general there is a clear evidence of persistence for the whole sample period, just over 25 years. However, this result does not hold for all subperiods. During the first two subperiods (1990–1997 and 1998–2007) the evidence Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

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Table 6 Simulated fund persistence using winner-loser and transition matrix approaches. This table reports the persistence results obtained by following the contingency table and transition matrix methodology. In each semester, past performance is estimated by means of (6) using simulated daily gross returns. Panel A shows the results when performance was estimated from model 4F and Panel B from 7F model. The two-way contingency tables rank funds as winners (losers) depending on whether the fund performance is above (below) the median relative performance of the group. The number of funds that are winners in both the current and the subsequent period is defined as WW (winner-winner). The inverse criterion is used to identify LL (loser-loser) funds. LW and W L correspond to funds with performance reversals. Then we compared the number of cases observed with the theoretical values under the null hypothesis of independence, i.e. absence of persistence in the group. The 2 tests, the Z-statistic tests (according to separate WW and LL analyses) and Z total tests with their respective p-values are reported. Style

Transition matrix

Contingency table 

2

p-value

Z total

p-value

PANEL A: Performance estimated by means of model 4F Sub-Sample 1990–1997 104.33 (0.000) 4.34 (0.000) Small Growth 59.76 (0.000) 3.29 (0.001) Small Blend 40.25 (0.000) 2.68 (0.004) Small Value Mid Growth 73.01 (0.000) 3.66 (0.000) 9.70 (0.002) 1.35 (0.089) Mid Blend Mid Value 2.97 (0.001) 49.65 (0.000) 264.26 (0.000) 6.91 (0.000) Large Growth 480.76 (0.000) 9.12 (0.000) Large Blend 321.97 (0.000) 7.50 (0.000) Large Value 35.26 (0.000) 2.55 (0.005) Index Sub-Sample 1998–2007 Small Growth 126.15 (0.000) 4.85 (0.000) 26.22 (0.000) 2.22 (0.013) Small Blend Small Value 1.78 (0.038) 16.84 (0.000) 35.11 (0.000) 2.57 (0.005) Mid Growth 19.18 (0.000) 1.90 (0.029) Mid Blend 35.28 (0.000) 2.57 (0.005) Mid Value 77.32 (0.000) 3.81 (0.000) Large Growth 216.44 (0.000) 6.36 (0.000) Large Blend 283.10 (0.000) 7.25 (0.000) Large Value 2.41 (0.120) −0.67 (0.750) Index Sub-Sample 2008–06/2015 28.05 (0.000) −2.30 (0.989) Small Growth 20.81 (0.000) −1.98 (0.976) Small Blend 29.99 (0.000) −2.37 (0.991) Small Value 12.75 (0.000) 1.55 (0.061) Mid Growth 0.54 (0.463) −0.32 (0.625) Mid Blend 2.57 (0.109) 0.70 (0.243) Mid Value 8.30 (0.004) −1.25 (0.895) Large Growth Large Blend 4.45 (0.035) −0.92 (0.820) 10.12 (0.001) −1.38 (0.916) Large Value 24.88 (0.000) −2.16 (0.985) Index Sample 1990–06/2015 65.32 (0.000) 3.51 (0.000) Small Growth 9.29 (0.002) 1.32 (0.093) Small Blend 0.08 (0.775) 0.12 (0.451) Small Value 28.09 (0.000) 2.30 (0.011) Mid Growth 1.09 (0.296) 0.45 (0.325) Mid Blend 5.58 (0.018) 1.03 (0.153) Mid Value 0.79 (0.374) 0.39 (0.350) Large Growth Large Blend 90.38 (0.000) 4.12 (0.000) 85.88 (0.000) 4.02 (0.000) Large Value 4.25 (0.039) −0.89 (0.815) Index

ZWW

p-value

ZLL

p-value

2

p-value

5.02 3.44 2.93 4.13 1.56 2.95 7.56 10.60 8.83 2.20

(0.000) (0.000) (0.002) (0.000) (0.059) (0.002) (0.000) (0.000) (0.000) (0.014)

5.19 4.29 3.42 4.42 1.55 4.09 8.70 11.32 9.11 3.80

(0.000) (0.000) (0.000) (0.000) (0.060) (0.000) (0.000) (0.000) (0.000) (0.000)

300.41 183.15 165.25 207.73 79.62 140.66 645.07 1162.23 637.29 302.89

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

5.57 2.55 1.81 2.94 2.17 2.83 4.37 7.45 8.66 −0.87

(0.000) (0.005) (0.035) (0.002) (0.015) (0.002) (0.000) (0.000) (0.000) (0.807)

5.66 2.57 2.30 2.98 2.21 3.11 4.42 7.27 8.17 −0.69

(0.000) (0.005) (0.011) (0.001) (0.014) (0.001) (0.000) (0.000) (0.000) (0.754)

631.61 164.55 112.97 438.04 152.90 191.21 729.51 894.53 761.97 531.90

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

−2.68 −2.36 −2.77 1.62 −0.47 0.71 −1.60 −1.05 −1.68 −2.61

(0.996) (0.991) (0.997) (0.053) (0.681) (0.238) (0.945) (0.853) (0.953) (0.995)

−2.62 −2.20 −2.70 1.95 −0.26 0.89 −1.28 −1.06 −1.50 −2.38

(0.996) (0.986) (0.997) (0.026) (0.603) (0.187) (0.899) (0.856) (0.934) (0.991)

168.56 162.19 87.88 224.81 117.18 119.09 846.83 718.59 371.79 311.79

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

4.14 1.48 −0.09 2.42 0.45 0.76 0.34 4.85 4.77 −1.27

(0.000) (0.070) (0.534) (0.008) (0.326) (0.223) (0.366) (0.000) (0.000) (0.898)

3.94 1.57 0.37 2.88 0.59 1.60 0.55 4.65 4.50 −0.79

(0.000) (0.058) (0.354) (0.002) (0.277) (0.055) (0.292) (0.000) (0.000) (0.785)

674.89 254.30 143.15 642.68 153.85 150.92 1143.14 1845.01 871.56 1032.38

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

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Table 6 (Continued) Style

Contingency table 2

p-value

Transition matrix Z total

p-value

PANEL B: Performance estimated by means of model 7F Sub-Sample 1990–1997 Small Growth 32.19 (0.000) 2.45 (0.007) 58.44 (0.000) 3.26 (0.001) Small Blend 78.11 (0.000) 3.63 (0.000) Small Value 65.35 (0.000) 3.47 (0.000) Mid Growth 45.23 (0.000) 2.87 (0.002) Mid Blend (0.000) 70.87 (0.000) 3.49 Mid Value 79.96 (0.000) 3.86 (0.000) Large Growth 413.56 (0.000) 8.51 (0.000) Large Blend 462.99 (0.000) 8.81 (0.000) Large Value 2.23 (0.013) 26.71 (0.000) Index Sub-Sample 1998–2007 Small Growth 75.06 (0.000) 3.75 (0.000) 13.42 (0.000) 1.59 (0.056) Small Blend Small Value 0.50 (0.480) 0.31 (0.380) 90.08 (0.000) 4.11 (0.000) Mid Growth Mid Blend 3.15 (0.001) 53.29 (0.000) 37.21 (0.000) 2.64 (0.004) Mid Value 5.22 (0.000) 145.42 (0.000) Large Growth 92.53 (0.000) 4.17 (0.000) Large Blend 163.29 (0.000) 5.52 (0.000) Large Value 20.58 (0.000) 1.97 (0.025) Index Sub-Sample 2008–06/2015 13.26 (0.000) 1.58 (0.057) Small Growth 11.37 (0.001) −1.46 (0.928) Small Blend 7.89 (0.005) −1.22 (0.888) Small Value 44.17 (0.000) 2.88 (0.002) Mid Growth 11.21 (0.001) 1.45 (0.073) Mid Blend 13.75 (0.000) 1.61 (0.054) Mid Value 96.60 (0.000) 4.26 (0.000) Large Growth 40.80 (0.000) 2.77 (0.003) Large Blend 26.50 (0.000) 2.23 (0.013) Large Value Index 10.69 (0.001) −1.42 (0.922) Sample 1990–06/2015 Small Growth 132.16 (0.000) 4.98 (0.000) Small Blend 31.05 (0.000) 2.42 (0.008) Small Value 11.56 (0.001) 1.48 (0.070) Mid Growth 125.62 (0.000) 4.86 (0.000) 69.15 (0.000) 3.60 (0.000) Mid Blend Mid Value 46.08 (0.000) 2.94 (0.002) 180.66 (0.000) 5.83 (0.000) Large Growth 249.69 (0.000) 6.84 (0.000) Large Blend Large Value 81.33 (0.000) 3.91 (0.000) 3.00 (0.083) 0.75 (0.226) Index

505 506 507 508 509 510 511 512 513 514 515

2

p-value

ZWW

p-value

ZLL

p-value

2.25 3.58 4.24 3.45 3.06 3.77 3.70 9.82 10.29 2.15

(0.012) (0.000) (0.000) (0.000) (0.001) (0.000) (0.000) (0.000) (0.000) (0.016)

3.43 4.07 4.60 4.63 3.67 4.65 5.25 10.51 11.22 3.04

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.001)

163.48 143.40 115.49 215.42 107.64 147.40 324.12 904.36 946.95 182.79

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

4.35 1.90 0.34 4.88 3.58 2.94 6.25 4.80 6.61 2.17

(0.000) (0.029) (0.367) (0.000) (0.000) (0.002) (0.000) (0.000) (0.000) (0.015)

4.31 1.77 0.37 4.61 3.72 3.16 5.81 4.82 6.17 2.37

(0.000) (0.039) (0.357) (0.000) (0.000) (0.001) (0.000) (0.000) (0.000) (0.009)

332.54 91.15 149.98 325.99 115.18 153.88 632.62 665.88 680.69 519.99

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

1.75 −1.75 −1.56 3.30 1.62 1.82 4.83 3.20 2.49 −1.66

(0.040) (0.960) (0.940) (0.000) (0.052) (0.034) (0.000) (0.001) (0.006) (0.951)

1.89 −1.63 −1.25 3.35 1.72 1.88 5.00 3.19 2.66 −1.61

(0.030) (0.948) (0.894) (0.000) (0.042) (0.030) (0.000) (0.001) (0.004) (0.947)

156.08 180.11 134.22 171.58 118.63 150.70 630.10 629.44 634.21 400.15

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

5.57 2.81 1.58 5.39 4.01 3.03 6.74 7.90 4.47 0.88

(0.000) (0.002) (0.057) (0.000) (0.000) (0.001) (0.000) (0.000) (0.000) (0.191)

5.93 2.76 1.82 5.82 4.31 3.76 6.70 7.90 4.54 0.86

(0.000) (0.003) (0.034) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.196)

771.00 340.01 313.58 652.69 277.35 288.27 1460.60 2080.27 1264.62 848.80

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

is similar, to the point that it is possible to claim that the results corresponding to these subperiods are driving the trends found for the entire period. In contrast, for the most recent period (from 2008 to June 2015), Fig. 2 shows how the lines are flatter, even showing a negative slope, as in the case of the Index mutual funds—i.e., contrarian evidence of persistence, given that investing in past winner (loser) Index mutual funds yields a worse (better) abnormal performance in the ensuing subperiods. Tables 7 and 8 show the values of the performance and statistical significance of the portfolios when performance was estimated by means of 4F model. The panels show two p-values for the estimates. The first, as shown by Eq. (13) (see below), is the standard p-value from regression model (6) with the Newey and West (1987) heteroskedasticity and autocorrelation consistent covariance estimator. The second p-value, as shown by Eq. (14) (see below), which we refer to as cross-sectional p-value, is the critical probability estimated by means of B simulations in each style-type mutual fund group. This Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

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5% 4% Small Growth

Annualized performance

3%

Small Blend 2%

Small Value Mid-Cap Growth

1%

Mid-Cap Blend

0%

Mid-Cap Value -1%

Large Growth

-2%

Large Blend Large Value

-3%

Index

-4% 1

2

3 Quintile

4

5

Fig. 1. Performance of portfolios based on mutual fund past performance (January 1990 to June 2015). The figure shows the annualized performance (vertical axis) of the portfolios Q1 to Q5 (horizontal axis) formed to assess mutual fund performance persistence. In each semester, past performance was estimated by means of 4F model using gross daily returns. The sample period runs from January 1990 to June 2015. For all styles, mutual funds are grouped in quintiles based on past performance. Portfolio Q1 consists of investing, over the next period, in the worst performing mutual funds, from the previous period, in the first quintile. The same pattern is followed by the rest of the portfolios up to Q5, which invests in the best mutual funds based on the performance achieved in the previous period. This procedure is repeated at the beginning of each semester. The performance of these portfolios is estimated by means of model 4F model.

3%

Annualized performance

2% 2%

Small Growth

1%

Small Blend

1%

Small Value

0%

Mid-Cap Growth Mid-Cap Blend

-1%

Mid-Cap Value

-1%

Large Growth -2%

Large Blend

-2%

Large Value

-3%

Index

-3% 1

2

3 Quintile

4

5

Fig. 2. Performance of portfolios based on mutual fund past performance (January 2008 to June 2015). The figure shows the annualized performance (vertical axis) of the portfolios Q1 to Q5 (horizontal axis) formed to assess mutual fund performance persistence. In each semester, past performance was estimated by means of 4F model using gross daily returns. The sample period runs from January 2008 to June 2015. For all styles, mutual funds are grouped in quintiles based on past performance. Portfolio Q1 consists of investing, over the next period, in the worst performing mutual funds, from the previous period, in the first quintile. The same pattern is followed by the rest of the portfolios up to Q5, which invests in the best mutual funds based on the performance achieved in the previous period. This procedure is repeated at the beginning of each semester. The performance of these portfolios is estimated by means of model 4F model.

Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

cross p-value

Q2

p-value

cross p-value

Q3

p-value

cross p-value

Q4

p-value

cross p-value

Panel A: 4F model. Sub-Sample 1990–1997 Small Growth −2.45% (0.160) (0.023) −0.77% (0.642) (0.049) Small Blend Small Value −0.23% (0.852) (0.055) Mid Growth −1.92% (0.198) (0.025) −2.91% (0.115) (0.015) Mid Blend Mid Value −1.35% (0.510) (0.034) Large Growth −0.16% (0.894) (0.341) −1.84% (0.093) (0.000) Large Blend −0.52% (0.609) (0.066) Large Value −1.22% (0.271) (0.115) Index

−0.17% −0.67% 1.38% −1.32% −1.61% −0.87% −0.81% −0.30% −0.35% −0.70%

(0.906) (0.644) (0.367) (0.318) (0.237) (0.521) (0.358) (0.532) (0.565) (0.339)

(0.463) (0.061) (0.694) (0.091) (0.103) (0.073) (0.052) (0.317) (0.125) (0.216)

−0.77% 3.68% 2.26% −1.64% 2.61% 3.80% −0.35% −0.48% −0.06% −0.01%

(0.550) (0.008) (0.203) (0.159) (0.204) (0.002) (0.655) (0.282) (0.911) (0.982)

(0.201) (0.035) (0.447) (0.051) (0.041) (0.022) (0.243) (0.205) (0.306) (0.542)

−0.33% 0.62% 2.56% −0.26% −0.24% 2.42% −0.31% 0.43% 0.09% −0.14%

(0.826) (0.667) (0.071) (0.837) (0.866) (0.061) (0.755) (0.487) (0.877) (0.772)

(0.372) (0.697) (0.362) (0.384) (0.372) (0.167) (0.267) (0.173) (0.571) (0.468)

Panel B: 4F model. Sub-Sample 1998–2007 Small Growth −3.75% (0.065) (0.000) Small Blend −1.96% (0.240) (0.000) Small Value −1.65% (0.289) (0.000) −1.68% (0.341) (0.000) Mid Growth −0.58% (0.702) (0.000) Mid Blend −0.65% (0.658) (0.001) Mid Value Large Growth −1.70% (0.111) (0.000) −2.00% (0.005) (0.000) Large Blend 0.07% (0.952) (0.544) Large Value −1.72% (0.166) (0.000) Index

−2.43% −1.33% −0.12% 0.54% 0.54% 0.03% −0.54% −1.11% −1.18% −0.20%

(0.189) (0.316) (0.939) (0.742) (0.663) (0.982) (0.543) (0.038) (0.212) (0.812)

(0.000) (0.000) (0.052) (1.000) (0.971) (0.987) (0.000) (0.000) (0.000) (0.668)

0.22% 0.08% 0.59% 2.80% 1.26% 2.27% −0.09% −0.58% −0.21% −0.62%

(0.885) (0.949) (0.681) (0.092) (0.267) (0.071) (0.921) (0.272) (0.844) (0.319)

(0.759) (0.704) (0.733) (0.307) (0.836) (0.296) (0.011) (0.106) (0.197) (0.242)

3.15% 2.03% 0.77% 4.10% 4.21% 3.49% 1.79% 0.09% 0.03% −0.07%

(0.037) (0.101) (0.647) (0.014) (0.001) (0.007) (0.093) (0.870) (0.977) (0.940)

(0.000) (0.002) (0.629) (0.002) (0.003) (0.016) (0.000) (0.070) (0.580) (0.785)

Q5

p-value

cross p-value

4.31% 4.03% 4.53% 5.14% 3.52% 1.44% 1.81% 1.91% 1.62% 1.59%

(0.026) (0.036) (0.005) (0.004) (0.053) (0.262) (0.207) (0.096) (0.115) (0.258)

(0.000) (0.019) (0.039) (0.000) (0.008) (0.427) (0.001) (0.000) (0.001) (0.011)

6.04% 3.23% 5.23% 6.64% 4.86% 4.00% 3.51% 2.21% 2.20% 0.83%

(0.002) (0.002) (0.000) (0.002) (0.000) (0.004) (0.011) (0.001) (0.041) (0.596)

(0.000) (0.000) (0.000) (0.000) (0.000) (0.002) (0.000) (0.000) (0.000) (0.001)

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Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

Table 7 Mutual fund persistence obtained by assessing performance of past-performance-based portfolios (4F model). This table reports the mutual fund performance persistence results obtained by assessing performance of past-persistence-based portfolios. In each semester, past performance is estimated by means of 4F model using daily gross returns. For all styles, mutual funds are grouped in quintiles based on past performance. Portfolio Q1 consists of investing, over the next period, in the worst performing mutual funds, from the previous period, in the first quintile. The same pattern is followed by the rest of the portfolios up to Q5, which invests in the best mutual funds based on the performance achieved in the previous period. This procedure is repeated at the beginning of each semester. The performance of these portfolios is estimated by means of 4F model. The panels show two p-values for the estimates. The first is the standard p-value from the regression 4F model with the Newey and West (1987) heteroskedasticity and autocorrelation consistent covariance estimator. The second, the cross-sectional p-value, is the critical probability estimated by means of simulations in each style-type mutual fund group.

Q1

p-value

cross p-value

Q2

cross p-value

Q3

p-value

cross p-value

Q4

p-value

cross p-value

Q5

p-value

cross p-value

Panel C: 4 Factors model. Sub-Sample 2008–06/2015 −0.27% (0.823) (0.721) −0.48% Small Growth −0.72% (0.467) (0.428) −0.65% Small Blend −0.50% (0.691) (0.301) −0.19% Small Value −0.95% (0.523) (0.009) 0.10% Mid Growth −1.49% (0.251) (0.039) −0.17% Mid Blend 1.04% (0.359) (0.584) 0.51% Mid Value Large Growth −0.69% (0.531) (0.395) −0.02% −1.05% (0.139) (0.232) −0.78% Large Blend −0.69% (0.380) (0.681) −1.54% Large Value 0.16% (0.860) (0.007) −0.20% Index

(0.639) (0.449) (0.831) (0.939) (0.887) (0.625) (0.979) (0.093) (0.016) (0.836)

(0.505) (0.492) (0.479) (0.381) (0.552) (0.902) (0.992) (0.583) (0.026) (0.944)

−0.84% −0.32% 0.25% 0.36% −0.08% 1.64% −0.64% −1.28% −0.80% −1.11%

(0.391) (0.681) (0.769) (0.778) (0.940) (0.074) (0.456) (0.003) (0.138) (0.145)

(0.208) (0.739) (0.264) (0.155) (0.604) (0.158) (0.472) (0.064) (0.556) (0.377)

−0.90% −1.23% −0.36% 0.16% 0.21% 0.67% −1.17% −0.72% −0.92% −1.26%

(0.358) (0.143) (0.683) (0.901) (0.835) (0.485) (0.164) (0.102) (0.121) (0.084)

(0.164) (0.110) (0.384) (0.319) (0.239) (0.840) (0.024) (0.658) (0.408) (0.281)

−0.06% −0.25% −0.08% 0.18% 0.16% 1.80% −0.62% −0.36% −0.33% −2.47%

(0.951) (0.780) (0.940) (0.884) (0.879) (0.061) (0.514) (0.567) (0.690) (0.024)

(0.857) (0.776) (0.540) (0.298) (0.261) (0.094) (0.499) (0.958) (0.943) (0.004)

Panel D: 4F model. Sample 1990–06/2015 −2.74% (0.010) (0.000) Small Growth −1.36% (0.194) (0.000) Small Blend −1.22% (0.205) (0.000) Small Value Mid Growth −1.96% (0.037) (0.000) Mid Blend −1.68% (0.092) (0.000) Mid Value −0.66% (0.526) (0.007) Large Growth −0.97% (0.151) (0.000) Large Blend −1.84% (0.001) (0.000) Large Value −0.27% (0.682) (0.642) −1.11% (0.122) (0.026) Index

(0.242) (0.284) (0.980) (0.592) (0.845) (0.739) (0.665) (0.035) (0.079) (0.497)

(0.002) (0.018) (0.203) (0.001) (0.172) (0.036) (0.022) (0.172) (0.004) (0.639)

−0.22% 0.58% 0.61% 0.58% 0.70% 1.48% −0.27% −0.76% −0.60% −0.51%

(0.775) (0.490) (0.502) (0.482) (0.407) (0.076) (0.604) (0.020) (0.275) (0.146)

(0.198) (0.141) (0.358) (0.471) (0.262) (0.076) (0.011) (0.120) (0.144) (0.416)

0.90% 0.40% 0.59% 1.10% 1.27% 1.25% 0.67% −0.29% −0.50% −0.37%

(0.238) (0.600) (0.523) (0.189) (0.135) (0.142) (0.294) (0.418) (0.362) (0.490)

(0.032) (0.247) (0.374) (0.071) (0.049) (0.147) (0.016) (0.904) (0.285) (0.599)

3.80% 1.71% 2.30% 3.40% 1.83% 1.60% 1.86% 0.90% 0.49% 0.18%

(0.000) (0.023) (0.006) (0.001) (0.045) (0.051) (0.017) (0.075) (0.468) (0.833)

(0.000) (0.001) (0.000) (0.000) (0.004) (0.049) (0.000) (0.000) (0.000) (0.020)

−1.08% −0.88% −0.02% −0.43% −0.16% −0.28% −0.23% −0.71% −0.94% −0.34%

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Table 7 (Continued)

cross p-value

Q2

p-value

cross p-value

Q3

p-value

cross p-value

Q4

p-value

cross p-value

Panel A: 7F model. Sub-Sample 1990–1997 Small Growth −0.35% (0.792) (0.403) 1.38% (0.385) (0.644) Small Blend Small Value −1.02% (0.475) (0.063) Mid Growth 0.57% (0.656) (0.783) −1.43% (0.438) (0.063) Mid Blend Mid Value −1.41% (0.464) (0.016) Large Growth 0.96% (0.386) (0.066) −1.53% (0.149) (0.019) Large Blend 0.78% (0.403) (0.212) Large Value −0.44% (0.667) (0.362) Index

2.83% 1.10% 2.04% −0.20% 1.38% 0.18% −0.59% −0.73% 0.07% −0.59%

(0.026) (0.275) (0.229) (0.853) (0.270) (0.897) (0.465) (0.208) (0.909) (0.387)

(0.000) (0.715) (0.261) (0.051) (0.321) (0.782) (0.067) (0.330) (0.798) (0.308)

1.59% 3.14% 0.33% −0.28% 0.31% 1.70% −0.60% −0.76% 0.15% −1.07%

(0.201) (0.083) (0.835) (0.789) (0.827) (0.120) (0.454) (0.207) (0.844) (0.005)

(0.004) (0.176) (0.723) (0.047) (0.624) (0.368) (0.066) (0.300) (0.750) (0.175)

2.42% 0.55% 2.34% 2.27% 0.30% 3.28% −0.44% 0.14% 0.45% −0.96%

(0.082) (0.698) (0.117) (0.067) (0.835) (0.016) (0.597) (0.800) (0.469) (0.339)

(0.001) (0.838) (0.198) (0.153) (0.626) (0.049) (0.118) (0.103) (0.485) (0.197)

Panel B: 7F model. Sub-Sample 1998–2007 Small Growth −3.19% (0.085) (0.000) Small Blend −1.51% (0.367) (0.001) Small Value −2.38% (0.131) (0.000) −2.18% (0.189) (0.000) Mid Growth −0.99% (0.520) (0.000) Mid Blend −0.88% (0.550) (0.000) Mid Value Large Growth −1.88% (0.063) (0.000) −2.24% (0.002) (0.000) Large Blend 0.49% (0.671) (0.895) Large Value −1.90% (0.158) (0.000) Index

−2.03% −2.33% 0.17% 0.50% −0.87% 0.71% −0.62% −0.60% 0.11% −1.08%

(0.229) (0.112) (0.916) (0.729) (0.475) (0.547) (0.483) (0.212) (0.908) (0.192)

(0.000) (0.000) (0.665) (1.000) (0.000) (0.935) (0.002) (0.032) (0.996) (0.092)

0.06% −0.27% −1.07% 1.96% 0.89% 2.04% −0.35% −0.60% 0.09% −0.55%

(0.970) (0.836) (0.467) (0.117) (0.303) (0.084) (0.681) (0.200) (0.926) (0.249)

(0.943) (0.251) (0.015) (0.600) (0.849) (0.461) (0.030) (0.030) (0.997) (0.531)

3.95% 0.52% 1.09% 4.48% 4.38% 3.23% 1.05% −0.03% 1.31% 0.17%

(0.003) (0.692) (0.520) (0.001) (0.000) (0.006) (0.265) (0.960) (0.190) (0.819)

(0.000) (0.243) (0.165) (0.000) (0.001) (0.049) (0.003) (0.669) (0.255) (0.012)

Q5

p-value

cross p-value

5.85% 3.28% 2.91% 4.22% 3.86% 1.61% 1.50% 0.46% 0.63% 1.69%

(0.003) (0.145) (0.077) (0.005) (0.011) (0.252) (0.283) (0.689) (0.539) (0.149)

(0.000) (0.154) (0.106) (0.001) (0.009) (0.392) (0.009) (0.023) (0.320) (0.001)

6.11% 4.22% 4.33% 5.73% 5.33% 4.45% 2.88% 2.70% 3.06% 0.55%

(0.000) (0.000) (0.000) (0.002) (0.000) (0.000) (0.033) (0.000) (0.004) (0.695)

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.001)

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Table 8 Mutual fund persistence obtained by assessing performance of past-performance-based portfolios (7F model). This table reports the mutual fund performance persistence results obtained by assessing performance of past-persistence-based portfolios. In each semester, past performance is estimated by means of 7F model using daily gross returns. For all styles, mutual funds are grouped in quintiles based on past performance. Portfolio Q1 consists of investing, over the next period, in the worst performing mutual funds, from the previous period, in the first quintile. The same pattern is followed by the rest of the portfolios up to Q5, which invests in the best mutual funds based on the performance achieved in the previous period. This procedure is repeated at the beginning of each semester. The performance of these portfolios is estimated by means of 7F model. The panels show two p-values for the estimates. The first is the standard p-value from the regression 7F model with the Newey and West (1987) heteroskedasticity and autocorrelation consistent covariance estimator. The second, the cross-sectional p-value, is the critical probability estimated by means of simulations in each style-type mutual fund group.

Q1

p-value

cross p-value

p-value

cross p-value

Q3

p-value

cross p-value

Q4

p-value

cross p-value

Q5

p-value

cross p-value

Panel C: 7F model. Sub-Sample 2008–06/2015 −1.42% (0.151) (0.172) Small Growth −1.95% (0.046) (0.066) Small Blend −0.83% (0.496) (0.507) Small Value −2.34% (0.028) (0.014) Mid Growth −2.68% (0.011) (0.040) Mid Blend −0.67% (0.522) (0.079) Mid Value Large Growth −1.33% (0.194) (0.137) −1.54% (0.025) (0.030) Large Blend −0.88% (0.223) (0.480) Large Value −0.87% (0.349) (0.729) Index

−1.00% −1.04% −1.82% −1.50% −1.47% −0.08% −0.42% −1.36% −1.56% −1.28%

(0.258) (0.175) (0.060) (0.080) (0.127) (0.913) (0.618) (0.004) (0.009) (0.146)

(0.505) (0.627) (0.080) (0.473) (0.483) (0.408) (0.993) (0.092) (0.022) (0.397)

−1.22% −1.28% −0.72% −1.33% −0.96% −0.09% −1.04% −1.10% −1.09% −1.39%

(0.129) (0.170) (0.433) (0.125) (0.195) (0.903) (0.213) (0.005) (0.061) (0.038)

(0.300) (0.440) (0.575) (0.642) (0.763) (0.400) (0.484) (0.337) (0.260) (0.313)

−1.44% −1.40% −0.58% −1.56% −1.86% −0.17% −1.42% −0.88% −1.17% −0.70%

(0.098) (0.169) (0.551) (0.079) (0.063) (0.840) (0.087) (0.025) (0.077) (0.267)

(0.159) (0.348) (0.666) (0.409) (0.268) (0.347) (0.073) (0.654) (0.177) (0.836)

−0.07% −0.34% −0.29% −0.66% −0.28% 1.08% −0.99% −0.06% 0.33% −1.60%

(0.936) (0.697) (0.776) (0.462) (0.760) (0.153) (0.277) (0.926) (0.680) (0.128)

(0.990) (0.957) (0.800) (0.988) (0.963) (0.021) (0.572) (0.998) (0.000) (0.187)

Panel D: 7F model. Sample 1990–06/2015 −2.52% (0.006) (0.000) Small Growth −1.46% (0.135) (0.000) Small Blend −1.88% (0.049) (0.000) Small Value Mid Growth −2.06% (0.014) (0.000) Mid Blend −2.17% (0.024) (0.000) Mid Value −1.43% (0.152) (0.000) Large Growth −1.06% (0.097) (0.000) Large Blend −2.04% (0.000) (0.000) Large Value −0.17% (0.780) (0.314) −1.17% (0.099) (0.050) Index

−0.37% −1.33% −0.13% −0.91% −0.83% −0.58% −0.53% −0.92% −0.66% −0.97%

(0.667) (0.098) (0.899) (0.193) (0.243) (0.435) (0.303) (0.004) (0.193) (0.055)

(0.006) (0.006) (0.613) (0.000) (0.077) (0.041) (0.005) (0.053) (0.003) (0.149)

0.03% 0.19% −1.15% −0.14% −0.49% 0.60% −0.41% −0.80% −0.58% −0.74%

(0.968) (0.833) (0.208) (0.832) (0.426) (0.392) (0.441) (0.007) (0.276) (0.014)

(0.936) (0.227) (0.056) (0.095) (0.204) (0.317) (0.024) (0.160) (0.007) (0.359)

1.92% −0.11% 0.37% 1.64% 1.20% 1.31% 0.39% −0.40% 0.12% −0.40%

(0.008) (0.889) (0.684) (0.021) (0.114) (0.089) (0.487) (0.238) (0.821) (0.401)

(0.003) (0.558) (0.114) (0.000) (0.013) (0.043) (0.039) (0.865) (0.233) (0.779)

4.31% 2.02% 1.66% 3.05% 2.36% 1.58% 1.69% 1.08% 0.99% 0.14%

(0.000) (0.011) (0.043) (0.001) (0.004) (0.039) (0.034) (0.032) (0.114) (0.859)

(0.000) (0.000) (0.000) (0.000) (0.000) (0.008) (0.000) (0.000) (0.000) (0.004)

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Table 8 (Continued)

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second p-value is necessary to differentiate between the performance per se of the portfolio and the performance achieved by following a strategy of investing in past worst or best mutual funds.

p − value =

⎧ ⎫ #{˛ ˆj < ˛ ˆ p} ⎪ ⎨ ⎬ if ˛p < 0 ⎪ B

⎪ ⎩ #{˛ˆ j > ˛ˆ p } if ˛ > 0 ⎪ ⎭ p

j = 1, . . ., B.

(13)

B

519

520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563

p − value = P[t(T −k,2) (

˛ ˆp )] ˆ ˛ˆ p

(14)

Take, for instance, the case of Mid Value mutual funds. As seen in Table 3, Panel B for the sub-sample from January 2008 to June 2015, these funds achieved the best performance in the case of the 4F model, with an annualized mean of 0.27%. Thus, any portfolio that invests in these funds will probably show a good performance per se, simply because these were good funds. Therefore, a portfolio that invests in the past worst or best Mid Value mutual funds is also likely to show good performance. In fact, Fig. 2 shows that the best performance is that of the portfolios, from Q1 to Q5, based on the past performance of the Mid Value mutual funds. If we observe Panel B of Table 7, the performance for these portfolios varies from 1.04% for Q1 to 1.80% for Q5. We then need to differentiate between the performance of the group of mutual funds and that achieved following a dynamic strategy based on past performance. To do this, we will form portfolios in the same way as the previous 50 portfolios based on past performance, but with the difference that now the funds invested in are not based on past performance, but selected randomly. If there is persistence in the added value from managers, worst or best mutual funds will repeat that ranking in the future and a strategy based on their past performance should achieve a better performance than a random strategy that invests in funds without any criteria. For B = 2000 each of the 10 style groups of mutual funds in the sample, 2000 synthetic equallyweighted portfolios were formed that invest randomly in a quintile of the group’s funds. This procedure is repeated for each sample period and each performance model. The daily return of the synthetic portfolios is computed and the corresponding model in Equation (6) is applied to estimate performance. Consequently, for each style group of mutual funds, sample period and performance model, a distribution of 2000 alphas is formed to test for the significance of the performance of following investment recommendations based on past performance. Next, for each of the portfolios based on past performance, the cross-sectional p-value is computed as the percentage of synthetic portfolios which produce an alpha greater than the corresponding value for that past-performance-based portfolio. In sum, Table 7 shows two p-values, the first (the standard p-value) measuring whether the performance of the past-performance-based portfolio is significantly different from zero; the second, the cross-sectional p-value measures whether this performance is linked to investment in past worst or best mutual funds, and thus if it is significantly different from the result of any random investment in these funds. As can be inferred from Fig. 1, when the entire sample period is considered and the 4F model was applied, Panel D of Table 7 provides an overall evidence of persistence. Performance achieved by following past-performance-based investment strategies is only significant in some specific cases. Thus, the performance achieved from investing in the past worst (Q1) Small Growth mutual funds is significant. It provides an annualized alpha of −2.74%, the standard p-value is 0.010, and the crosssectional p-value is 0.000. Also, for Mid Growth, Mid Blend and Large Blend the negative abnormal performance of Q1 portfolios is negative (−1.96%, −1.68% and −1.84%, respectively), and significant. For the rest of the styles, the alphas are also negative but not significant. When shifting rightwards in the same panel, for the intermediate quintile-portfolios (Q2, Q3 and Q4) the alphas take positive values first and negative values at the end, but they are never significant. The last columns on the right of Panel D show the abnormal performance and significance corresponding to Q5, namely, the portfolio that follows a strategy of investing in the mutual funds with best past performance. We can observe that for all styles the alpha is positive and significant in most cases, with the exception of Large Value and Index. The highest performance is achieved for Small Growth, with an annualized value of 3.80%. In sum, we find evidence of persistence in the performance of mutual funds in the extreme quintiles, Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

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564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617

31

it being higher for Q5, i.e., for the case of best past mutual funds. This evidence is not coincidental for all mutual fund styles: for instance, it seems that selecting (avoiding) past good (poor) Small Growth funds is a suitable strategy to attempt to achieve (avoid) a good (poor) performance in the next periods. In contrast, for Large Value and Index funds, the investment strategy based on past performance does not seem as fruitful. Panels A, B and C in Table 7 allow us to analyze performance in different subperiods. In the first two panels, corresponding to the subperiods 1990–1997 and 1998–2007, the evidence is similar to that discussed above for the entire sample period, i.e., negative alphas in Q1 which increase and become positive in Q5. However, the asymmetry in the higher persistence for the best past mutual funds is still more marked for both subperiods. This behavior is particularly relevant in the second subperiod (panel B), during which even in Q4 most alphas are positive, and significant for half of the styles. Then in Q5 virtually all alphas are positive and significant, reaching very high values. For instance, investing in the best past Mid Growth mutual funds yields an annualized alpha of 6.64%. In sum, for the 1990–2007 subperiod we find significant evidence of persistence in the performance of the best past mutual funds. However, the evidence for the most recent sample subperiod, corresponding to January 2008 to June 2015, is different to that found in previous subperiods. As shown in Panel C of Table 7, the lack of significance in the alphas is quite apparent for virtually every quintile portfolios and styles. In addition, the alphas do not follow an upward trend from Q1 to Q5. Actually, in Q5 some styles have negative alphas, namely, contrary to what we might expect should persistence exist. This situation was discussed previously when analyzing Fig. 2, i.e., flat lines and even a negative slope for the case of Index mutual funds. In this case, in Panel C of Table 7 the performance ranges from 0.16% for Q1 to −2.47% for Q5; the latter is significant with a standard p-value equal to 0.024 and a cross-sectional p-value of 0.004. That is, strategies that invest in past best (worst) mutual funds exhibit worse (better) performance. This result contradicts the idea of mutual fund performance persistence. Table 8 reports analogous results to Table 7, but using the 7F factor model instead of the 4F model. Although there may be some differences with respect to the value and significance of some specific alphas, in general the results are quite similar for both tables. To test the robustness of this methodology we analyze the persistence of the performance of the simulated mutual funds. Tables 9 and 10 show the performance of the quintile portfolios based on past performance of simulated funds when 4F and 7F models are used. We will only comment on the results of Table 9 because both models lead to similar conclusions. Panel D in Table 9 shows the results for the whole sample. In general, the alphas are not significant for most cases. Because funds are passive and simulated, and in theory they do not add any management value, we would not expect to find evidence of significant persistence. Fig. 3 is drawn from the alphas in Panel D for the whole sample. In this figure, and in general, lines are flatter, except for Small funds, which show positive slopes—i.e. no evidence of persistence in found except for Small funds. As simulated funds are passive, a comparison of Fig. 3 and Fig. 1 leads to the conclusion that, in general, the evidence of persistence found in mutual funds is not due to passive strategies not captured by the performance model, but are actually due to active management. However for Small mutual funds, part of the persistence found would be due to the underlying performance of the assets in which they invest, and that has not been captured by the performance model. To examine this issue, we can compare the results in Panel D of Tables 7 and 9. For instance, for Small Growth funds, the annualized alpha in Q1 is −2.74% and −1.45% in Tables 7 and 9, respectively, which implies that the difference (−1.29% = −2.74 % −1.45 %) would correspond to the abnormal performance achieved by investing in past poor mutual funds, and not due to investing in passive funds within this style. For this style, the alpha corresponding to Q5 is 3.80% in Table 7 and −0.68% in Table 9 and, therefore, the difference (4.48% =3.80 % −0.68 %) would correspond to the value added from investing in the past best mutual funds, regardless of the performance of passive investments in the same style. Analogous results can be inferred for the remaining cases. Panels A, B and C of Table 9 show the results for subperiods. We can extrapolate the comments made on the results in Panel D (corresponding to the entire sample period). However, in these periods the increase in alpha from Q1 to Q5 is obvious for other styles—apart from Small funds. For instance, in Panel A for Mid Growth style and Q1, the alpha is −1.92% in Table 7 and −1.66% in Table 9 (so the Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

cross p-value

Q2

p-value

cross p-value

Q3

p-value

cross p-value

Q4

p-value

cross p-value

Q5

p-value

cross p-value

Panel A: 4F model. Sub-Sample 1990–1997 Small Growth −2.14% (0.146) (0.107) −2.31% (0.055) (0.044) Small Blend Small Value −2.33% (0.001) (0.117) Mid Growth −1.66% (0.145) (0.002) 0.11% (0.941) (0.225) Mid Blend Mid Value −2.85% (0.000) (0.000) Large Growth −0.72% (0.273) (0.000) −0.91% (0.295) (0.000) Large Blend −1.67% (0.033) (0.000) Large Value −1.69% (0.067) (0.074) Index

−2.41% −2.22% −2.19% −1.48% −1.34% −1.12% −0.56% −0.73% −1.02% −0.17%

(0.007) (0.001) (0.000) (0.020) (0.007) (0.047) (0.165) (0.004) (0.003) (0.663)

(0.022) (0.060) (0.181) (0.006) (0.127) (0.428) (0.002) (0.001) (0.163) (0.368)

−1.64% −2.21% −1.83% −1.00% −1.48% −1.43% −0.44% −0.19% −0.93% 0.12%

(0.011) (0.006) (0.000) (0.063) (0.012) (0.008) (0.130) (0.319) (0.002) (0.552)

(0.550) (0.061) (0.398) (0.147) (0.092) (0.230) (0.014) (0.208) (0.295) (0.418)

−1.32% −1.61% −1.41% −0.68% −1.33% −0.19% 0.27% −0.22% −0.57% 0.31%

(0.043) (0.022) (0.013) (0.289) (0.016) (0.673) (0.572) (0.460) (0.038) (0.452)

(0.862) (0.264) (0.658) (0.426) (0.130) (0.947) (0.105) (0.171) (0.845) (0.267)

−0.96% 2.24% −0.60% 1.81% 1.27% 0.66% 1.46% 2.16% 0.16% 1.18%

(0.518) (0.061) (0.422) (0.195) (0.405) (0.335) (0.095) (0.061) (0.704) (0.212)

(0.979) (0.000) (0.954) (0.000) (0.013) (0.001) (0.000) (0.000) (0.000) (0.020)

Panel B: 4F model. Sub-Sample 1998–2007 Small Growth −3.96% (0.015) (0.000) Small Blend −3.10% (0.036) (0.000) Small Value −2.13% (0.139) (0.000) −1.21% (0.490) (0.000) Mid Growth −1.56% (0.250) (0.000) Mid Blend −1.61% (0.191) (0.000) Mid Value Large Growth 0.94% (0.464) (0.423) 0.57% (0.463) (0.031) Large Blend −0.10% (0.919) (0.017) Large Value −1.45% (0.291) (0.000) Index

−2.40% −2.10% −1.27% 0.95% 0.50% −0.10% 1.15% 0.47% −0.01% −0.13%

(0.069) (0.104) (0.329) (0.484) (0.645) (0.921) (0.031) (0.393) (0.995) (0.867)

(0.000) (0.000) (0.016) (0.997) (0.917) (0.042) (0.046) (0.158) (0.118) (0.601)

−1.15% −1.03% −0.99% 2.19% 0.77% 0.50% 0.74% 0.56% 0.21% −0.06%

(0.375) (0.379) (0.477) (0.156) (0.420) (0.673) (0.239) (0.221) (0.829) (0.902)

(0.000) (0.284) (0.269) (0.023) (0.750) (0.461) (0.885) (0.042) (0.173) (0.718)

0.61% 0.32% −0.67% 3.34% 1.76% 1.74% 0.50% −0.05% 0.25% 0.07%

(0.684) (0.774) (0.629) (0.050) (0.136) (0.135) (0.605) (0.940) (0.795) (0.950)

(0.000) (0.000) (0.847) (0.000) (0.031) (0.001) (0.998) (0.000) (0.088) (0.120)

2.08% 1.54% 0.66% 3.20% 3.69% 1.88% 1.23% 0.12% 0.25% 0.67%

(0.276) (0.241) (0.621) (0.133) (0.040) (0.175) (0.504) (0.909) (0.821) (0.659)

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.013) (0.967) (0.089) (0.000)

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Table 9 Simulated persistence obtained by assessing performance of past-performance-based portfolios (4F model). This table reports the performance persistence results of simulated funds obtained by assessing performance of past-persistence-based portfolios. In each semester, past performance is estimated by means of 4F model using daily gross returns. For all styles, mutual funds are grouped in quintiles based on past performance. Portfolio Q1 consists of investing, over the next period, in the worst performing simulated funds, from the previous period, in the first quintile. The same pattern is followed by the rest of the portfolios up to Q5, which invests in the best simulated funds based on the performance achieved in the previous period. This procedure is repeated at the beginning of each semester. The performance of these portfolios is estimated by means of 4F model. The panels show two p-values for the estimates. The first is the standard p-value from the regression 4F model with the Newey and West (1987) heteroskedasticity and autocorrelation consistent covariance estimator. The second, the cross-sectional p-value, is the critical probability estimated by means of simulations in each style-type mutual fund group.

Q1

p-value

cross p-value

p-value

cross p-value

Q3

p-value

cross p-value

Q4

p-value

cross p-value

Q5

p-value

cross p-value

Panel C: 4F model. Sub-Sample 2008–06/2015 1.17% (0.120) (0.000) Small Growth 0.63% (0.399) (0.000) Small Blend 1.10% (0.200) (0.000) Small Value 1.74% (0.070) (0.000) Mid Growth 2.26% (0.020) (0.000) Mid Blend 1.93% (0.021) (0.000) Mid Value Large Growth 1.85% (0.019) (0.000) 1.55% (0.017) (0.000) Large Blend 1.64% (0.009) (0.000) Large Value 0.01% (0.991) (0.139) Index

0.20% 0.03% −0.25% 1.10% 1.37% 1.14% 1.21% 0.53% 0.66% 0.37%

(0.785) (0.962) (0.715) (0.244) (0.071) (0.158) (0.034) (0.083) (0.088) (0.609)

(0.019) (0.000) (0.996) (0.040) (0.001) (0.026) (0.000) (0.000) (0.000) (0.005)

0.28% −0.50% −0.88% 0.88% 0.82% 0.84% 0.80% 0.32% −0.37% 0.10%

(0.702) (0.323) (0.174) (0.361) (0.254) (0.260) (0.113) (0.206) (0.272) (0.745)

(0.004) (0.716) (0.468) (0.614) (0.341) (0.465) (0.120) (0.116) (0.020) (0.076)

−0.04% −0.97% −1.39% 0.67% 0.11% 0.73% 0.28% −0.14% −1.07% 0.12%

(0.958) (0.109) (0.061) (0.477) (0.879) (0.348) (0.570) (0.569) (0.018) (0.869)

(0.813) (0.001) (0.004) (0.990) (1.000) (0.736) (1.000) (0.000) (0.000) (0.063)

−1.00% −2.04% −3.01% 0.12% −0.86% −0.56% −0.56% −1.15% −1.89% −1.84%

(0.223) (0.024) (0.007) (0.891) (0.291) (0.489) (0.383) (0.053) (0.010) (0.081)

(0.000) (0.000) (0.000) (1.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

Panel D: 4F model. Sample 1990–06/2015 (0.000) Small Growth −1.45% (0.086) −1.44% (0.089) (0.053) Small Blend −2.32% (0.009) (0.000) Small Value Mid Growth 0.11% (0.896) (0.870) Mid Blend −0.29% (0.715) (0.084) Mid Value −0.85% (0.240) (0.003) Large Growth 0.93% (0.092) (0.000) Large Blend 0.20% (0.708) (0.008) Large Value −0.05% (0.938) (1.000) −0.67% (0.320) (0.039) Index

−1.53% −1.25% −1.75% 0.10% 0.22% −0.54% 0.73% 0.10% −0.34% 0.02%

(0.029) (0.072) (0.036) (0.873) (0.698) (0.441) (0.018) (0.774) (0.497) (0.962)

(0.000) (0.225) (0.136) (0.878) (0.165) (0.101) (0.000) (0.214) (0.923) (0.204)

−1.44% −1.30% −1.49% 0.31% 0.45% −0.08% 0.40% 0.05% −0.59% 0.03%

(0.024) (0.047) (0.066) (0.635) (0.397) (0.906) (0.249) (0.873) (0.226) (0.897)

(0.000) (0.160) (0.567) (0.301) (0.020) (0.869) (0.768) (0.487) (0.001) (0.186)

−0.86% −1.12% −1.10% 0.48% −0.24% −0.12% 0.27% −0.13% −0.55% 0.07%

(0.211) (0.050) (0.162) (0.544) (0.661) (0.863) (0.584) (0.671) (0.265) (0.892)

(0.003) (0.431) (0.984) (0.039) (0.124) (0.824) (0.996) (0.004) (0.013) (0.141)

−0.68% −0.41% −0.83% 0.26% −0.02% 0.05% −0.05% −0.01% −0.60% −0.08%

(0.504) (0.576) (0.335) (0.819) (0.981) (0.940) (0.952) (0.985) (0.289) (0.917)

(0.028) (0.999) (1.000) (0.494) (0.442) (0.034) (0.000) (0.192) (0.000) (0.602)

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Table 9 (Continued)

cross p-value

Q2

p-value

cross p-value

Q3

p-value

cross p-value

Q4

p-value

cross p-value

Q5

p-value

cross p-value

Panel A: 7F model. Sub-Sample 1990–1997 Small Growth −0.67% (0.531) (0.472) −1.16% (0.147) (0.252) Small Blend Small Value −1.35% (0.022) (0.566) Mid Growth −0.64% (0.540) (0.052) −0.01% (0.995) (0.608) Mid Blend Mid Value −2.00% (0.001) (0.016) Large Growth 0.10% (0.879) (0.080) −0.15% (0.828) (0.666) Large Blend −1.09% (0.015) (0.025) Large Value −1.02% (0.252) (0.156) Index

−0.87% −1.84% −2.11% −0.67% −0.46% −1.70% −0.45% −0.54% −0.90% 0.30%

(0.227) (0.013) (0.000) (0.301) (0.313) (0.004) (0.268) (0.025) (0.013) (0.357)

(0.279) (0.032) (0.129) (0.046) (0.381) (0.054) (0.096) (0.108) (0.126) (0.304)

−0.75% −1.02% −1.83% 0.11% −0.37% −0.35% −0.69% −0.73% −0.69% −0.32%

(0.353) (0.191) (0.002) (0.856) (0.441) (0.522) (0.046) (0.001) (0.027) (0.150)

(0.384) (0.321) (0.258) (0.322) (0.424) (0.839) (0.007) (0.020) (0.410) (0.297)

−0.80% 1.16% −1.30% 0.06% −0.94% −0.81% −0.29% −0.28% −0.50% −0.44%

(0.290) (0.187) (0.026) (0.913) (0.141) (0.126) (0.523) (0.164) (0.068) (0.257)

(0.342) (0.029) (0.594) (0.359) (0.162) (0.557) (0.304) (0.456) (0.723) (0.267)

−0.01% −0.42% −0.88% 0.88% 0.47% 0.31% 0.34% 0.46% 0.00% 0.96%

(0.992) (0.683) (0.207) (0.539) (0.731) (0.672) (0.707) (0.756) (0.997) (0.237)

(0.957) (0.637) (0.832) (0.008) (0.185) (0.012) (0.006) (0.001) (0.998) (0.033)

Panel B: 7F model. Sub-Sample 1998–2007 Small Growth −4.48% (0.005) (0.000) Small Blend −3.98% (0.011) (0.000) Small Value −2.85% (0.068) (0.000) (0.000) Mid Growth −1.18% (0.368) −1.87% (0.134) (0.000) Mid Blend −1.52% (0.240) (0.000) Mid Value Large Growth 0.07% (0.945) (0.993) −0.37% (0.643) (0.000) Large Blend −0.08% (0.929) (0.000) Large Value −2.54% (0.050) (0.000) Index

−2.63% −2.77% −1.67% 0.66% 0.26% 0.12% 0.70% 0.42% 0.67% −0.19%

(0.049) (0.045) (0.226) (0.496) (0.781) (0.914) (0.192) (0.409) (0.457) (0.761)

(0.000) (0.000) (0.009) (0.993) (0.968) (0.968) (0.013) (0.533) (0.988) (0.755)

−0.77% −1.08% −1.03% 1.73% 0.86% 1.13% 0.45% 0.61% 1.05% 0.09%

(0.494) (0.394) (0.470) (0.107) (0.321) (0.268) (0.379) (0.159) (0.264) (0.816)

(0.013) (0.567) (0.838) (0.034) (0.596) (0.117) (0.336) (0.075) (0.048) (0.016)

0.54% 0.07% −0.89% 2.48% 2.38% 2.00% 0.49% 0.80% 1.27% 0.39%

(0.663) (0.956) (0.520) (0.043) (0.005) (0.079) (0.537) (0.191) (0.180) (0.664)

(0.000) (0.000) (0.960) (0.000) (0.000) (0.001) (0.220) (0.001) (0.000) (0.000)

2.27% 2.14% 0.33% 2.67% 3.20% 2.04% 0.21% 0.67% 1.58% 0.65%

(0.121) (0.098) (0.803) (0.102) (0.019) (0.103) (0.895) (0.441) (0.135) (0.640)

(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.897) (0.029) (0.000) (0.000)

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Table 10 Simulated fund persistence obtained by assessing performance of past-performance-based portfolios (7F model). This table reports the performance persistence results of simulated funds obtained by assessing performance of past-persistence-based portfolios. In each semester, past performance is estimated by means of 7F model using daily gross returns. For all styles, mutual funds are grouped in quintiles based on past performance. Portfolio Q1 consists of investing, over the next period, in the worst performing simulated funds, from the previous period, in the first quintile. The same pattern is followed by the rest of the portfolios up to Q5, which invests in the best simulated funds based on the performance achieved in the previous period. This procedure is repeated at the beginning of each semester. The performance of these portfolios is estimated by means of 7F model. The panels show two p-values for the estimates. The first is the standard p-value from the regression 7F model with the Newey and West (1987) heteroskedasticity and autocorrelation consistent covariance estimator. The second, the cross-sectional p-value, is the critical probability estimated by means of simulations in each style-type mutual fund group.

Q1

p-value

cross p-value

Q2

cross p-value

Q3

p-value

cross p-value

Q4

p-value

cross p-value

Q5

p-value

cross p-value

Panel C: 7 Factors model. Sub-Sample 2008–06/2015 (0.000) 0.01% Small Growth 0.56% (0.442) 0.10% (0.900) (0.000) −0.08% Small Blend 0.55% (0.570) (0.000) −0.16% Small Value (0.099) 0.05% Mid Growth −0.18% (0.826) 0.56% (0.489) (0.001) 0.55% Mid Blend 0.36% (0.642) (0.018) 0.05% Mid Value Large Growth 0.67% (0.306) (0.001) 0.86% 0.77% (0.152) (0.000) 0.34% Large Blend 0.73% (0.199) (0.000) 0.45% Large Value −1.03% (0.311) (0.001) −0.71% Index

(0.983) (0.894) (0.832) (0.945) (0.391) (0.940) (0.121) (0.194) (0.197) (0.428)

(0.033) (1.000) (1.000) (0.180) (0.002) (0.398) (0.000) (0.041) (0.000) (0.061)

-0.17% −0.74% −1.40% 0.11% −0.24% 0.05% 0.42% 0.23% −0.19% 0.00%

(0.773) (0.201) (0.061) (0.871) (0.665) (0.934) (0.381) (0.315) (0.583) (0.993)

(0.814) (0.858) (0.165) (0.070) (0.135) (0.393) (0.679) (0.363) (0.333) (0.052)

−0.37% −1.37% −2.17% 0.10% −0.11% 0.48% 0.31% 0.13% −0.63% 0.73%

(0.529) (0.045) (0.017) (0.866) (0.826) (0.425) (0.493) (0.591) (0.171) (0.222)

(0.469) (0.000) (0.000) (0.082) (0.329) (0.004) (0.976) (0.843) (0.000) (0.000)

−0.61% −2.31% −2.82% −0.32% −0.91% −0.89% −0.01% −0.47% −1.12% −0.74%

(0.385) (0.013) (0.012) (0.541) (0.181) (0.247) (0.980) (0.340) (0.112) (0.511)

(0.117) (0.000) (0.000) (0.004) (0.000) (0.000) (0.000) (0.000) (0.000) (0.051)

Panel D: 7 Factors model. Sample 1990–06/2015 (0.000) −1.26% Small Growth −1.63% (0.041) −1.94% (0.021) (0.001) −2.05% Small Blend −3.23% (0.000) (0.000) −2.36% Small Value Mid Growth −0.31% (0.669) (0.050) −0.29% Mid Blend −1.03% (0.158) (0.000) −0.35% Mid Value −1.91% (0.008) (0.000) −0.48% Large Growth 0.52% (0.274) (0.000) 0.34% Large Blend −0.23% (0.640) (0.005) −0.11% Large Value −0.48% (0.385) (0.000) −0.28% −1.09% (0.108) (0.000) −0.56% Index

(0.054) (0.005) (0.004) (0.605) (0.585) (0.467) (0.285) (0.687) (0.563) (0.152)

(0.000) (0.000) (0.063) (0.066) (0.421) (0.685) (0.001) (0.229) (0.097) (0.117)

−1.13% −1.23% −2.41% −0.09% −0.01% −0.41% −0.04% −0.04% −0.24% −0.09%

(0.065) (0.053) (0.004) (0.874) (0.979) (0.520) (0.903) (0.882) (0.619) (0.718)

(0.000) (0.702) (0.039) (0.531) (0.924) (0.795) (0.055) (0.633) (0.257) (0.832)

−0.82% −1.31% −1.37% 0.05% −0.18% −0.23% −0.09% 0.10% 0.02% 0.20%

(0.207) (0.033) (0.084) (0.939) (0.716) (0.734) (0.845) (0.732) (0.972) (0.643)

(0.026) (0.568) (1.000) (0.104) (0.735) (0.962) (0.012) (0.005) (0.000) (0.007)

−0.29% −0.32% −0.78% 0.13% 0.11% 0.21% −0.38% −0.05% −0.02% 0.26%

(0.764) (0.662) (0.358) (0.899) (0.877) (0.758) (0.625) (0.935) (0.975) (0.751)

(0.413) (1.000) (1.000) (0.031) (0.024) (0.000) (0.000) (0.596) (0.999) (0.004)

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Table 10 (Continued)

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Small Growth

1% Annualized performance

Small Blend Small Value Mid-Cap Growth

0%

Mid-Cap Blend Mid-Cap Value Large Growth

-1%

Large Blend Large Value Index

-2%

-3% 1

2

3 Quintile

4

5

Fig. 3. Performance of portfolios based on simulated fund past performance (January 1990 to June 2015). The figure shows the annualized performance (vertical axis) of the portfolios Q1 to Q5 (horizontal axis) formed to assess simulated fund performance persistence. In each semester, past performance was estimated by means of 4F model using gross daily returns. The sample period runs from January 1990 to June 2015. For all styles, simulated funds are grouped in quintiles based on past performance. Portfolio Q1 consists of investing, over the next period, in the worst performing simulated funds, from the previous period, in the first quintile. The same pattern is followed by the rest of the portfolios up to Q5, which invests in the best simulated funds based on the performance achieved in the previous period. This procedure is repeated at the beginning of each semester. The performance of these portfolios is estimated by means of model 4F model.

618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642

difference is −0.26%, corresponding to −1.92% −1.66 %), and for Q5 the alpha is 5.14% in Table 7 and 1.81% in the Table 9 (then the difference is 3.33%, corresponding to 5.14% −1.81 %). In sum, although in the majority of cases in Table 9 panels the performance of the portfolios in the different quintiles is not significant, it is useful for estimating which part of the performance in Table 7 can be obtained passively, and which part is actually due to persistence in the value added (positive or negative) of the managers. From that comparison, we can conclude that the evidence on persistence found in Table 7 (panels A and B) for mutual funds during the 1990–2007 subperiod is robust, especially for the case of past best mutual funds. Fig. 4 shows the alphas corresponding to the quintile portfolios in Table 9 (Panel C), i.e., for the last subperiod (January 2008–June 2015). The lines represent a negative slope for all styles, which implies that investing in past best (worst) simulated funds leads to worse (better) performance. Therefore, in this subperiod, investing according to the past performance of passive funds implies contrarian behavior. This evidence of contrarian behavior in terms of performance persistence is not attributable to active management because simulated funds are passive by construction. In this vein, there is a large body of literature on contrarian investment strategy from De Bondt and Thaler (1985), Chan (1988), or Yao (2012), among others. De Haan and Kakes (2012) show how institutional investors tend to be contrarian traders, buying past losers and selling past winners, and how this behaviour may have a stabilizing impact on financial markets. The contrarian effect is the opposite of the momentum investment strategy: buy past winners and sell past losers, also well documented in the literature by Jegadeesh and Titman (1993), Griffin, Ji, and Martin (2003), or Wang and Wu (2011), among others. Although an analysis of these issues goes beyond the scope of this study, our results from simulated funds support the existence of a contrarian effect. Therefore, our evidence of the contrarian effect is linked to a contrarian or reversal effect in the different style class of stocks. In a similar way, Teo and Woo (2004) find strong evidence that stocks in styles that performed poorly in the past, relative to Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

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3% 2%

Annualized performance

Small Growth Small Blend

1%

Small Value Mid Growth

0%

Mid Blend Mid Value

-1%

Large Growth Large Blend

-2%

Large Value Index

-3% -4% 1

2

3 Quintile

4

5

Fig. 4. Performance of portfolios based on simulated fund past performance (January 2008 to June 2015). The figure shows the annualized performance (vertical axis) of the portfolios Q1 to Q5 (horizontal axis) formed to assess simulated fund performance persistence. In each semester, past performance was estimated by means of 4F model using gross daily returns. The sample period runs from January 2008 to June 2015. For all styles, simulated funds are grouped in quintiles based on past performance. Portfolio Q1 consists of investing, over the next period, in the worst performing simulated funds, from the previous period, in the first quintile. The same pattern is followed by the rest of the portfolios up to Q5, which invests in the best simulated funds based on the performance achieved in the previous period. This procedure is repeated at the beginning of each semester. The performance of these portfolios is estimated by means of model 4F model.

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other styles, tend to do well in the future. Thus, in our case, simulated funds that are winners (losers) in one period tend to be losers (winners) in the next period and for this reason Q1 performs better than Q5. However when strategies based on past performance are computed for the real mutual funds, this contrarian effect is not present in Fig. 2 and Panel C of Table 7, except for Index mutual funds. Thus, active management is what makes mutual funds differ from passive portfolios, and the performance across periods will not be reversed. Concretely, according to our evidence, the relationship of mutual fund performance between consecutive periods is in general flat and neither positive (persistence) nor negative (reversal or contrarian).

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5. Conclusions

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The topic of mutual fund performance has attracted a great deal of attention from both researchers and practitioners and, within this field, it is particularly interesting to analyze whether the performance obtained by the funds is persistent over time. In this context, the main objective of our study was to analyze the robustness of some of the methodologies used to measure mutual fund performance persistence. With this aim, our contribution lies primarily in the analysis of potential biases due to systematic risk factor exposures. To avoid these biases, the first aim of this study was to evaluate the persistence separately, by grouping mutual funds according to their styles. The reason for this is that if persistence was analyzed for all mutual fund styles considered jointly, evidence of persistence might be due not to the value added by active management, but rather to the behavior of the underlying classes of stocks in which the mutual fund invests. The second objective was to compare the results obtained for mutual funds with those found with simulated passively managed funds that replicate their style. This procedure enables us to analyze the robustness of the methodologies applied since, in principle, for passive funds we should find performance which is not significantly different from zero—and then, Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

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absence of persistence. In addition, performance and persistence are estimated with both net and gross returns and, in this way, we avoid mutual fund performance persistence being driven by persistence in mutual fund expenses. Regarding the empirical application, the paper has examined the performance and persistence of a sample of 4467 US equity mutual funds over the period from January 1990 to June 2015. First, for the performance results, we find that from net returns, abnormal performance is negative in general. Performance improves when gross returns are considered. In short, although there are differences at the individual level, in aggregate and after considering management and operational expenses, mutual funds do not add value for final investors. These results follow the pattern established previously in the literature. However, results vary depending on the subperiod analyzed. For the first subperiod (1990–1997) we find evidence of positive abnormal performance for many mutual fund groups. However, performance deteriorates over time, to the point that in the last subperiod (2008–2015) the abnormal performance takes negative values for most mutual fund styles. In the analysis of performance persistence, we first applied methodologies based on a winner-loser approach, namely, contingency tables, Z-tests and transition probability matrices. When comparing the persistence results of mutual funds with those achieved by simulated passive funds, the conclusion is that these methodologies are biased to show persistence much too easily. This result might call into question the validity of previous empirical findings in the literature on performance persistence when these types of methodologies are applied. The second methodology applied to measure performance is the recursive portfolio. This approach assesses persistence by estimating the performance of recursive portfolios that follow investment recommendations according to the past performance of mutual funds. In the case that persistence existed, one would expect that investing in the worst (best) mutual funds in the past would result in worse (better) performance in the future. The study also attempts to make a methodological contribution to this approach. Specifically, we propose a cross-sectional test to control for the significance of the recursive portfolios. This implies that it is necessary to correctly identify whether abnormal performance of recursive portfolios is due, precisely, to a dynamic investment strategy based on mutual fund past performance, or whether it is obtained per se by simply investing in a particular style group of mutual funds. When we controlled for mutual fund group style type and considered cross-sectional significance, the results of the recursive portfolio approach show evidence of persistence, particularly for the case of the best past mutual funds. However this result does not hold for all the subperiods considered. Specifically, for the subperiods from 1990 to 2007 we find evidence of persistence, implying that investing especially in the past best mutual funds yields a noteworthy positive performance. However, for the latest subperiod (2008–2015) there is no performance persistence—we even find contrarian behavior in persistence for Index mutual funds. When these results were compared with those achieved by investing according to the past performance of simulated mutual funds, active management was shown to compensate a reversal effect in the dynamic performance of passive portfolios. In short, our results show evidence of differences in performance and persistence depending on the subperiod analyzed over the past 25 years. For the first two thirds of the sample period the funds were able to give some value added before accounting for the effect of fees and expenses. This enabled persistence to be present, especially for the case of the best funds, since they were able to generate value without discontinuities. However, in the last and most recent subperiod the performance of the funds has been remarkably negative and therefore, in contrast to the results found for the two first subperiods, it was not possible to expect any sort of continuity in the value added of the best funds, since it never existed.

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Appendix A. Supplementary data

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Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.najef.2016.01.002. Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002

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Please cite this article in press as: Matallín-Sáez, J. C., et al. On the robustness of persistence in mutual fund performance. North American Journal of Economics and Finance (2016), http://dx.doi.org/10.1016/j.najef.2016.01.002