Factor fund classification and performance evaluation

In the first empirical section of our paper, we investigate if mutual funds following factor investing strategies based on equity asset pricing anomalies, such as the small-cap, value, and momentum effects, earn higher alphas than traditional actively managed mutual funds. For these analyses we employ three statistical techniques: return-based style analysis to classify factor funds; cross- sectional regressions to evaluate the performance of factors funds, and bootstrap analyses to test the robustness of our results.

Our fund classification method closely follows the methodology employed by Van Gelderen and Huij (2014). We download monthly factor returns from Kenneth

French’s data library. For each fund, we run the 5-factor Fama and French model augmented with momentum using all available return observations

𝑅𝑖,𝑡= 𝛼𝑖+ 𝛽𝑖∙ (𝑅𝑀,𝑡− 𝑅𝑓,𝑡) + 𝑠𝑖∙ 𝑆𝑀𝐵𝑡+ ℎ𝑖∙ 𝐻𝑀𝐿𝑡+

𝑤𝑖∙ 𝑊𝑀𝐿𝑡+ 𝑟𝑖∙ 𝑅𝑀𝑊𝑡+ 𝑐𝑖∙ 𝐶𝑀𝐴𝑡+ 𝜀𝑖,𝑡 (4.1) where 𝑅𝑖,𝑡 is the excess return of mutual fund i in month 𝑡, 𝑅𝑓,𝑡 is the risk-free return in period 𝑡, 𝛼𝑖 is the alpha of fund i, 𝑅𝑀,𝑡 is the return on the market portfolio in period 𝑡, SMB, HML, WML, RMW, and CMA are returns of long- short factor mimicking portfolios for the size, value, momentum, profitability, and investments factors, respectively. 𝛽, 𝑠, ℎ, w, r, and 𝑐 are the estimated fund specific factor coefficients, and 𝜀𝑖,𝑡 is the residual return of fund i in month t,

under the assumption of iid. Similar to Van Gelderen and Huij (2014) we classify a fund as being a factor fund if the regression coefficient on the respective factor is positive and statistically significant. For example, if the SMB beta coefficient of fund i is higher than 2 we identify fund i as a small cap fund. A fund is considered to be a low-beta fund when its 𝛽 is smaller than 0.8. Funds can have multiple factor fund classifications simultaneously.

To measure fund performance we use the intercept from the following one- factor model:

We use CAPM alpha instead of the intercept from regression (1) as our main return performance as we want to measure the excess return coming from exposures to one of the six factors. Following Van Gelderen and Huij (2014) we limit the effect of outliers by calculating the z-score of fund alphas, winsorizing it at -2 and 2

𝑧_𝐴𝑙𝑝ℎ𝑎𝑖= 𝑚𝑖𝑛 (2, 𝑚𝑎𝑥 (−2,

𝛼_𝑖−𝜇𝛼

𝜎_𝛼 )) (4.3) where 𝛼𝑖 is the alpha of fund i from the one-factor model, 𝜇𝛼 is the average alpha across all funds in the sample, and 𝜎𝛼 is the cross sectional standard deviation of all fund alphas.

We use the following cross-sectional regression to evaluate the performance of factor funds:

𝑧_{𝐴𝑙𝑝ℎ𝑎 𝑖}= 𝛼𝑖+ 𝑏1∙ 𝐿𝑜𝑤_𝑏𝑒𝑡𝑎 + 𝑏2∙ 𝑆𝑚𝑎𝑙_𝑐𝑎𝑝+ 𝑏3∙ 𝑉𝑎𝑙𝑢𝑒 + 𝑏4∙

𝑀𝑜𝑚𝑒𝑛𝑡𝑢𝑚 + 𝑏5∙ 𝑃𝑟𝑜𝑓𝑖𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 + 𝑏6∙ 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑠 + 𝜀𝑖 (4.4) where Low_beta, Small_cap, Value, Momentum, Profitability, and Investments

are 1 if the fund is classified as a low-beta, small cap, value, momentum, profitability, or investments factor fund, or 0 otherwise.

We also run an augmented version of this regression:

𝑧_𝐴𝑙𝑝ℎ𝑎𝑖= 𝛼𝑖+ 𝑏1∙ 𝐿𝑜𝑤𝑏𝑒𝑡𝑎+ 𝑏2∙ 𝑆𝑚𝑎𝑙𝑐𝑎𝑝+ 𝑏3∙ 𝑉𝑎𝑙𝑢𝑒 + 𝑏4∙ 𝑀𝑜𝑚𝑒𝑛𝑡𝑢𝑚 + 𝑏5∙ 𝑃𝑟𝑜𝑓𝑖𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 + 𝑏6∙ 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑠 + 𝑏7∙ log 𝑎𝑔𝑒 + 𝑏8∙ log 𝑠𝑖𝑧𝑒 + 𝑏19∙ expratio+ 𝑏10∙ 𝑡𝑢𝑟𝑛𝑟𝑎𝑡𝑖𝑜+ 𝜀𝑖 (4.5) where log 𝑎𝑔𝑒 is the natural logarithm of fund age, calculated as the number of months with available return observations, log 𝑠𝑖𝑧𝑒 is the natural logarithm of fund size, measured as its average total net assets, exp_ratio is the average total expense ratio, and turn_ratio is the average turnover ratio. In our Global markets sample, we do not include exp_ratio, and turn_ratio in our regressions due to the underlying data being unavailable.

To rigorously test the robustness of our results we employ a bootstrap method in the spirit of Fama and French (2010). In the distribution of active manager returns, we see that on average fund alpha is negative after cost with approximately the average cost level. This implies that funds on average

produce alpha which is insufficient to cover the fees they charge. However, the fact that some managers tend to be on the positive side of the distribution might indicate that they have some level of skill or that they just generated high returns by chance. To control for this we do a bootstrap analysis where we simulate mutual fund alpha distribution with a true alpha equal to zero. To do so we simulate 5,000 cross-sectional zero-alpha distributions. First, we subtract the one-factor alpha from the returns of each fund to force its true alpha to zero. Second, at each run, we select a random number of months with replacement similar to Fama and French (2010). By selecting the same number of months for all funds we keep the cross-sectional properties of mutual fund performance which is directly related to the alpha distribution. Third, to control for difference in number of observations for each fund we compare their performance based on the t-statistic of alpha (t(α)) and not on alpha itself. After having 5,000 simulated

t(α)we calculate our bootstrapped distribution by calculating the average t(α) at

each percentile over all 5,000 runs. The resulting cross-sectional distribution has an implicit assumption that all managers have enough skills to cover their fees. As we know that the true alpha is zero that means that all alphas which are different from zero are observed by luck. As such, to infer that a manager has skills exceeding their fees the t(α) of the actual distribution should be higher than the simulated t(α) at a certain percentile.