Do active Mutual Fund Managers Deserve their Fees? A Return-Based Style Analysis on their Performance

In this chapter we analyze and discuss the main setting and structure of our analysis of mutual funds managers performance. In our analysis we take into consideration six different factors and build six indexes based on each of them, to capture the expected premium connected with these factors with respect to the return of the stocks of S&P 500 Index. After selecting the stocks and constructing the indexes with the proper weighting criteria, we employ the constructed indexes as the six variables to perform a multiple linear regression on the performance of the mutual funds selected for our study.
The mutual funds that we analyze are chosen based on specific criteria that are developed in chapter 4. Our analysis is commonly referred to as “Style Analysis” and allows us to determine which are the factors that can best explain the excess returns of the selected mutual funds. Starting from the results of our multiple regression, we will then assess whether or not the mutual funds managers really deserve their annual fees.
The chapter describes the construction of the six indexes and compares the returns among them and with respect to the reference index, the S&P 500.

The Six Factors Indexes and the Selection Criteria
As previously mentioned in chapter 2, over 300 relevant factors have been identified by the researchers. However, we are going to perform our analysis just by selecting the six factors that have been considered most relevant in the majority of papers on factor investing and whose historical premium have strong foundations. The aforementioned factors are the following: size, value, momentum, high quality, low volatility and dividend yield.
In our analysis, we obtained and gathered data from Bloomberg, ranking S&P 500 stocks depending on their specific characteristics and then built the relative indexes, which will then represent the variables of our constrained multiple regression over the excess return achieved by the mutual funds under examination. The stocks taken under consideration were only the stocks included in the S&P 500 Index in the period between March 31st 1999 and December 31st 2019. All values are adjusted for dividends and stock splits, so that the adjusted close price at the end of the day represent the actual price of the stock without being influenced by any of these operations.
We perform a full revaluation of our indexes every three months, in order to have a rebalancing frequency that can approximate that of mutual funds. Rebalancing the portfolio leads to some costs, such as transaction and computational costs. Every time the portfolio is rebalanced, the data is gathered for all securities available on the revaluation date and an updated ranking is produced. Based on that, the indexes are reweighted and an ideal portfolio manager mirroring the index would have to perform the necessary transactions in the market, adding new stocks, unwinding positions or changing her exposure. This is not computationally cumbersome or particularly time-consuming, since all the calculations are pretty simple, but the managers incur in transaction costs that can’t be ignored.
The reasons to choose only S&P 500 stocks are manifold: the abundance of immediately accessible data via Bloomberg, the dimensions of the firms, the accuracy of their reports, the large number of funds whose strategy is exclusively based on S&P 500 and the very high liquidity in the market. Furthermore, many researchers have already applied factor investing theory to this market, finding the interesting results discussed in chapter 2.
We now turn to the introduction of the factor indexes and the relative criteria implemented to rank the stocks.

Size Index
The size factor is the most common factor, brought to the attention of investors since the early stages of factor investing in 1992 by Eugene Fama and Kenneth French in their Three Factor Model. The factor captures the premium linked to smaller firms, by market capitalization, with respect to the other companies included in the reference set. Market capitalization can be defined both as full or as free float; the latter is the one we have selected from Bloomberg to rank our firms.
An important drawback of this way of constructing indexes is the number of firms that are excluded from S&P 500 Index during each 3 months period and, subsequently, fall out of our universe portfolio too. If they are not included in our indexes, no problem arises, otherwise we face the risk of survivor bias. This bias, particularly exacerbated among the smallest firms of S&P 500, is fully addressed in section 5.5.
In line with the findings of the researchers E. Fama and K. French, who highlighted this factor as one the most relevant in determining the premium gained by stock market investors, the 20-year historical performance of the Size Index resulted in a very large 927.87%, more than six fold the return of the S&P 500 Index in the same period. In the following graph we confront the returns of the two indexes over time, where the difference in the cumulative performance is extremely clear.