Using Risk Factors to Understand Long/Short Equity Mutual Fund Returns: Part 2

Using Risk Factors to Understand Long/Short Equity Mutual Fund Returns: Part 2

In our prior article[1] we described how we are using common risk factors to understand the returns of long/short equity (LSE) mutual funds. In this article we show the results of using the standard Fama-French factors (size and book-to-market) as well as a dividend-yield factor (the return on high-dividend-yield stocks minus the return on low-dividend-yield stocks) and a volatility factor (the return on high-volatility stocks minus the return on low-volatility stocks). To be sure we are capturing all the effects the factors may explain in terms of return, we also look for linear and nonlinear influences. Table 1 is a top-level look at the results of our tests.

Table 1. R² and F Test Results

 Source: Lipper

First, we note that all the model fits are statistically significant, since all the p-values of the F test[2] are significant at the 1% level. Since the model fits are significant, it appears all the funds have a highly significant exposure to at least one factor. Next, we note that 36 of the 45 funds have an R² greater than 50%. For these 36 LSE funds it is clear that the risk factor(s) explain an important part (but not all) of the long/short strategy they use; the R² s for these 36 LSE funds range between 53% and 85%.

As for the factor(s) each fund is exposed to, all but two of the funds have a positive exposure or tilt to the dividend-yield factor. Therefore, a common earnings factor across most LSE funds is a positive tilt toward high-dividend-yield stocks versus low-dividend-yield stocks.

The next most common significant factor is small-cap versus large-cap stocks. Twelve of the 45 stocks have a positive tilt for this factor. All the remaining significant factors, which vary quite a bit from fund to fund, are nonlinear relations such as the dividend-yield factor’s relationship to the volatility factor. When we write that there is a nonlinear relationship between the dividend-yield factor and the volatility factor, we mean that the size of the effect of the dividend yield factor depends on the fund’s exposure to the volatility factor.

To give an example, if we look at the Caldwell & Orkin fund, the coefficient of the dividend yield/volatility interaction is minus 0.53. The dividend yield factor on its own has a coefficient of 0.59, i.e., there is a positive tilt toward higher dividend-yield stocks in the portfolio. If the exposure to the volatility factor were to go to zero, i.e., the current tilt toward lower volatility goes to zero, the fund would have just one factor—the dividend-yield factor. Therefore, returns would rise, but volatility would go up as well. If the volatility-factor exposure were to increase 20% (become increasingly negative and have a greater tilt toward lower volatility), the change in the volatility exposure would reduce the effect of the existing exposure to the dividend-yield factor. This result makes sense, since a fund seeking low(er) volatility (which many LSE funds do) often means it is accepting a reduction in return.

The various nonlinear relationships in the model fits are important to understand, since many of the funds have at least one—if not more than one—nonlinear relationship that involves the volatility factor. This implies there is a fairly common tradeoff occurring (or having the potential to occur) between the tilt toward low volatility and the (positive) tilt toward one or more of the other factors. The importance of the volatility factor in these nonlinear interactions is something we will discuss in our conclusions to this series of articles.

We note before closing that only two of the LSE funds have a positive alpha that is statistically significant. There are 30 other LSE funds that have positive alphas, but their alphas are not statistically significant, i.e., they are no different than zero.

In the final article in this series we will review our efforts to include a commodity factor in our modeling as well as an optionality overlay. We will also present the conclusions of our analysis.