Jensen’s Alpha
“Alpha” in this post will mean the CAPM alpha, that is, the intercept in the CAPM regression. It was first used to measure mutual fund performance by Michael Jensen, and, when used in that context, it is called Jensen’s alpha. It is worth stressing to students that a positive alpha does not mean that an investor should move all of his or her money into the fund. A fund can have a positive alpha but have a lower Sharpe ratio than the market. In fact, a fund has a positive alpha if and only if its Sharpe ratio is larger than the market’s Sharpe ratio multiplied by the correlation between the fund and the market. Because correlations are less than one, the Sharpe ratio hurdle for a fund to earn positive alpha is lower than the market Sharpe ratio. An interactive figure illustrating this principle can be found here. An extreme example is a fund with a zero beta. Such a fund has a positive alpha if and only if its Sharpe ratio is positive, meaning that it beats the risk-free return on average.
While investors should not necessarily move all of their money to a positive alpha fund, they should move some of their money to the fund, assuming they care only about mean and variance and not higher moments. Mean-variance efficiency can be improved by shifting money from the market to a positive alpha fund. This is shown by Dybvig and Ross (Journal of Finance, 1985).
In an earlier post, I explained how to use Julius to run the CAPM regression, using stock prices from Yahoo and using market and risk-free returns from French’s data library. We can do the same with a mutual fund ticker. Rather than using the most recent 60 months as in the earlier post, I prefer to run the regression for this exercise using all available data. Then, we can ask Julius to compute the beta-hedged mutual fund return each month. By beta hedging, I mean taking out the market exposure as R - beta * (Rm - Rf). According to the CAPM, the average value of this beta-hedged return should be the risk-free return Rf. We can ask Julius to compound the risk-free returns and compound the beta-hedged mutual fund returns over time and plot them. If the beta-hedged returns outperform the risk-free returns, then the fund earned alpha. It is useful to ask for a log scale on the y axis in the plot. Then, we can easily see the periods in which the fund did better than it should have given its market exposure (the slope of the hedged fund curve is greater than the slope of the risk-free curve) and the periods in which it did worse.
A good example for this exercise is Fidelity Magellan (ticker=FMAGX). The fund was an extreme outlier in terms of performance under the stewardship of Peter Lynch but underperformed substantially afterwards. Of course, we expect outliers in a random sample.
Also on substack at kerryback.substack.com