Portfolio Metrics: Alpha

Posted by Dan Hung

September 12, 2007

So, now you know how to calculate beta and figure out how volatile your portfolio or individual stocks have been relative to the market. Essentially, a backwards looking statistic on how much “risk” (more appropriately how much volatility) you took on in the last x-periods with x being how ever far back you decided to calculate.

This is all well and good, but how do you know that the risk you took on was worthwhile? Well, how about a little metric called alpha. With hedge funds every where, alpha’s the hottest thing on the street. Alpha is a measure of “excess return.” Alpha is defined as the intercept of the security characteristics line. This is basically the line we described yesterday which matches the returns of a portfolio with the returns of the market (typically the S&P 500). We can also calculate it using this definition after calculating beta. The formula would be: Rp - beta*Rm where Rp is mean portfolio return, beta is our portfolio beta, and Rm is the mean market return. Here’s an example of a basic calculation:

Alpha of the Dow

This data set doesn’t really make sense given that I’m finding the beta and alpha of the Dow versus the S&P yet clearly the Dow is not actively managed. But, we can see that the Dow has actually be slightly more volatile than the S&P over the last year with a 1.016 beta but the return alpha was .002.

What does this alpha mean? Basically, we’ve returned .2% above what can be expected given the market’s return and the beta of the portfolio. If you didn’t notice from the equation given, alpha basically implies that one should be able to expect their portfolio volatility multiplied by the market return. To return more than this gives positive alpha and less than this negative alpha. Positive alpha implies that you’ve created value with your stock choices, but negative alpha implies that you’ve destroyed value.