Measuring Fund Performance: Alpha/Beta

(For those of you who don't know, Jayant and I are working at a hedge fund in Connecticut. We don't know anything about investing or finance, but we sort of have to learn, so in the spirit of learning, Jayant and I will be presenting a series of posts, each explaining a specific topic related to finance or financing.)

Evaluating the performance of actively managed portfolios is an important topic. Percentage increase in value (return) may not necessarily give a complete picture of how well the fund or strategy worked. Many other factors may confound the relevance of the return percentage metric. Just as a batter's RBI alone doesn't tell you how good the player is, return (absent any other factors) is a poor measure of a fund's performance.

An important component missing is the idea of a benchmark - I tell you that I got an 67 on my final. Is that good or bad? Obviously, you need to know the mean to tell how well I did. Similarly, a fund's return is like my score - we need context.

Another component is adjusting for risk. In investing, risk encompasses both risk of losing value and risk of gaining value. Perhaps a better term would be "luck" - we want to subtract out the component of luck in the success or failure of a fund.

The model of evaluation is this: first, we select a baseline that we wish to compare our fund to. The S&P500 is a common choice.

Second, we adjust for risk by subtracting out each year's return by a risk-free asset (cash, for example, is a risk-free asset). Note that we do not have to take inflation into account - we are merely looking at percent changes. The actual value of the investment is irrelevant.

Next, we correlate the risk-adjusted returns with the risk-adjusted returns of our baseline fund. We create a set of pairs that we can then plot and perform a linear regression. The terms of the regression, alpha (the y-intercept) and beta (the slope) are the factors that we use to evaluate the fund's performance.

Alpha is a measure of how much better than baseline the fund performed. An alpha of 0 is no improvement (imagine plotting the baseline versus itself - the regression would necessarily pass through the origin). The higher the alpha, the more money the fund made over the baseline.

Beta is a measure of how much more or less volatile the fund's performance is relative to the baseline. If beta equals 1, the fund is just as volatile as the baseline (once again, imagine plotting the baseline against itself). Beta = 0 means the fund is perfectly stable - a horizontal regression line means that the fund performed the same no matter how well the baseline was doing.

In summary, returns do not give a complete picture of the performance of a fund. Instead, we evaluate the fund relative to a baseline, usually the S&P 500 or a similar index, adjust for risk, and evaluate a fund in terms of 2 factors: alpha, how much the fund would return if the baseline would have returned 0, and beta, the volatility or instability of the fund. These 2 factors together provide a slightly more complete view of fund performance.

-chris