Equity Valuation and Portfolio Management

INFORMATION RATIO

Alpha is the average active return over a time period. Since backward-looking tracking error measures the standard deviation of a portfolio's active return, it is different from alpha. A portfolio does not have backward-looking tracking error simply because of outperformance or underperformance. For instance, consider a portfolio that outperforms (or underperforms) its benchmark by exactly 10 basis points every month. This portfolio would have a backward-looking tracking error of zero and a positive (negative) alpha of 10 basis points. In contrast, consider a portfolio that outperforms its benchmark by 10 basis points during half the months and underperforms by 10 basis points during the other months. This portfolio would have a backward-looking tracking error that is positive but an alpha equal to zero. (Note that in some texts, alpha and tracking error are calculated respectively as the average and the standard deviation of the beta-adjusted active return, instead of the total active return.)

The information ratio combines alpha and tracking error as follows:

The information ratio is essentially a reward-to-risk ratio. The reward is the average of the active return, that is, alpha. The risk is the standard deviation of the active return, the tracking error, and, more specifically, backward-looking tracking error. The higher the information ratio, the better the ...