Refining the Sharpe Ratio (Digest Summary)

The Sharpe ratio is a measure of volatility-adjusted performance and is calculated by
dividing excess return by the standard deviation of excess return. Excess return is
defined as the return in excess of the risk-free rate of return—for example, the
three-month T-bill rate. When portfolio performance is ranked by using the Sharpe
measure, a higher value indicates better risk-adjusted performance. Although one might
interpret excess return to be a positive number, it can be negative at times, such as
during long market downturns. As mentioned by other authors and demonstrated by the
author in this article, the reliability of the Sharpe ratio as an evaluating measure
comes into question when excess return, and thus the calculated Sharpe ratio, is
negative. The author illustrates the issue with a hypothetical example that compares two
funds in which the second fund has a lower return and higher volatility than the first
fund and thus has a larger (less negative) Sharpe ratio. He presents a modification to
the Sharpe ratio to resolve this counterintuitive result that appears when excess return
is negative.

The author’s solution is to add an exponent to the denominator of the Sharpe ratio
(standard deviation of excess return). The exponent is excess return divided by the
absolute value of excess return. Using this modification in the hypothetical example
mentioned earlier results in an intuitive ranking, with the second fund now having a
smaller (more negative) Sharpe ratio than the first fund does. The author presents
graphical and statistical correlations of U.S. equity fund rankings with the two Sharpe
measures and observes that correlations are tighter when he uses the modified Sharpe
ratio. He concludes that when excess returns are negative, rankings produced by the
Sharpe metric are improved by adding the exponent to the denominator.