Edhec-Risk: Two simple performance indicators are often used to rank funds. The first one, the Sharpe ratio, was introduced by Sharpe (1966). It estimates the fund's excess return with regard to the risk-free rate divided by its standard deviation. The second one, the information ratio, is defined in a similar way by replacing the risk-free rate with a benchmark portfolio. The denominator of this ratio is therefore the fund's tracking-error. Israelsen points out that these two indicators may lead to spurious fund rankings when excess returns become negative. In that case, the fund with the higher ratio is not always the best one. <>

In order to correct this anomaly, Israelsen suggests modifying the standard information and Sharpe ratios in the following way. He proposes to introduce an exponent to the denominator. This exponent is made up of the excess return divided by its absolute value. When excess return is positive, the ratios are unchanged. When the excess return is negative, it causes a consequent modification in the result [=(excess return)*sd]. The author considered 25 US equity mutual funds [with negative excess return over the period 1999–2003] and ranked them according to the traditional information ratio and according to the modified information ratio... He plotted excess return and tracking error on the same graph, by increasing fund ranking. Using the ranking drawn from the modified information ratio, a coherent relationship appears between excess return, tracking error and ranking, which is not the case without the modification. The author notes that the modification in the ratio causes an enormous range in its size. As a result, the size of the ratio gives no useful information and should only be used as a ranking criterion. [Source]