Nonparametric Finance

Chapter 10Performance Measurement

When the performance of a fund is measured, there is a temptation to look only at the past return on the investment. However, it is important to measure the performance by taking the risk into account. An investor can increase both the expected return and the risk by leveraging, so that it is of interest to find the inherent quality of the fund, and leave the choice of the leveraging factor to the investor. The Sharpe ratio is defined as the ratio of the expected excess return to the standard deviation of the excess return. This is an example of a performance measure that penalizes the expected return with the risk.

The measures of performance are usually single numbers, but we cannot hope to completely reduce the characteristics of a fund into a single number. For example, the Sharpe ratio is a single number, but we obtain more information by giving separately the expected excess return and the standard deviation of the excess return, instead of giving only their ratio.

Section 9.2 discussed the ranking of return distributions from the point of view of portfolio selection. This discussion is relevant for the performance measurement. For example, in portfolio selection we could be interested in the conditional expected utility

10.1

where is a ...