Two main measures of risk are generally used, namely total risk and non-diversifiable risk. Total risk is normally measured by the variance or standard deviation of return, whereas non-diversifiable risk is normally measured by the β coefficient; see section 5.3.4.
Friend, Blume & Crockett  examined the mean return earned by a group of unit trusts compared to those of randomly generated portfolios. In the study, variance was used as a measure of risk. The funds were divided into three risk categories, high, medium, and low. Random portfolios with risks approximating those of the unit trusts were generated. For this measure during the period unit trusts under-performed randomly selected portfolios. Friend, Blume & Crockett  then repeated their analysis using β as a measure of risk. Again, they divided unit trusts into low, medium and high risk categories, and matched these with randomly selected portfolios. However, they obtained different results. The study shows that the method used to construct random portfolios affects the conclusions on unit trust performance.
Most fund performance evaluation services3 choose as a benchmark the performance of portfolios administered by other managers, rather than that of random portfolios. In evaluating fund managers, they examine both the fund's risk and the return earned over a period compared with the risk/return of other fund managers. Generally, both the standard deviation of return and systemic risk as measured by β are used as measures of risk. The same service may present comparisons using each measure separately. However, as comparisons are not generally being made between funds of the same risk, it is often difficult to form an overall opinion about fund performance.
In order for a comparison to be made between investments with different levels of risk, a risk/return trade-off needs to be defined. There are four main performance measures that have been proposed in the literature to achieve this. As outlined above, these measures differ in the definition of risk and their assumptions about the ability of investors to adjust the risk level of any fund in which they may invest.
3For example, BARRA, Lipper and Wilshire, all based in the US, and CAPS, W. F. Corroon and the WM Company in the UK.