We consider a model of search when the distribution of prices (wages) is unknown. The effect of changing the objective function from minimizing expected costs to maximizing expected utility is examined.

The statistical relationship between estimated composite performance measures and their risk proxies are derived in accordance with statistical distribution theory. It is found that the estimated composite performance measures are generally highly correlated with their risk proxies. In general, sample size, investment horizon and the market condition are three important factors in determining the degree of relationship above-mentioned. It is shown that a larger number of historical observation and an appropriate investment horizon can generally be used to reduce the sample correlation between the estimated performance measures and their risk proxy. Sampling distributions for both Sharpe and Treynor measures are also derived.