A probabilistic risk-to-reward measure for evaluating the performance of financial securities

Abstract

Existing risk-to-reward measures, such as the Sharpe ratio [1] or M2 [2], are based on the idea of quantifying the excess return per unit of deviation in an investment. In this preliminary article we introduce a new probabilistic measure for evaluating investment performance. Randomness Deficiency Coefficient (RDC) expresses the likelihood that the observed excess return of an investment has been generated by chance. Some of the advantages of RDC over existing measures are that it can be used with small historical datasets, is time-frame independent, and can be easily adjusted to take into account the familywise error rate which results from selection bias. We argue that RDC captures the fundamental relationship between risk and reward and prove that it converges with Sharpe's ratio.