Reward-risk ratios

We introduce three new families of reward-risk ratios, study their properties and compare them with existing examples. All ratios in the three families are monotonic and quasiconcave, which means that they prefer more to less and encourage diversification. Members of the second family are also scale-invariant. The third family is a subset of the second, and all its members depend only on the distribution of a return. In the second part of the paper, we provide an overview of existing reward-risk ratios and discuss their properties. For instance, we show that, like the Sharpe ratio, every reward-deviation ratio violates the monotonicity property.