“…Note that due to the presence of negative average returns, the traditional Sharpe ratio turned out to be inappropriate for comparisons across allocation strategies, models, periods and hedging presence. In fact, given two assets, A and B, with the same negative average return, say -1%, and the volatility of A twice the volatility of B, 20% and 10%, respectively, the Sharpe ratio of A would be higher than that of B, -0.05 versus -0.1 (see Caporin et al, 2012 for additional comments). To overcome this limitation, we considered the modified Sharpe of Israelsen (2005) where the average returns are multiplied by the volatility if it is negative, thus restoring the appropriate ordering.…”