Sharpe Ratios and Alphas in Continuous Time
在连续时间模型中修正了夏普比率和詹森阿尔法，修正后的夏普比率等于普通夏普比率加上基金波动率的一半，修正阿尔法也包含二阶矩调整，两者可能改变基金排名，且基于动态组合理论证明其合理性。
Abstract This paper proposes modified versions of the Sharpe ratio and Jensen's alpha, which are appropriate in a simple continuous-time model. Both are derived from optimal portfolio selection. The modified Sharpe ratio equals the ordinary Sharpe ratio plus half of the volatility of the fund. The modified alpha also differs from the ordinary alpha by a second-moment adjustment. The modified and the ordinary Sharpe ratios may rank funds differently. In particular, if two funds have the same ordinary Sharpe ratio, then the one with the higher volatility will rank higher according to the modified Sharpe ratio. This is justified by the underlying dynamic portfolio theory. Unlike their discrete-time versions, the continuous-time performance measures take into account that it is optimal for investors to change the fractions of their wealth held in the fund vs. the riskless asset over time.