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...

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...

We show that if the intercept and slope of the instantaneous capital market line are deterministic, then investors will not hold any hedge portfolios in the sense of Merton [1973, 1990]. They will choose portfolios that plot on the capital market line, and they will slide up and down the capital...

Differentiability is a convenient property of von Neumann-Morgenstern utility functions which is almost always imposed but has not been translated into behavioral terms. In applications, expected utility is usually maximized subject to a constraint, and the maximization is carried out by...