This paper proposes instantaneous versions of the Sharpe ratio and Jensen’s alpha as performance measures for managed portfolios. Both are derived from optimal portfolio selection theory in a dynamic model. The instantaneous Sharpe ratio equals the discrete Sharpe ratio plus half of the...

This paper shows that a strictly increasing and risk averse utility function with decreasing absolute risk aversion is necessarily differentiable with a positive and absolutely continuous derivative. The cumulative absolute risk aversion function, which is defined as the negative of the...

This paper simplifies Merton’s (1973) fund separation theorem by showing that investors will hold hedge funds in their optimal portfolio only to hedge against changes in the slope or position of the instantaneous capital market line. This result allows for incomplete markets and does not...

In the mean-variance capital asset pricing model without a riskless asset, the possibility of satiation sometimes leads to nonexistence of general equilibrium. Moreover, because portfolio preferences are not necessarily monotone, equilibrium asset prices, when they exist, may be negative or...

Some equilibrium prices in the capital asset pricing model may be negative because of nonmonotonicity of preferences. The authors identify several sets of sufficient conditions for prices to be positive. The central conditions impose bounds on the investors' risk aversion. These bounds do not...

If a stochastically monotone function of asymmetrically informed individuals' expectations of a random vector is common knowledge up to some observation error, then all the individuals must agree on their expectations. This result generalizes the 1986 theorem of R. D. McKelvey and T. Page from...