We show that in order to determine whether one decision-maker is more risk averse than another, it is sufficient to consider their attitudes towards a given two-parameter family of risks. When all risks belong to this family, useful comparisons of risk aversion can be made even in situations of...

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...