Small Sample Analysis of Performance Measures in the Asymmetric Response Model

This paper reviews and extends definitions and properties of the three classical performance statistics (the Sharpe Ratio, the Treynor Index, and Jensen's Alpha) by locating them in a more general framework: the Asymmetric Response Mode. This allows various notions of beta, which can be related to downside risk, to be employed, and includes, as special cases, a market timing model and the mean-variance CAPM. Due to the general lack of data on fund performance in practice, our emphasis is on small sample analysis where possible. We illustrate our results empirically using data on 15 U.S.-based emerging markets investment funds.