A Measure for Evaluating the Distributions of Ex-Ante Forecast Returns

Masahito Shimizu, Tokyo Institute of Technology

In this paper, we study an investment that maximizes the Sharpe ratio using an ex-ante forecast return distribution that may differ from the ex-post realized distribution. The risk forecast plays an important role in the portfolio construction processes of the mean-variance approach. We introduce a measure that evaluates an ex-ante forecast with respect to risk and return. Additionally, we show that the realized Sharpe ratio is the product of the measure multiplied by the absolute value of the market Sharpe ratio. Our findings indicate that the measure is separate from the market conditions. We also show numerical examples of the measure using an investment of ten weekly S&P sector total return indices.