Entropic Discounting of Geometric Means: An Index for Lotteries and Portfolios

This paper models choice under risk, whether such choices are over simple lotteries or over lotteries that arise from a portfolio of endogenously generated shares of assets. Our model satisfies various prudence and risk aversion conditions, is consistent with Allais paradox rankings, and generates various insurance-related results. Within a portfolio framework with compounded reinvestments, our index fits the risks/rewards data from post-war US stock market returns and recent international markets, at least as well as does the standard deviation measures more typically used. It also generates returns that are consistent with the equity premium puzzle. 1