The Aumann–Serrano Performance Index for Multi-Period Gambles in Stock Data

Abstract

We present an empirical study of the Aumann-Serrano performance index for multi-period gambles when the underlying stochastic process is assumed to be a normal mixture process with time-varying volatility. We compare the Aumann-Serrano performance index for multi-period gambles with that for one-period gambles as well as the Sharpe ratio. Our empirical study is obtained using a selection of U.S. stock data and shows evaluation of a selection of stocks becomes more distinct in multi-period gambles than in one-period gambles in the sense that a favorable evaluation score becomes even better in multi-period gambles than in one-period gambles while an unfavorable evaluation score becomes even worse in multi-period gambles than in one-period gambles.