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.

Putting the Aumann–Serrano Riskiness Index to work

“…The abovementioned theoretical studies introduce the Riskiness Index and its applications. The Riskiness Index has also been empirically demonstrated as a risk measurement: measuring the performances of mutual funds and comparing them with the Sharpe ratio (Homm and Pigorsch, 2012) or measuring the financial risks and performances of assets in the USA, China and Japan (Gang et al , 2019; Hodoshima and Yamawake, 2020, 2022). Based on these past theoretical developments, we empirically examine the convergence of the Riskiness Index to its value with respect to the order of the statistical moments.…”