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Aumann–Serrano index of risk in portfolio optimization

Tiantian Li (), Young Shin Kim (), Qi Fan () and Fumin Zhu ()
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Tiantian Li: Barclays
Young Shin Kim: Stony Brook University
Qi Fan: Barclays
Fumin Zhu: Shenzhen University

Mathematical Methods of Operations Research, 2021, vol. 94, issue 2, No 2, 197-217

Abstract: Abstract The paper is devoted to study the portfolio optimization problem for an investor who aims to minimize the exposure to equity markets measured by the Aumann–Serrano index of riskiness. The ARMA–GARCH model with normal variance–mean mixture innovations is employed to capture the stylized facts of stock returns. Using a two-step scheme, we convert the high-dimensional optimization problem into a two-dimensional one. We further prove that the dimension reduction technique preserves the convexity of the problem as long as the risk measure is convex and monotonic. In the empirical study, we observe that the optimal portfolio outperforms benchmarks based on a 10-year backtesting window covering the financial crisis.

Keywords: Aumann–Serrano index of riskiness; Portfolio optimization; Normal variance–mean mixture; Convex risk measure; Average value-at-risk; 46N10; 91B28; 91B84 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00186-021-00753-x

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