Aumann–Serrano index of risk in portfolio optimization

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.