We propose a new theoretical framework based on the large deviations theory to select an optimal investment strategy for a large portfolio such that the probability of the portfolio return underperforming an investable benchmark (we hereafter call this probability as the risk) is minimal. This problem is of practical importance because hedge funds' optimal investment strategies often involve a large number of risky assets. In particular, we examine the effect of two types of asymmetric dependence: (1) asymmetry in a portfolio return distribution, and (2) asymmetric dependence between asset returns on the optimal holdings in two risky assets. We calibrate our method with equity data, namely, S&P 500 and Bangkok SET. The empirical evidence confirms that there is a significant impact of asymmetric dependence on optimal portfolio and risk.

Asymmetric gamma distribution, Large deviations, Nonlinear correlations, Optimal portfolio, Overfall probability, Shortfall probability, The Edgeworth approximation
Department of Economics

Chu, B, Knight, J. (John), & Satchell, S. (Stephen). (2010). Optimal investment and asymmetric risk: A large deviations approach. Optimization, 59(1), 3–27. doi:10.1080/02331930903500241