Optimal Investment and Asymmetric Risk for A Large Portfolio: A Large Deviations Approach

Motivated by the fact that hedge funds staffs more often than not face the problem of optimal asset allocation for large portfolios of investable stocks, In this study 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 risk, which is defined as the probability that the portfolio return underperforms an investable benchmark, is minimal. As a particular case, 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 portfolio invested in two risky assets. Furthermore, since our analysis is based on a parametric framework, this allows us to formulate a close-form relationship between the measures of correlation and the optimal portfolio. Finally, 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. JEL classification: C4; D8; G11