Optimal Investment and Asymmetric Risk for a Large Portfolio: A Large Deviations Approach
Posted: 4 Sep 2008
Date Written: September 3, 2008
In reality, 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 method based on the large deviations theory to select an optimal investment 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.
Keywords: Optimal portfolio, The Edgeworth expansion, Asymmetric Risk, Large deviations, Asymmetric Gamma distribution, Nonlinear correlations, Value at Risk
JEL Classification: C4, D8, G11
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