Optimal Asset Allocation with Extreme Returns and a VaR Constraint

Yen, H. S., and Hsing, M. . 2007. Optimal Asset Allocation with Extreme Returns and a VaR Constraint. NTU Management Review, 17 (2): 041-068

Simon H. Yen, Professor, Department of Finance, National Chengchi University
Mei- Hsing Lee, Lecturer, Department of Statistics, National Taipei University; Ph. D. Candidate, Department of Finance, National Chengchi University

Abstract

This study investigates how deviations from normality affect asset choices made by risk managers. This study applies the Gram-Charlier expansion for negatively skewed and excess kurtosis. Following Basak and Shapiro (2001), this study examines how negatively skewed and excess kurtosis affects asset allocations when investors manage market-risk exposure using Value-at-Risk-based risk management (VaR-RM). It is important for risk managers to precisely forecast the loss. The analytical results imply that the impact of leptokurtic asset returns is based on the shape of asset returns, and a correct measurement of leptokurtic asset returns is helpful to risk managers seeking to precisely forecast the loss. A risk manager cannot reduce the loss in bad states, but can reduce the value of α, the probability that a loss exceeds VaR, and the agent will suffer from reduced terminal wealth in both the good and bad states.  


Keywords

Gram-Charlier expansion Value-at-risk-based risk management Leptokurtic asset returns


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