考慮極値與VaR限制之最適資產配置

Optimal Asset Allocation with Extreme Returns and a VaR Constraint

顔錫銘(Simon H. Yen) ； 李美杏(Mei-Hsing Lee)

《臺大管理論叢》 17卷2期 (2007/06) Pp. 41-68

https://doi.org/10.6226/NTURM2007.17.2.41

摘要

許多實證研究顯示資產報酬分配呈左偏和肥尾。本文探討當資產報酬分配呈左偏和肥尾時，對風險管理者資產配置之影響。Basak與Shapiro(2001)是首位將風險限制式(VaR)納入效用函數內，再極大化投資人之效用函數而求出最適資產配置。本文依據他們的方法，採用Gram-Charlier expansion描述資產報酬左偏和肥尾之特性，探討當資產報酬分配在非常態分配下，其資產配置的變化。對風險管理者而言，最重要的工作就是準確預測損失與發生損失的機率。瞭解資產報酬的型態將有助於準確的預測損失，我們無法降低損失，但可以降低發生損失的機率，本文建議可以降低α值（期末財富損失大於VaR之機率）來達成，而降低α值會使期末財富在好的狀態與壞的狀態的財富稍減。

關鍵字

極值 ； 左偏 ； 肥尾

並列摘要

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.

並列關鍵字

Gram-Charlier expansion ； value-at-risk-based risk management ； leptokurtic asset returns

參考文獻

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