考慮厚尾分配之避險比率與風險值模型

Hedging and Value at Risk with Heavy Tailed Distribution

林玉森(Yu-Sen Lin)

指導教授 ： 朱香蕙

國立暨南國際大學/管理學院/財務金融學系/碩士(2011年)

https://doi.org/10.6837/NCNU.2011.00101

摘要

金融資產報酬為非常態分配，利用常態分配假設去配適非常態分配資料無法捕抓到偏態或峰態，考量非常態分配特性以求得精確避險方法是重要的課題。本文延伸Cao, Harris和Shen(2010)模型探討不同風險測量模型之避險績效。以黃金、英國金融時報100指數、台灣加權股價指數為現貨與其對應指數期貨為避險工具，分析極小化Student-t風險值、極小化Student-t條件風險值、極小化Cornish-Fisher風險值、極小化Cornish-Fisher條件風險值、最小變異數等研究方法在避險組合之標準差、偏態、峰態、風險值、條件風險值減少程度。實證結果顯示使用最小變異數法、極小化Cornish-Fisher風險值法與極小化Cornish-Fisher條件風險值法所求算之避險組合的標準差、風險值、條件風險值皆下降，但是風險值、條件風險值減少程度不如標準差大。此外，避險組合之分配呈現更左偏與高狹峰，此結果與Cao, Harris和Shen(2010)相同。本文提出極小化Student-t風險值、極小化Student-t條件風險值法也會使避險組合分配左偏與高狹峰，但在風險值與條件風險值減少程度上優於其他方法。最後，本文利用回溯測試檢視模型評估市場風險的能力，實證結果顯示只有極小化Student-t風險與極小化Student-t條件風險值法通過檢驗，代表極小化Student-t風險值與極小化Student-t條件風險值法不但在避險績效上優於其他方法並且能精準地預測風險值。

關鍵字

避險比率 ； 風險值 ； 最小變異數法 ； t分配風險值 ； 回溯測試

並列摘要

The non-normality of financial asset returns has been recognized as an important implication for hedging. The most basic minimum variance hedge ratio assumes that the returns are normally distributed. This assumption makes the hedge results inaccurate since the measure of risk that fails to capture all of the characteristics of portfolio returns while the returns distribution has fat-tailed. In this paper, we expand on the models of Cao, Harris and Shen(2010) and evaluate the effect of non-normality of financial asset returns on optimal hedge ratio. This article proposes a procedure for estimating minimum Value at Risk (VaR) and minimum Conditional Value at Risk (CVaR) hedge ratios based on the student-t distribution. Using spot and futures returns for the FTSE 100, Gold, Taiwan Weighted Stock Indices we examine this new approach, standard minimum-variance hedging model, minimum VaR and minimum CVaR models based on Cornish–Fisher expansion and compare their effect on the reduction of standard deviation, skewness, kurtosis, VaR and CVaR. The empirical results show that among various models the minimum student-t VaR and minimum student-t CVaR approach present more efficient results. Moreover, by backtesting, the empirical results show that new approach can accurately evaluate the market risk of hedging portfolios.

並列關鍵字

Hedge Ratio ； Value at Risk ； Minimum-Variance Method ； Student-t distribution VaR ； Backtesting

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