使用變形函數之同調風險衡量討論暨實證分析

Abstract

風險衡量〈risk measure〉的意義乃將風險〈Loss〉可能之機率分配量化成一數值做為指標，試圖透過這個簡單的數據以得知可能蒙受損失的大小，其主要目的為量化及比較風險。為了讓衡量風險的方式更客觀一致，學者發展出尾部條件期望值和以變形函數〈distortion function〉定義的數種同調風險衡量。 本研究首先介紹數種同調風險衡量之變形函數，討論各變形函數之參數與風險測量值大小之關係，並針對不同變形函數做比較與分析，發現使用危險比例變形函數 來衡量右偏資料的風險所得到的風險測量值會比使用雙重次方變形函數 衡量所得到的風險測量指標大。 本研究同時以台灣股票市場八大類股指數報酬率作為實證分析的對象，分別針對長、短期報酬率資料以歷史模擬法計算出各種風險衡量指標，並且說明這幾種風險衡量方式所具有的特性。實證發現： 1. 使用長期資料分析時，若要使用涉險值，應該同時參考針對損失之刪減資料分配的涉險值，方能做出較正確的風險斷定。若是想要風險衡量比較能反應分配的右偏情形，我們可以使用危險比例變形函數gph來衡量， 2. 對於需要爭取時間效率的短期資料，選用不同風險衡量的方式得到之結果並沒有太大不同，因此我們建議使用簡單的涉險值 或條件尾端期望值VaR作為風險衡量即可，如此可以爭取時效，但為了同調性質，條件尾端期望值CTE仍是較好的風險衡量。

There are many reasons to develop risk measurement system. Two general uses of such a system are to quantify and to compare risk. Keeping this in mind, we must ensure any risk measurement system produces coherent result. The coherency of a risk measure has been discussed in Artzner et al. (1997、1999). He also proposed Conditional Tail Expectation as a coherent risk measure. Furthermore, coherent risk measure derived from distortion functions has later been discussed in Wang〈1996〉. In the first section of this study, we consider some distortion functions and discuss relationship between each risk measure and the parameter. We have also compared different distortion functions. We present that we can obtain larger risk measure of the loss data which is right skewed by using Proportional Hazards Distortion rather than using Dual Power Distortion. In this paper we also conduct empirical study on the returns of eight industry indexes both in the long run and in the short run. We state the characteristics of each risk measure by using historical simulation approach. And we obtain that : 1. As to the long-term research, when VaR is adopted as a risk measure, the VaR which is calculated from the loss data censored at zero is suggested to be referable. If we want to reflect the skew of the loss distribution, Proportional Hazards distortion would be a good choice. 2. In the short-run analysis, there’s no significant difference between different risk measures. The coherent risk measure CTE is easily understood. In order to save our time, it may be the best choice.