利用自助法計算在隨機波動模型下新興市場的風險值

Abstract

近年來，風險管理成為一門重要的議題，其中風險值(VaR)是用來衡量並且管理市場風險的一個指標。而新興市場的投資標的物更是引起各界很大的關注，本文將選取九個新興市場國家的主要股價指數，利用自助法計算他們的風險值，同時加入美國S&P 500指數以及MSCI EM (Emerging Markets)指數來做一個比較。許多研究指出，新興市場的報酬具有高峰及厚尾的特性，且其波動性相對較大又會隨時間變動；由於隨機波動模型擁有厚尾的性質，而且此模型也可以描述隨時間變動又較高的波動特性，所以我們用隨機波動模型來建構這些股價指數的分配。模擬的結果發現，利用自助法求算隨機波動模型下的風險值與實際的風險值相差不遠；以相同的方法步驟求算各個國家股價指數的風險值時，利用回顧測試來檢驗模型的正確性，發現隨著不同國家股價指數所表現出來不同程度的厚尾分配，我們必須將殘差(epsilon)變換不同的分配〈例如N(0,1)、t(6)或是t(4)>，才能適當的描述不同國家之間股價指數的分配。其中美國S&P 500指數如同預期，有較小的估計風險值；土耳其、印度、墨西哥、俄羅斯、印尼的股價指數計算出較大的估計風險值；泰國、韓國、 台灣、以及馬來西亞的股價指數則計算出較小的估計風險值；而MSCI EM Index則不如預期的，反而計算出較大的估計風險值，顯示出在新興市場中，不同市場風險分散的效果並不大。

Nowadays, risk management is an important issue. A standard benchmark used to measure and to manage market risks is the Value-at-Risk (VaR). Emerging markets have drawn considerable interest in recent years. Since it is very popular for financial institutions to have long positions in emerging stock indices, this article applies bootstrap method to calculate the VaR estimate of nine emerging market stock indices. And we also conduct the US S&P 500 composite index and MSCI EM (Emerging Markets) Index for comparison. Previous studies showed that the returns in emerging markets are leptokurtic and the volatility is higher and time-varying. Since stochastic volatility models have properties of fat tails, high and time-varying volatility, we use this model with different distributions of epsilon to fit these indices. A back-test is then employed to see which model is more proper for each index. Simulation results show that the VaR estimate is not far from the true VaR. A back-test tells that stochastic volatility models with epsilon ~ N(0,1) or ~ t(6) or ~ t(4) can fit different indices undertaken in this article. The VaR estimates are relatively high in Turkey, India, Mexico, Russia and Indonesia; while Thailand, Korea, Taiwan and Malaysia have relatively low VaR estimates. As we expect, S&P 500 index has relatively low VaR estimate. But the result that MSCI EM Index has relatively high VaR estimate indicates that the diversification effects are not significant between emerging markets.