報酬與風險抵換關係之分量迴歸分析

Abstract

當股票市場的波動增加時，要求報酬隨之增加似乎是合理的現象。然而，實證研究中之報酬與風險之抵換關係卻無法確定，實證上之衝突性結果，刺激我們進一步研究這個議題。本篇論文採用實現變幅(Realized Range)和實現變異(Realized Variance)，以及一般化自我迴歸條件異質變異數(GARCH)與條件變幅自我相關(CARR)波動模型等方法，捕捉標準普爾500(S&P 500)與那斯達克100(NASDAQ-100)指數期貨之條件變異，再藉由分量迴歸掌握整個報酬之條件分配，而非侷限於條件均數的行為，進一步解釋報酬與風險間之關係。 在跨期資本資產訂價模式(ICAPM)的實證分析上，提供強大證據證明標準普爾500之報酬與風險間存在顯著的正向關係，但此關係卻無法在那斯達克100中找到。分量迴歸之結果則顯示報酬與風險間的關係相當複雜，風險對於不同分量的報酬有不同的影響。我們發現美國股票市場之報酬與風險之關係，在報酬率分配的左尾為負向關係，右尾則為正向關係，且兩者效果相當，報酬與風險之關係在左右尾呈現對稱。這個結果可對過去研究報酬與風險關係之不顯著結果或是負向關係提出合理解釋，並對資產管理上的避險策略或是套利操作提供參考資訊。

Most asset pricing models assume the relation between return and risk is positive. However the empirical evidence on the sign of the intertemporal mean–variance relation is inconclusive. We examine United States stocks’ mean–variance trade-off relationship by introducing four estimators of the conditional variance including the realized range (RR), realized variance (RV), GARCH model, and CARR model. Previous studies using OLS regression to test the mean–variance trade-off can merely describe how the risk relates to the return on average. In this study, quantile regression is adopted to provide construction on relationships between risk and return in detail. Our study provides strong evidence of a positive relation between risk and return for the S&P 500 futures when the OLS regression is used. However, there is no such a significant relation between risk and return for the NASDAQ-100 futures. The empirical results of quantile regression show that the mean–variance relations are quite complex. The risk has symmetrically negative and positive effects on return across quantiles. This finding helps us to explain the existence of the mean–variance relation and the conflict between the sign of mean–variance trade-off relationship.