股票與債券報酬相關性之研究--以DCCX模型為研究方法

Abstract

本篇論文根據Engle(2002)所提出的動態條件相關係數模型(Dynamic Conditional Correlation model；DCC)為基準，擴充為加入外生變數影響的DCCX模型來探討美國S&P500股票和十年期公債間報酬的動態時變相關性，並加入了市場不確定性的代理變數:芝加哥選擇權交易所(CBOE)的波動性指數(VIX)與S&P500的股票週轉率，本篇論文的樣本期間為，1990/1/2-2007/9/7，在本文的實證分析上證實了波動性指數與股票週轉率的確會對股票和債券的報酬相關性造成顯著的差異，由實證結果的支持，發現當波動性指數或股票週轉率的變動幅度 增強時，往往股票和債券的報酬相關性會呈負值，此外分別探討在1990-1997與1998-2007中，也發現同樣的結果，當波動性或是股票週轉率增加時，往往可以觀察到股票和債券的報酬相關係數呈現負向的情況，因此在避險以及風險分散上，本篇論文的研究結果可為投資人提供避險上以及資產配置的一個參考依據。

We develop a new, modified Dynamic Conditional Correlation (DCC) model, called DCCX,which allows exogenous variables in the evolution of the conditional correlations in the standard DCC model of Engle (2002). Structural modeling of the dynamic conditionalcorrelations enriches the standard DCC, which is basically a reduced-form model. We apply this new model to explain temporal variations of the correlation between the stock and bond returns in U.S. Throughout the nineties until 1997/1998, we find a high positive correlation in the neighborhood of 0.3 to 0.6, exhibiting a stable and close relationship between returns of the S&P500 and 10-year-treasury-bonds. However, a sharp decline in the equity-bond correlation occurred in 1997/1998, followed by a sudden reversion, then plunged back to the negative range in 2000. Such a great decoupling of the equity-bond correlation persisted until 2007. The correlation in the twenties fluctuates widely but mostly remains in the negative range of -0.2 to -0.5, a stark contrast to the high positive correlation in the nineties. Using the DCCX model, we find such a dramatic variation in the equity-bond relationship can be partly explained by the stock market uncertainty (measured by CBOE’s VIX) and the liquidity of the market (measured by the turnover of S&P500). Specifically, the surge of the VIX in the late nineties and the speedup of the stock turnovers both contributed to the drop in the stock-bond correlations in the last decade. It is suggested that stock market uncertainty has important cross-market pricing influences and that stock-bond diversification benefits increase with stock market uncertainty. On the other hand, sudden shifts of asset correlations may also call for necessary rebalancing of great magnitude on hedging positions and the grave danger of inactions. The recent sub-prime crisis may be viewed as a case in point.