偏斜指數與總體經濟變數對S&P 500指數之影響

當1987年10月19日美國發生被稱為〝黑色星期一〞的股災後，隱含波動率與履約價的關係從微笑曲線變成偏斜曲線，美國芝加哥選擇權交易所(CBOE)在24年之後，終於在2011年推出偏斜指數，以期幫助投資人捕捉市場突然發生的黑天鵝事件。由於該指數迄今才推出六年半，因此有關CBOE 偏斜指數與股票市場相關之文獻甚少。偏斜指數(SKEW index)主要是用來測量波動率曲線(即恐慌指數(VIX))的偏斜程度，而曲線的陡峭程度與SKEW值的大小成正比，值越高代表尾端風險越大。本研究因而探討偏斜指數的變動率對S&P500指數報酬率之影響。首先，本研究先說明偏斜指數與恐慌指數之不同點。其中偏斜指數是透過計算S&P500指數選擇權價格的偏離程度，來衡量市場對重大意外事件的擔憂程度，以期捕捉市場的尾部風險。在數學上，偏斜指數屬於三階動差，主要係以偏離係數來衡量分配的不對稱程度。而恐慌指數則是一種投資人對市場未來大幅波動的預警指標，其主要係衡量S&P500指數的近期選擇權價格之波動性風險的高低，在數學上屬於二階動差。因此，偏斜指數係衡量災難事件的發生機率與市場的恐慌程度，且其針對金融市場上的投資人或是主管機關而言，確實為一評估未來風險的重要參考指標。有鑑於此，本研究特別探討偏斜指數的變動率與總體經濟變數之變動率對於S&P 500指數報酬率之影響。經單根檢定及迴歸分析後，本研究歸納實證結果於下： 1. 本研究發現偏斜指數變動率、原油價格變動率、美國信用利差變動率與美國期限利差變動率等四個變數，皆會影響S&P 500指數報酬率，表示偏斜指數能用來揭露許多風險資訊，因而可作為評估未來風險的一個很好的參考指標，且偏斜指數亦可預測未來股市之走勢。 2. 本研究亦發現偏斜指數變動率、原油價格變動率及美國期限利差變動率對S&P 500指數報酬率呈現顯著正向影響，但美國信用利差變動率對S&P 500指數報酬率則呈現顯著負向影響。此負向影響的可能解釋如下：由於信用利差代表信用評等Aaa級與Baa級借款成本的差異，而在近十年來美國的景氣狀況良好，因而使得信用利差縮小，從而使得信用利差變動率與S&P500指數報酬率呈現顯著負相關。

關鍵字

股價指數；信用利差；原油價格；偏斜指數；黃金價格；期限利差；最小平方法

並列摘要

After the stock market had been crashed in the United States on October 19, 1987 (which was called “Black Monday”), the relationship between implied volatility and the call strike price was changed from a smile curve to a skewed curve. Twenty four years later, the Chicago Board of Exchange (CBOE) launched a SKEW Index in 2011 to provide investors with the opportunity to capture the black swan incident in the market. The SKEW index is an indicator of potential risk in financial markets. Similar to the VIX index, the SKEW index can be a representative of the overall attitude of investors. However, SKEW index measures the recognized tail risk of the market via the pricing of out-of-the money options. For example, the tail of the distribution is fatter on the left would cause negative skewness. Mathematically, skewness belongs to the third central moment, which usually measures the lopsidedness of the distribution. In most cases, a rise in SKEW index shows that safety is in demand among institutional investors. However, VIX is an important indicator of market expectation of near-term fluctuation transferred by S&P 500 stock index option price. The VIX belongs to a second central moment, which usually measures the option price at the money. This study investigates the influence of the SKEW index and three macroeconomic factors on the S&P 500 index. The conclusions are listed as follows: 1. We found that the volatility of the SKEW index, oil price, the US credit spread and the US term spread all significantly affected the rate of return on the S&P 500 index, indicating that the SKEW index was revealed much risk information when assessing potential risks. 2. Empirical findings indicated that the fluctuation of the SKEW index, oil price, and the US term spread have a significantly positive effect on the rate of return on the S&P 500 index, while the US credit spread fluctuation has a significantly negative influence on the rate of return on S&P 500 index. The possible explanation was that, as US credit spread represents the difference between credit rating Aaa level and Baa level, as the boom condition for the past decade improved, the credit spread shrank. Therefore, the credit spread had a significantly negative impact on the rate of return on S&P 500 index.

並列關鍵字

Credit spread ； gold price ； least square regression ； oil price ； SKEW index ； S&P 500 index ； term interest spread

參考文獻

Zhen, F., & Zhang, J. E. (2014). A Theory of the CBOE SKEW: Working paper, University of Otago. URL: http://www.aut.ac.nz/__data/assets/pdf_file/0008/573155/F-Zhen-CBOE_SKEW.pdf

Albuquerque, R. (2012). "Skewness in Stock Returns: Reconciling the Evidence on Firm Versus Aggregate Returns". The Review of Financial Studies, 25(5), 1630-1673. doi: 10.1093/rfs/hhr144

Amaya, D., Christoffersen, P., Jacobs, K., & Vasquez, A. (2015). "Does Realized Skewness Predict the Cross-Section of Equity Returns?". Journal of Financial Economics, 118(1), 135-167. doi: https://doi.org/10.1016/j.jfineco.2015.02.009

Bakshi, G., Kapadia, N., & Madan, D. (2003). "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options". The Review of Financial Studies, 16(1), 101-143. doi: 10.1093/rfs/16.1.0101

Bali, T. G., & Murray, S. (2013). "Does Risk-Neutral Skewness Predict the Cross-Section of Equity Option Portfolio Returns?". Journal of Financial and Quantitative Analysis, 48(4), 1145-1171. doi: 10.1017/S0022109013000410

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偏斜指數與總體經濟變數對S&P 500指數之影響

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