臺灣博碩士論文加值系統

被市場稱作黑天鵝指數的CBOE SKEW指數在2015年10月12日來到了歷史新高148.92，這比2006年房地產泡沫破滅前及1998年長期資本管理公司倒閉時觸及的水準還要高，亦同時加劇了市場恐慌的心理。實際觀察股市後續發展，並未發生崩跌的現象，這引起我們的好奇心究竟SKEW指數該如何解讀。
CBOE於2011年推出SKEW指數，本文針對SKEW指數探究其資訊內含並建構交易策略。首先透過一系列的時間序列分析對SKEW指數有基本的認識。透過時間序列分析加以驗證SKEW指數與VIX指數是兩個捕捉不同資訊內涵的指數。VIX指數捕捉的是報酬的標準差，而標準差僅描述平均數附近的報酬分布。但S&P500指數報酬並非常態分配，SKEW指數能額外捕捉VIX指數捕捉不到的尾端風險。SKEW指數還能用來預測未來大盤走勢，在不同資料頻率比較下以預測大盤週報酬的效果最好。
本文進一步採用SKEW指數建構交易策略。以採用固定轉換機率馬可夫轉換模型下VIX指數所偵測的狀態轉換為比較基準，比較增加SKEW指數作為訊息因子後所採用的時序變動型馬可夫轉換模型是否能提升模型偵測狀態轉換的能力。樣本期間為2002年4月15日至2013年3月29日，透過模型偵測到狀態轉換的時點，於隔日以開盤價在市場上建立相應部位。當再次偵測到狀態轉換時，隔日以開盤價做反向部位，如此反覆操作。實證結果發現以VIX指數作為應變數並搭配SKEW指數作為訊息因子下的時序變動型馬可夫轉換模型偵測狀態轉換的能力最佳，其中多頭部位表現又都較空頭部位表現好。以SKEW指數作為訊息因子的TVTP模型在不考慮稅、手續費及股利下年化報酬有13.61%，考慮稅、手續費及股利後年化報酬仍有12.47%。

This paper divided into two parts to investigate on the information content of CBOE SKEW Index. For the first part, we do time series analysis to observe the relationship between SKEW Index and other variables. First, we found that SKEW index is totally different from VIX index. VIX index is a proxy for the standard deviation of the returns. The standard deviation describes the average spread of the distribution of returns around its mean. This is not a sufficient measure of risk because the distribution of S&P 500 log returns is not normal. SKEW Index captures the tail risk of the distribution. Next, SKEW Index is good at predict future S&P500 ETF returns especially weekly speaking. Also, we found that the correlation between SKEW index & S&P500 index is too unstable to interpret. We argue that it’s not easy to interpret SKEW Index directly but we can combine SKEW Index with VIX Index.
Regarding the above reason, in second part, we combined SKEW Index with VIX Index to construct trading strategy under Markov Switching Model. By comparing with FTP Model, which included VIX index only, we found that TVTP model, which encompassed VIX Index and SKEW Index together, significantly outperform others. When the model detected regime switching, we buy/short SPY ETF in the market separately. We did the simulation test from 2002.4.15 to 2013.3.29. Without considering tax, fee and dividend, we earned yearly average rate of return 13.61%. After considering tax, fee and dividend, we earned yearly average rate of return 9.51%.

第一章 緒論 1
第一節 CBOE SKEW Index 1
第二節 研究背景 7
第三節 研究架構 8

第二章 文獻回顧 9
第一節 偏態係數 9
第二節 時間序列分析 9
第三節 馬可夫轉換模型 11

第三章 研究方法 13
第一節 時間序列分析 13
(一) ADF單根檢定 13
(二) Granger 因果關係檢定 14
第二節 馬可夫轉換模型 14
(一) 固定機率馬可夫轉換模型 14
(二) 時序變動型馬可夫轉換模型 15
(三) 參數估計 16
(四) 概似比檢定 17

第四章 實證結果與分析 18
第一節 樣本選取 18
第二節 時間序列分析 19
(一) 偏態係數與波動度間的關係 20
(二) 恐慌指標 21
(三) 預測SPY ETF未來報酬 23
(四) 跨期因果關係 24
第三節 採馬可夫轉換模型建構交易策略 25
(一) 馬可夫轉換模型建構 25
(二) 交易策略之形成 30

第五章 結論與建議 33

第六章 參考文獻 36

附錄－實際投資模擬結果 39

i. 國外文獻
Atilgan, Y., Bali, T. G., & Demirtas, K. O. (2010). Implied volatility spreads, skewness and expected market returns. Georgetown McDonough School of Business Research Paper, (1511970).
Bakshi, G., Kapadia, N., & Madan, D. (2003). Stock return characteristics, skew laws, and the differential pricing of individual equity options. Review of Financial Studies, 16(1), 101-143.
Baba, N., & Sakurai, Y. (2011). Predicting regime switches in the VIX index with macroeconomic variables. Applied Economics Letters, 18(15), 1415-1419.
Carr, P., & Wu, L. (2009). Variance risk premiums. Review of Financial Studies, 22(3), 1311-1341.
Chang, B. Y., Christoffersen, P., & Jacobs, K. (2013). Market skewness risk and the cross section of stock returns. Journal of Financial Economics, 107(1), 46-68.
CBOE. (2010). The CBOE Skew Index. CBOE White Paper.
Chung, S. L., Tsai, W. C., Wang, Y. H., & Weng, P. S. (2011). The information content of the S&P 500 index and VIX options on the dynamics of the S&P 500 index. Journal of Futures Markets, 31(12), 1170-1201.
Conrad, J., Dittmar, R. F., & Ghysels, E. (2013). Ex ante skewness and expected stock returns. The Journal of Finance, 68(1), 85-124.
Dennis, P., & Mayhew, S. (2002). Risk-neutral skewness: Evidence from stock options. Journal of Financial and Quantitative Analysis, 37(03), 471-493.
Ding, Z. (2012). An implementation of markov regime switching model with time varying transition probabilities in matlab. Available at SSRN 2083332.
Filardo, A. J. (1994). Business-cycle phases and their transitional dynamics. Journal of Business & Economic Statistics, 12(3), 299-308.
Giot, P. (2003). The Asian financial crisis: the start of a regime switch in volatility. Available at SSRN 410844.
Goldfeld, S. M., & Quandt, R. E. (1973). A Markov model for switching regressions. Journal of econometrics, 1(1), 3-15.
Guo, W., & Wohar, M. E. (2006). Identifying regime changes in market volatility. Journal of Financial Research, 29(1), 79-93.
Hamilton, J. D. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica: Journal of the Econometric Society, 357-384.
Han, B. (2008). Investor sentiment and option prices. Review of Financial Studies, 21(1), 387-414.
Harvey, C. R., & Siddique, A. (2000). Conditional skewness in asset pricing tests. The Journal of Finance, 55(3), 1263-1295.
Kozhan, R., Neuberger, A., & Schneider, P. (2013). The skew risk premium in the equity index market. Review of Financial Studies, 26(9), 2174-2203.
Liu, Z. F. (2013). State prices, market volatility and skewness.
Marabel Romo, J. (2011). Volatility regimes for the VIX index. Revista de Economía Aplicada, XX,(2012), 114-134.
Perlin, M. (2015). MS_Regress-the MATLAB package for Markov regime switching models. Available at SSRN 1714016.
Quandt, R. E. (1958). The estimation of the parameters of a linear regression system obeying two separate regimes. Journal of the american statistical association, 53(284), 873-880.
Ramzi, K. (2012). Estimating a MS-TVTP Model with Matlab Software. Available at SSRN 2097260.
Rehman, Z., & Vilkov, G. (2012). Risk-neutral skewness: Return predictability and its sources. Available at SSRN 1301648.
Sun, Y., & Wu, X. (2009). A Nonparametric Study of Dependence Between S&P 500 Index and Market Volatility Index (VIX).
Wang, P. (2008). Financial econometrics.
Whaley, R. E. (2008). Understanding vix. Available at SSRN 1296743.
Xing, Y., Zhang, X., & Zhao, R. (2010). What does the individual option volatility smirk tell us about future equity returns?.

ii. 國內文獻
黃裕烈(1996) 「Markov Switching Model：台灣實質GNP的應用」，國立台灣大學經濟研究所碩士論文。
徐士勖(2000) 「台灣景氣波動之計量分析」，國立台灣大學經濟研究所碩士論文。
董慧萍(2000) 「股市價量互動非線性模型之研究－應用TVTP Markov-Switching模型」，國立政治大學國際經營與貿易研究所碩士論文。
戴天君(2013) 「以VIX指數偵測危機狀態之效果探討─TVTP方法之應用」，國立政治大學金融研究所碩士論文。
陳威光(2015) 「期貨與選擇權原理」，新陸文化。