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題名 應用Copula之配對交易策略
Pairs Trading with Copulas作者 余冠緯
Yu, Kuan-Wei貢獻者 張興華
余冠緯
Yu, Kuan-Wei關鍵詞 統計套利
配對交易
關聯結構
共整合關係
statistical arbitrage
pairs trading
copula
cointegration
ARMA
GARCH日期 2020 上傳時間 3-Aug-2020 17:39:35 (UTC+8) 摘要 配對交易在國內外證券市場是一種被廣泛運用的統計套利投資策略，它通過同時建構成對資產的多空部位來賺取資產價差收斂的損益。配對交易策略的顯著優點在於通過對沖機制來有效規避了該資產的系統性風險，即使在市場整體面臨下行風險的時候配對交易仍然能夠獲得比較穩定的收益。過去關於配對交易的文獻大致上專注在兩個方面，一是研究如何挑選出性質良好的配對以及相關交易模型，另一則是研究如何制定最優的交易策略使得交易績效得到最大化。本研究著重在後者，也就是引入一種基於關聯結構 (Copula) 函數和條件機率的股票配對交易策略來比較過去大眾所熟知的共整合策略以及最小距離策略的績效實證。最後經由本研究之實證顯示，關聯結構法不論在絕對績效或是風險調整後的績效上均勝過傳統的交易策略，同時也間接印證過去文獻提及最小距離策略在 2002 年之後可能獲得負報酬之事。
Pairs trading is a kind of statistical arbitrage strategy which is widely used in oversea security markets. By creating both long and short position for two different assets, we can earn arbitrage profit through the converging of two assets’ prices. Obviously, the most important advantage of pairs trading is that it could earn profit steadily during either bear market or bull market. The researches in the past mainly focused on two aspects. One was that looking for the better way to find out what kind of pair of assets had a better performance and their relative trading strategy, another was that making a better strategy to maximize our profit. This paper mainly focuses on the latter. We introduce a stock pairs trading strategy based on Copula function and conditional probability and compare it to the strategy invented by previous papers: cointegration method and distance method. Generally speaking, the Copula method definitely has greater excess return and risk-adjusted return. We also incidentally confirm that some of the paper mentioned that distance method had a poor performance after 2002.參考文獻 [1] 林展源 (2019)。反向型 ETF 與波動型 ETF 之避險績效 ──應用 Copula-GJR-GARCH 模型。國立政治大學國際經營與貿易學系研究所碩士論文，台北市。[2] 鄭瑩 (2013)。D-Vine Copulas 之模型化相依性：台灣電子產業類股實證分析。國立屏東商業技術學院財務金融系研究所碩士論文，屏東縣。[3] Aas, K., Czado, C., Frigessi, A., Bakken, H., 2009. Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics 44 (2), 182–198.[4] Andrade, S., Di Pietro, V., Seasholes, M., 2005. Understanding the profitability of pairs trading. Unpublished working paper, UC Berkeley, Northwestern University.[5] Baillie, R. T., Myers, R. J., 1991. Bivariate GARCH Estimation of the Optimal Commodity Futures Hedge. Journal of Applied Econometrics, 6 (2), 109-124.[6] Bedford, T., Cooke, R. M., 2002. Vines: A new graphical model for dependent random variables. Annals of Statistics, 1031–1068.[7] Bollerslev, T., 1987. A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return. The Review of Economics and Statistics 69 (3), 542-547.[8] Box, G. E. P., Jenkins, G. M., 1970. Time Series Analysis: Forecasting and Control. San Francisco: Holden-Day.[9] Broussard, J. P., Vaihekoski, M., 2012. Profitability of pairs trading strategy in an illiquid market with multiple share classes. Journal of International Financial Markets, Institutions and Money 22 (5), 1188–1201.[10] Chen, H., Chen, S. J., Li, F., 2012. Empirical investigation of an equity pairs trading strategy. Working paper, University of British Columbia, University of Michigan.[11] Clayton, D. G., 1978. A model for association in bivariate life tables and its applications in epidemiological studies of familial tendency in chronic disease incident. Biometrika 65, 141-151.[12] Clegg, M., Krauss, C., 2016. Pairs trading with partial cointegration. FAU Discussion Papers in Economics, University of Erlangen-Nurnberg.[13] Dickey, D. A., Fuller, W. A., 1979. Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association 74 (366), 427–431.[14] Ding, P., 2016. On the conditional distribution of the multivariate t distribution. The American Statistician (just-accepted), 00–00.[15] Do, B., Faff, R., 2010. Does simple pairs trading still work? Financial Analysts Journal 66 (4), 83–95.[16] Do, B., Faff, R., 2012. Are Pairs Trading Profits Robust to Trading Costs? Financial Analysts Journal 35 (2), 261–287.[17] Dragulescu, A. A., 2014. xlsx: Read, write, format Excel 2007 and Excel 97/2000/XP/2003 files. R package version 0.5.7.[18] Elliott, R. J., Hoek, V. D., John, Malcolm, W. P., 2005. Pairs trading. Quantitative Finance 5 (3), 271–276.[19] Engle, R. F., 1982. Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica: Journal of the Econometric Society 50 (4), 987-1007.[20] Engle, R. F., Granger, C. W., 1987. Co-integration and error correction: Representation, estimation, and testing. Econometrica: Journal of the Econometric Society 55 (2), 251–276.[21] Frank, M. J., 1979. On the Simultaneous Associativity of F(x, y) and x + y − F(x, y). Aequationes Mathematicae 19, 194–226.[22] Galenko, A., Popova, E., Popova, I., 2012. Trading in the presence of cointegration. Journal of Alternative Investments 15 (1), 85–97.[23] Gatev, E., Goetzmann, W. N., Rouwenhorst, K. G., 2006. Pairs trading: Performance of a relative-value arbitrage rule. Review of Financial Studies 19 (3), 797–827.[24] Gonzalez-Fernandez, Y., Soto, M., 2015. vines: Multivariate dependence modeling with vines. R package version 1.1.3.[25] Gumbel, E. J., 1960. Bivariate Exponential Distributions. Journal of the American Statistical Association 55, 698–707.[26] Hansen, B. E., 1994. Autoregressive Conditional Density Estimation. International Economic Review 35 (3), 705-730.[27] Huck, N., 2010. Pairs trading and outranking: The multi-step-ahead forecasting case. European Journal of Operational Research 207 (3), 1702–1716.[28] Huck, N., 2015. Pairs trading: does volatility timing matter? Applied Economics, 1–18.[29] Huck, N., Afawubo, K., 2015. Pairs trading and selection methods: is cointegration superior? Applied Economics 47 (6), 599–613.[30] Jacobs, H., Weber, M., 2015. On the determinants of pairs trading profitability. Journal of Financial Markets 23, 75–97.[31] Joe, H., 1997. Multivariate models and dependence concepts. Chapman & Hall, London.[32] Joe, H., Xu, J. J., 1996. The Estimation Method of Inference Functions for Margins for Multivariate Models. Technical Report 166, Department of Statistics, University of British Columbia.[33] Kotz, S., Nadarajah, S., 2004. Multivariate t-distributions and their applications. Cambridge University Press.[34] Krauss, C., 2016. Statistical arbitrage pairs trading strategies: Review and outlook. Journal of Economic Surveys, forthcoming.[35] Liew, R. Q., Wu, Y., 2013. Pairs trading: A copula approach. Journal of Derivatives & Hedge Funds 19 (1), 12–30.[36] Lin, Y., McCrae, M., Gulati, C., 2006. Loss protection in pairs trading through minimum profit bounds: A cointegration approach. Advances in Decision Sciences 2006.[37] Nadarajah, S., Kotz, S., 2005. Mathematical properties of the multivariate t distribution. Acta Applicandae Mathematica 89 (1-3), 53–84.[38] Nelsen, R. B., 1999. An introduction to copulas. Springer-Verlag.[39] Nelsen, R. B., 2007. An introduction to copulas. Springer Science & Business Media.[40] Perlin, M. S., 2009. Evaluation of pairs-trading strategy at the Brazilian financial market. Journal of Derivatives & Hedge Funds 15 (2), 122–136.[41] Peterson, B. G., Carl, P., 2014. PerformanceAnalytics: Econometric tools for performance and risk analysis. R package version 1.4.3541.[42] Rad, H., Low, Rand Kwong Yew, Faff, R. W., 2016. The profitability of pairs trading strategies: Distance, cointegration and copula methods. Quantitative Finance, 1–18.[43] Rmetrics Core Team, Wuertz, D., Setz, T., 2014. fCopulae: Rmetrics - bivariate dependence structures with copulae. R package version 3011.81.[44] Rmetrics Core Team, Wuertz, D., Setz, T., Chalabi, Y., 2015. timeSeries: Rmetrics - financial time series objects. R package version 3012.99.[45] Ryan, J. A., 2015. quantmod: Quantitative financial modelling framework. R package version 0.4-5.[46] Ryan, J. A., Ulrich, J. M., 2014. xts: eXtensible time series. R package version 0.9-7.[47] Sharpe, W. F., 1964. Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk. Journal of Finance. 19 (3), 425-442.[48] Sklar, A., 1959. Fonctions de répartition à n dimensions et leurs marges. Publications de I’ Institut deStatistique de l’University de Paris (8), 229-231.[49] Trapletti, A., Hornik, K., 2016. tseries: Time series analysis and computational finance. R package version 0.10-35.[50] Vidyamurthy, G., 2004. Pairs trading: Quantitative methods and analysis. J. Wiley, Hoboken, N.J.[51] Wickham, H., Francois, R., 2016. dplyr: A grammar of data manipulation. R package version 0.5.0.[52] Wuertz, D., 2013. fUnitRoots: Trends and unit roots. R package version 3010.78.[53] Wu, Y., 2013. Pairs trading: A copula approach. Journal of Derivatives & Hedge Funds 19 (1), 12 – 30.[54] Xie, W., Liew, Q. R., Wu, Y., Zou, X., 2014. Pairs trading with copulas. Working paper, Nanyang Technological University.[55] Xie, W., Wu, Y., 2013. Copula-based pairs trading strategy. Asian Finance Association (AsFA) 2013 Conference.[56] Zeileis, A., Grothendieck, G., Ryan, J. A., 2015. zoo: S3 infrastructure for regular and irregular time series (z’s ordered observations). R package version 1.7-12. 描述 碩士
國立政治大學
金融學系
107352034資料來源 http://thesis.lib.nccu.edu.tw/record/#G0107352034 資料類型 thesis dc.contributor.advisor 張興華 zh_TW dc.contributor.author (Authors) 余冠緯 zh_TW dc.contributor.author (Authors) Yu, Kuan-Wei en_US dc.creator (作者) 余冠緯 zh_TW dc.creator (作者) Yu, Kuan-Wei en_US dc.date (日期) 2020 en_US dc.date.accessioned 3-Aug-2020 17:39:35 (UTC+8) - dc.date.available 3-Aug-2020 17:39:35 (UTC+8) - dc.date.issued (上傳時間) 3-Aug-2020 17:39:35 (UTC+8) - dc.identifier (Other Identifiers) G0107352034 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/130997 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 金融學系 zh_TW dc.description (描述) 107352034 zh_TW dc.description.abstract (摘要) 配對交易在國內外證券市場是一種被廣泛運用的統計套利投資策略，它通過同時建構成對資產的多空部位來賺取資產價差收斂的損益。配對交易策略的顯著優點在於通過對沖機制來有效規避了該資產的系統性風險，即使在市場整體面臨下行風險的時候配對交易仍然能夠獲得比較穩定的收益。過去關於配對交易的文獻大致上專注在兩個方面，一是研究如何挑選出性質良好的配對以及相關交易模型，另一則是研究如何制定最優的交易策略使得交易績效得到最大化。本研究著重在後者，也就是引入一種基於關聯結構 (Copula) 函數和條件機率的股票配對交易策略來比較過去大眾所熟知的共整合策略以及最小距離策略的績效實證。最後經由本研究之實證顯示，關聯結構法不論在絕對績效或是風險調整後的績效上均勝過傳統的交易策略，同時也間接印證過去文獻提及最小距離策略在 2002 年之後可能獲得負報酬之事。 zh_TW dc.description.abstract (摘要) Pairs trading is a kind of statistical arbitrage strategy which is widely used in oversea security markets. By creating both long and short position for two different assets, we can earn arbitrage profit through the converging of two assets’ prices. Obviously, the most important advantage of pairs trading is that it could earn profit steadily during either bear market or bull market. The researches in the past mainly focused on two aspects. One was that looking for the better way to find out what kind of pair of assets had a better performance and their relative trading strategy, another was that making a better strategy to maximize our profit. This paper mainly focuses on the latter. We introduce a stock pairs trading strategy based on Copula function and conditional probability and compare it to the strategy invented by previous papers: cointegration method and distance method. Generally speaking, the Copula method definitely has greater excess return and risk-adjusted return. We also incidentally confirm that some of the paper mentioned that distance method had a poor performance after 2002. en_US dc.description.tableofcontents 第一章 緒論 1第二章 相關理論概述 4第一節 邊際分配模型 4第二節 Copula理論與模型 8第三章 研究方法 13第一節 資料篩選及預處理 13第二節 最小距離法 14第三節 共整合法 15第四節 關聯結構法 18第四章 實證結果分析 23第一節 績效評量 23第二節 交易績效敘述統計與評估 24第五章 結論與建議 29參考文獻 31 zh_TW dc.format.extent 1033303 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0107352034 en_US dc.subject (關鍵詞) 統計套利 zh_TW dc.subject (關鍵詞) 配對交易 zh_TW dc.subject (關鍵詞) 關聯結構 zh_TW dc.subject (關鍵詞) 共整合關係 zh_TW dc.subject (關鍵詞) statistical arbitrage en_US dc.subject (關鍵詞) pairs trading en_US dc.subject (關鍵詞) copula en_US dc.subject (關鍵詞) cointegration en_US dc.subject (關鍵詞) ARMA en_US dc.subject (關鍵詞) GARCH en_US dc.title (題名) 應用Copula之配對交易策略 zh_TW dc.title (題名) Pairs Trading with Copulas en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] 林展源 (2019)。反向型 ETF 與波動型 ETF 之避險績效 ──應用 Copula-GJR-GARCH 模型。國立政治大學國際經營與貿易學系研究所碩士論文，台北市。[2] 鄭瑩 (2013)。D-Vine Copulas 之模型化相依性：台灣電子產業類股實證分析。國立屏東商業技術學院財務金融系研究所碩士論文，屏東縣。[3] Aas, K., Czado, C., Frigessi, A., Bakken, H., 2009. Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics 44 (2), 182–198.[4] Andrade, S., Di Pietro, V., Seasholes, M., 2005. Understanding the profitability of pairs trading. Unpublished working paper, UC Berkeley, Northwestern University.[5] Baillie, R. T., Myers, R. J., 1991. Bivariate GARCH Estimation of the Optimal Commodity Futures Hedge. Journal of Applied Econometrics, 6 (2), 109-124.[6] Bedford, T., Cooke, R. M., 2002. Vines: A new graphical model for dependent random variables. Annals of Statistics, 1031–1068.[7] Bollerslev, T., 1987. A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return. The Review of Economics and Statistics 69 (3), 542-547.[8] Box, G. E. P., Jenkins, G. M., 1970. Time Series Analysis: Forecasting and Control. San Francisco: Holden-Day.[9] Broussard, J. P., Vaihekoski, M., 2012. Profitability of pairs trading strategy in an illiquid market with multiple share classes. Journal of International Financial Markets, Institutions and Money 22 (5), 1188–1201.[10] Chen, H., Chen, S. J., Li, F., 2012. Empirical investigation of an equity pairs trading strategy. Working paper, University of British Columbia, University of Michigan.[11] Clayton, D. G., 1978. A model for association in bivariate life tables and its applications in epidemiological studies of familial tendency in chronic disease incident. Biometrika 65, 141-151.[12] Clegg, M., Krauss, C., 2016. Pairs trading with partial cointegration. FAU Discussion Papers in Economics, University of Erlangen-Nurnberg.[13] Dickey, D. A., Fuller, W. A., 1979. Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association 74 (366), 427–431.[14] Ding, P., 2016. On the conditional distribution of the multivariate t distribution. The American Statistician (just-accepted), 00–00.[15] Do, B., Faff, R., 2010. Does simple pairs trading still work? Financial Analysts Journal 66 (4), 83–95.[16] Do, B., Faff, R., 2012. Are Pairs Trading Profits Robust to Trading Costs? Financial Analysts Journal 35 (2), 261–287.[17] Dragulescu, A. A., 2014. xlsx: Read, write, format Excel 2007 and Excel 97/2000/XP/2003 files. R package version 0.5.7.[18] Elliott, R. J., Hoek, V. D., John, Malcolm, W. P., 2005. Pairs trading. Quantitative Finance 5 (3), 271–276.[19] Engle, R. F., 1982. Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica: Journal of the Econometric Society 50 (4), 987-1007.[20] Engle, R. F., Granger, C. W., 1987. Co-integration and error correction: Representation, estimation, and testing. Econometrica: Journal of the Econometric Society 55 (2), 251–276.[21] Frank, M. J., 1979. On the Simultaneous Associativity of F(x, y) and x + y − F(x, y). Aequationes Mathematicae 19, 194–226.[22] Galenko, A., Popova, E., Popova, I., 2012. Trading in the presence of cointegration. Journal of Alternative Investments 15 (1), 85–97.[23] Gatev, E., Goetzmann, W. N., Rouwenhorst, K. G., 2006. Pairs trading: Performance of a relative-value arbitrage rule. Review of Financial Studies 19 (3), 797–827.[24] Gonzalez-Fernandez, Y., Soto, M., 2015. vines: Multivariate dependence modeling with vines. R package version 1.1.3.[25] Gumbel, E. J., 1960. Bivariate Exponential Distributions. Journal of the American Statistical Association 55, 698–707.[26] Hansen, B. E., 1994. Autoregressive Conditional Density Estimation. International Economic Review 35 (3), 705-730.[27] Huck, N., 2010. Pairs trading and outranking: The multi-step-ahead forecasting case. European Journal of Operational Research 207 (3), 1702–1716.[28] Huck, N., 2015. Pairs trading: does volatility timing matter? Applied Economics, 1–18.[29] Huck, N., Afawubo, K., 2015. Pairs trading and selection methods: is cointegration superior? Applied Economics 47 (6), 599–613.[30] Jacobs, H., Weber, M., 2015. On the determinants of pairs trading profitability. Journal of Financial Markets 23, 75–97.[31] Joe, H., 1997. Multivariate models and dependence concepts. Chapman & Hall, London.[32] Joe, H., Xu, J. J., 1996. The Estimation Method of Inference Functions for Margins for Multivariate Models. Technical Report 166, Department of Statistics, University of British Columbia.[33] Kotz, S., Nadarajah, S., 2004. Multivariate t-distributions and their applications. Cambridge University Press.[34] Krauss, C., 2016. Statistical arbitrage pairs trading strategies: Review and outlook. Journal of Economic Surveys, forthcoming.[35] Liew, R. Q., Wu, Y., 2013. Pairs trading: A copula approach. Journal of Derivatives & Hedge Funds 19 (1), 12–30.[36] Lin, Y., McCrae, M., Gulati, C., 2006. Loss protection in pairs trading through minimum profit bounds: A cointegration approach. Advances in Decision Sciences 2006.[37] Nadarajah, S., Kotz, S., 2005. Mathematical properties of the multivariate t distribution. Acta Applicandae Mathematica 89 (1-3), 53–84.[38] Nelsen, R. B., 1999. An introduction to copulas. Springer-Verlag.[39] Nelsen, R. B., 2007. An introduction to copulas. Springer Science & Business Media.[40] Perlin, M. S., 2009. Evaluation of pairs-trading strategy at the Brazilian financial market. Journal of Derivatives & Hedge Funds 15 (2), 122–136.[41] Peterson, B. G., Carl, P., 2014. PerformanceAnalytics: Econometric tools for performance and risk analysis. R package version 1.4.3541.[42] Rad, H., Low, Rand Kwong Yew, Faff, R. W., 2016. The profitability of pairs trading strategies: Distance, cointegration and copula methods. Quantitative Finance, 1–18.[43] Rmetrics Core Team, Wuertz, D., Setz, T., 2014. fCopulae: Rmetrics - bivariate dependence structures with copulae. R package version 3011.81.[44] Rmetrics Core Team, Wuertz, D., Setz, T., Chalabi, Y., 2015. timeSeries: Rmetrics - financial time series objects. R package version 3012.99.[45] Ryan, J. A., 2015. quantmod: Quantitative financial modelling framework. R package version 0.4-5.[46] Ryan, J. A., Ulrich, J. M., 2014. xts: eXtensible time series. R package version 0.9-7.[47] Sharpe, W. F., 1964. Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk. Journal of Finance. 19 (3), 425-442.[48] Sklar, A., 1959. Fonctions de répartition à n dimensions et leurs marges. Publications de I’ Institut deStatistique de l’University de Paris (8), 229-231.[49] Trapletti, A., Hornik, K., 2016. tseries: Time series analysis and computational finance. R package version 0.10-35.[50] Vidyamurthy, G., 2004. Pairs trading: Quantitative methods and analysis. J. Wiley, Hoboken, N.J.[51] Wickham, H., Francois, R., 2016. dplyr: A grammar of data manipulation. R package version 0.5.0.[52] Wuertz, D., 2013. fUnitRoots: Trends and unit roots. R package version 3010.78.[53] Wu, Y., 2013. Pairs trading: A copula approach. Journal of Derivatives & Hedge Funds 19 (1), 12 – 30.[54] Xie, W., Liew, Q. R., Wu, Y., Zou, X., 2014. Pairs trading with copulas. Working paper, Nanyang Technological University.[55] Xie, W., Wu, Y., 2013. Copula-based pairs trading strategy. Asian Finance Association (AsFA) 2013 Conference.[56] Zeileis, A., Grothendieck, G., Ryan, J. A., 2015. zoo: S3 infrastructure for regular and irregular time series (z’s ordered observations). R package version 1.7-12. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202000826 en_US
