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題名 共變異數矩陣估計方法 對效率前緣與投資組合之影響
The Impact of Estimating Covariance Matrix on Efficient Frontier and Investment Portfolio作者 葉冠廷 貢獻者 郭維裕
葉冠廷關鍵詞 投資組合績效
共變異數矩陣
全域最小變異組合日期 2013 上傳時間 1-Apr-2014 11:14:10 (UTC+8) 摘要 1952年Markowitz 提出平均數－變異數投資組合模型（Mean-Variance Model，簡稱MV 模型）後，開創了投資組合理論的先河，他認為風險與報酬是影響資產配置的兩大因素，其中Markowitz在估計共變異數矩陣時，使用樣本共變異數矩陣模型（Sample Covariance Model）做運算。雖然MV 模型具權威性，但仍存在估計誤差的問題，因此許多共變異數矩陣的估計方法應運而生，包括Litterman and Winklemann（1998）的高盛衰退率共變異數矩陣模型以及Ledoit and Wolf（2003）的單一指數濃縮估計法。本文比較各種共變異數矩陣的效率前緣（efficient frontier）；並採用全域最小變異組合（Global Minimum Variance Point），檢驗樣本共變異數矩陣模型、高盛衰退率共變異數矩陣模型及單一指數濃縮估計法所建構的投資組合，其績效是否優於市值加權的台灣50指數；且以滾動視窗（rolling window）方式，比較三種方法績效之異同優劣。本研究實證結果顯示三種方法相對於大盤均有較佳表現，各方法間則以單一指數濃縮估計法表現較佳。
Markowitz indicated Mean-Variance Model and initiated the portfolio theory in 1952. He proved that risk and return are two important components to impact on asset allocation, and used sample covariance model to calculate covariance matrix. However, MV model exists estimation error. Therefore, many covariance matrix methods was proposed including Goldman Sachs decay rate covariance matrix model of Litterman and Winklemann（1998）, and shrinkage to single-index covariance matrix method of Ledoit and Wolf（2003）. This study compares the efficient frontier build by different covariance matrix methods. Also, this study adopts global minimum portfolio and rolling window to discuss performance of portfolio constructed by these three methods. The conclusion is that the performance of portfolio constructed by these three covariance matrix methods is better than market index, and shrinkage to single-index covariance matrix is the best method to construct portfolio.參考文獻 中文文獻： 1.范沛綱，2006，「最佳投資組合研究-以台灣50 指數為例」，國立中央大學，碩士論文。 英文文獻： 1.Alexander, C. and Dimitriu A. 2005. “Indexing, cointegration and equity market regimes.” International Journal of Finance and Economics, 10, 213-231. 2.Alexander K. and Christoph M. 2006. “Estimating the global minimum Variance Portfolio” Schmalenbach Business Review, Vol. 58, 332-348. 3.Benoit Mandelbrot. 1963. “The Variation of Certain Speculative Prices.” The Journal of Business, University of Chicago Press, vol. 36, pages 394 4.Bera, A.K. and Higgins, M. L. 1992. “A Test for Conditional Heteroskedesticity in Time Series Models.” Journal of Time Series Analysis, 13, 501-519 5.Bengtsson, C. and J. Holst. 2002. “On Portfolio Selection: Improved Covariance Matrix Estimation for Swedish Asset Returns.” Working paper, Lund University and Lund Institute of Technology 6.Chan, L. K. C., Karceski, J. and Lakonishok, J. 1999. “On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model,” Review of Financial Studies, Vol.12, 937-974. 7.Chopra, V.K. and Ziemba W.T. 1993. “The Effect of Errors in Means,Variances,and Covariances on Optimal Portfolio Choice ,“ Journal of Portfolio Management,19,6-11. 8.David J. Disatnik and Simon Benninga. 2007. “Shrinking the Covariance Matrix-Simpler is better.” The Journal of Portfolio Management.33.4:55-63. 9.Eugene F. Fama. 1965. “ The Behavior of Stock-Market Prices.” The Journal of Business, Vol. 38, No. 1. pp. 34-105. 10.Efron, Bradley, and Carl Morris. 1977. “Stein’s Paradox in Statistics.” Scientific American, 236, 119-127. 11.Edwin J. Elton, Martin J. Gruber, Christopher R. Blake. 1996. “Survivor bias and mutual fund performance.” The Review of Financial Studies, Vol.9, No.4, pp. 1097-1120. 12.Fama, E. F. 1970. “Efficient Capital Markets: A Review of Theory and Empirical Work”, Journal of Finance 25, 383-417 13.Gary P. Brinson, Brian D. Singer and Gilbert L. Beebower. 1991. “Determinants of Portfolio Performance II: An Update.” Financial Analysts Journal, May-June, 40-48. 14.Holmes, M. 2007. “Improved Study Finds Index Management Usually Outperforms Active Management.” Journal of Financial Planning 20, 48-58. 15.Jorion, Philippe. 1977. “Bayes-Stein Estimation for Portfolio Analysis.” Journal of Financial and Quantitative Analysis, 279-292. 16.Jagannathan, Ravi and Tongshu Ma. 2003. “Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps.” Journal of Finance 58, 1651-1683. 17.Litterman, R. and K. Winkelmann.1998. “Risk Management Series：Estimating Covariance Matrices.” 18.Lo, Andrew W., and Pankaj N. Patel. 2008. “130/30: The new long-only.” Journal of Portfolio Management 34, 12-38 19.Ledoit, Olivier, and Michael Wolf. 2003. “Improved Estimation of the Covariance Matrix of Stock Returns with an Application to Portfolio Selection.” Journal of Empirical Finance, 10, 603-621. 20.Markowitz, H.1952. “Portfolio Selection.” Journal of Finance. 21.Michaud, R.1989. “The Markowitz Optimization Enigma：Is Optimized Optimal.” Financial Analysis Journal. 22.Merton, R. C. 1980. “On Estimating the Expected Return on the Market: An Exploratory Investigation,” Journal of Financial Economics, Vol.8, 323-361. 23.Stein, Charles. 1955. “Inadmissibility of the Usual Estimator for the Mean of a Multivariate Normal Distribution.” In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. Berkeley: University of California Press, 197-206. 24.Sharpe, William F. 1963. “A Simplified Model for Portfolio Analysis.” Management Science, vol. 9, no. 1, 277-293. 25.Sorensen, E. H., K. L. Miller, and V. Samak. 1998. “Allocating Between Active and Passive Management.” Financial Analysts Journal 54, 18-31. 26.Sz. Pafka and I. Kondor. 2004. “Estimated correlation matrices and portfolio optimization” Physica A343, 623-634 描述 碩士
國立政治大學
國際經營與貿易研究所
100351037
102資料來源 http://thesis.lib.nccu.edu.tw/record/#G1003510371 資料類型 thesis dc.contributor.advisor 郭維裕 zh_TW dc.contributor.author (Authors) 葉冠廷 zh_TW dc.creator (作者) 葉冠廷 zh_TW dc.date (日期) 2013 en_US dc.date.accessioned 1-Apr-2014 11:14:10 (UTC+8) - dc.date.available 1-Apr-2014 11:14:10 (UTC+8) - dc.date.issued (上傳時間) 1-Apr-2014 11:14:10 (UTC+8) - dc.identifier (Other Identifiers) G1003510371 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/65056 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 國際經營與貿易研究所 zh_TW dc.description (描述) 100351037 zh_TW dc.description (描述) 102 zh_TW dc.description.abstract (摘要) 1952年Markowitz 提出平均數－變異數投資組合模型（Mean-Variance Model，簡稱MV 模型）後，開創了投資組合理論的先河，他認為風險與報酬是影響資產配置的兩大因素，其中Markowitz在估計共變異數矩陣時，使用樣本共變異數矩陣模型（Sample Covariance Model）做運算。雖然MV 模型具權威性，但仍存在估計誤差的問題，因此許多共變異數矩陣的估計方法應運而生，包括Litterman and Winklemann（1998）的高盛衰退率共變異數矩陣模型以及Ledoit and Wolf（2003）的單一指數濃縮估計法。本文比較各種共變異數矩陣的效率前緣（efficient frontier）；並採用全域最小變異組合（Global Minimum Variance Point），檢驗樣本共變異數矩陣模型、高盛衰退率共變異數矩陣模型及單一指數濃縮估計法所建構的投資組合，其績效是否優於市值加權的台灣50指數；且以滾動視窗（rolling window）方式，比較三種方法績效之異同優劣。本研究實證結果顯示三種方法相對於大盤均有較佳表現，各方法間則以單一指數濃縮估計法表現較佳。 zh_TW dc.description.abstract (摘要) Markowitz indicated Mean-Variance Model and initiated the portfolio theory in 1952. He proved that risk and return are two important components to impact on asset allocation, and used sample covariance model to calculate covariance matrix. However, MV model exists estimation error. Therefore, many covariance matrix methods was proposed including Goldman Sachs decay rate covariance matrix model of Litterman and Winklemann（1998）, and shrinkage to single-index covariance matrix method of Ledoit and Wolf（2003）. This study compares the efficient frontier build by different covariance matrix methods. Also, this study adopts global minimum portfolio and rolling window to discuss performance of portfolio constructed by these three methods. The conclusion is that the performance of portfolio constructed by these three covariance matrix methods is better than market index, and shrinkage to single-index covariance matrix is the best method to construct portfolio. en_US dc.description.tableofcontents 第一章 緒 論.............................1 第一節 研究背景與動機.......................1 第二節 研究目的........................... 2 第三節 研究架構........................... 3 第二章 理論基礎與文獻回顧................... 5 第一節 台灣五十指數介紹..................... 5 第二節 投資組合策略....................... 7 第三節 相關理論文獻....................... 9 第三章 研究方法和設計.......................14 第一節 資料來源與資料處理...................14 第二節 研究方法...........................15 第三節 共變異數矩陣估計.....................18 第四節 投資組合績效衡量......................26 第五節 研究方法與流程.......................28 第四章 實證分析............................29 第一節 實證方法概述.........................29 第二節 對權重、共變異數矩陣及效率前緣影響.......32 第三節 對樣本外資產配置績效影響...............41 第五章 研究結論與建議.......................46 第一節 實證研究結論........................46 第二節 研究限制與後續研究建議................50 參考文獻................................. 52 附錄.................................... 55 zh_TW dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G1003510371 en_US dc.subject (關鍵詞) 投資組合績效 zh_TW dc.subject (關鍵詞) 共變異數矩陣 zh_TW dc.subject (關鍵詞) 全域最小變異組合 zh_TW dc.title (題名) 共變異數矩陣估計方法 對效率前緣與投資組合之影響 zh_TW dc.title (題名) The Impact of Estimating Covariance Matrix on Efficient Frontier and Investment Portfolio en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) 中文文獻： 1.范沛綱，2006，「最佳投資組合研究-以台灣50 指數為例」，國立中央大學，碩士論文。 英文文獻： 1.Alexander, C. and Dimitriu A. 2005. “Indexing, cointegration and equity market regimes.” International Journal of Finance and Economics, 10, 213-231. 2.Alexander K. and Christoph M. 2006. “Estimating the global minimum Variance Portfolio” Schmalenbach Business Review, Vol. 58, 332-348. 3.Benoit Mandelbrot. 1963. “The Variation of Certain Speculative Prices.” The Journal of Business, University of Chicago Press, vol. 36, pages 394 4.Bera, A.K. and Higgins, M. L. 1992. “A Test for Conditional Heteroskedesticity in Time Series Models.” Journal of Time Series Analysis, 13, 501-519 5.Bengtsson, C. and J. Holst. 2002. “On Portfolio Selection: Improved Covariance Matrix Estimation for Swedish Asset Returns.” Working paper, Lund University and Lund Institute of Technology 6.Chan, L. K. C., Karceski, J. and Lakonishok, J. 1999. “On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model,” Review of Financial Studies, Vol.12, 937-974. 7.Chopra, V.K. and Ziemba W.T. 1993. “The Effect of Errors in Means,Variances,and Covariances on Optimal Portfolio Choice ,“ Journal of Portfolio Management,19,6-11. 8.David J. Disatnik and Simon Benninga. 2007. “Shrinking the Covariance Matrix-Simpler is better.” The Journal of Portfolio Management.33.4:55-63. 9.Eugene F. Fama. 1965. “ The Behavior of Stock-Market Prices.” The Journal of Business, Vol. 38, No. 1. pp. 34-105. 10.Efron, Bradley, and Carl Morris. 1977. “Stein’s Paradox in Statistics.” Scientific American, 236, 119-127. 11.Edwin J. Elton, Martin J. Gruber, Christopher R. Blake. 1996. “Survivor bias and mutual fund performance.” The Review of Financial Studies, Vol.9, No.4, pp. 1097-1120. 12.Fama, E. F. 1970. “Efficient Capital Markets: A Review of Theory and Empirical Work”, Journal of Finance 25, 383-417 13.Gary P. Brinson, Brian D. Singer and Gilbert L. Beebower. 1991. “Determinants of Portfolio Performance II: An Update.” Financial Analysts Journal, May-June, 40-48. 14.Holmes, M. 2007. “Improved Study Finds Index Management Usually Outperforms Active Management.” Journal of Financial Planning 20, 48-58. 15.Jorion, Philippe. 1977. “Bayes-Stein Estimation for Portfolio Analysis.” Journal of Financial and Quantitative Analysis, 279-292. 16.Jagannathan, Ravi and Tongshu Ma. 2003. “Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps.” Journal of Finance 58, 1651-1683. 17.Litterman, R. and K. Winkelmann.1998. “Risk Management Series：Estimating Covariance Matrices.” 18.Lo, Andrew W., and Pankaj N. Patel. 2008. “130/30: The new long-only.” Journal of Portfolio Management 34, 12-38 19.Ledoit, Olivier, and Michael Wolf. 2003. “Improved Estimation of the Covariance Matrix of Stock Returns with an Application to Portfolio Selection.” Journal of Empirical Finance, 10, 603-621. 20.Markowitz, H.1952. “Portfolio Selection.” Journal of Finance. 21.Michaud, R.1989. “The Markowitz Optimization Enigma：Is Optimized Optimal.” Financial Analysis Journal. 22.Merton, R. C. 1980. “On Estimating the Expected Return on the Market: An Exploratory Investigation,” Journal of Financial Economics, Vol.8, 323-361. 23.Stein, Charles. 1955. “Inadmissibility of the Usual Estimator for the Mean of a Multivariate Normal Distribution.” In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. Berkeley: University of California Press, 197-206. 24.Sharpe, William F. 1963. “A Simplified Model for Portfolio Analysis.” Management Science, vol. 9, no. 1, 277-293. 25.Sorensen, E. H., K. L. Miller, and V. Samak. 1998. “Allocating Between Active and Passive Management.” Financial Analysts Journal 54, 18-31. 26.Sz. Pafka and I. Kondor. 2004. “Estimated correlation matrices and portfolio optimization” Physica A343, 623-634 zh_TW
