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Danh mục đầu tư lớn tối ưu theo phương pháp trung bình – phương sai: Kỹ thuật hướng dẫn đơn giản dựa trên định lý tách biệt hai quỹ
Springer Science and Business Media LLC - Trang 1-23 - 2022
Tóm tắt
Trong bài viết này, chúng tôi xem xét lại Định lý Tách biệt Hai Quỹ như một kỹ thuật đơn giản cho việc tối ưu hóa theo phương pháp Trung bình – Phương sai của các danh mục đầu tư lớn. Phương pháp được đề xuất nhanh chóng và có thể mở rộng, cung cấp kết quả tương đương với các kỹ thuật học máy thường được sử dụng nhưng với thời gian tính toán khác biệt tính bằng giờ (1 phút so với vài giờ). Trong ứng dụng thực nghiệm, chúng tôi xem xét ba khu vực địa lý (thị trường chứng khoán Trung Quốc, Hoa Kỳ và Pháp) và cho thấy rằng Định lý Tách biệt Hai Quỹ hoàn toàn đúng khi không có ràng buộc nào được áp dụng và gần đúng với các ràng buộc dương (thực tế) về trọng số. Kỹ thuật này được chứng minh là có lợi cho cả các nhà nghiên cứu và thực hành tham gia vào các nhiệm vụ tối ưu hóa danh mục đầu tư.
Từ khóa
#Tối ưu hóa danh mục đầu tư #Định lý tách biệt hai quỹ #Trung bình - phương sai #Học máyTài liệu tham khảo
Abadie, J. (1969). Generalization of the Wolfe reduced gradient method to the case of nonlinear constraints. Optimization, 22, 37–47.
Anagnostopoulos, K., & Mamanis, G. (2011). The mean-variance cardinality constrained portfolio optimization problem: An experimental evaluation of five multi-objective evolutionary algorithms. Expert Systems with Applications, 38(11), 14208–14217.
Andrews, D. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica, 59, 817–858.
Andrews, D., & Monahan, J. (1992). An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica, 60, 953–966.
Bai, L., Newsom, P., & Zhang, J. (2011). Teaching utility theory with an application in modern portfolio optimization. Decision Sciences Journal of Innovative Education, 9(1), 107–112.
Belloni, A., & Chernozhukov, V. (2011). penalized quantile regression in high-dimensional sparse models. The Annals of Statistics, 39(1), 82–130.
Bernard, C., De Vecchi, C., & Vanduffel, S. (2021). When do two-or three-fund separation theorems hold? Quantitative Finance, 21, 1–15.
Black, F. (1972). Capital market equilibrium with restricted borrowing. The Journal of Business, 45(3), 444–455.
Black, F., & Litterman, R. (1992). Global portfolio optimization. Financial Analysts Journal, 48(5), 28–43.
Bonaccolto G., Caporin, M., & Maillet, B. (2021). Large financial network via conditional expected shortfall. Mimeo. R&R in the European Journal of Operational Research.
Bonaccolto, G., Caporin, M., & Paterlini, S. (2018). Asset allocation strategies based on penalized quantile regression. Computational Management Science, 15(1), 1–32.
Bonaccolto, G., & Paterlini, S. (2020). Developing new portfolio strategies by aggregation. Annals of Operations Research, 292(2), 933–971.
Breuer, T., & Csiszár, I. (2013). Systematic stress tests with entropic plausibility constraints. Journal of Banking & Finance, 37(5), 1552–1559.
Breuer, T., Jandacka, M., Rheinberger, K., & Summer, M. (2009). How to find plausible, severe, and useful stress scenarios. International Journal of Central Banking, 5, 205–224.
Britten-Jones, M. (1999). The sampling error in estimates of mean-variance efficient portfolio weights. The Journal of Finance, 54(2), 655–671.
Broadie, M. (1993). Computing efficient frontiers using estimated parameters. Annals of Operations Research, 45(1), 21–58.
Brodie, J., Daubechies, I., De Mol, C., Giannone, D., & Loris, I. (2009). Sparse and stable Markowitz portfolios. Proceedings of the National Academic Science of the USA, 106(30), 12267–12272.
Cairns, A. J., Blake, D., & Dowd, K. (2006). Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans. Journal of Economic Dynamics and Control, 30(5), 843–877.
Candelon, B., Hurlin, C., & Tokpavi, S. (2012). Sampling error and double shrinkage estimation of minimum variance portfolios. Journal of Empirical Finance, 19(4), 511–527.
Cass, D., & Stiglitz, J. (1970). The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds. Journal of Economic Theory, 2(2), 122–160.
Chang, T., Meade, N., Beasley, J., & Sharaiha, Y. (2000). Heuristics for cardinality constrained portfolio optimisation. Computers & Operations Research, 27(13), 1271–1302.
Dahlquist, M., Farago, A., & Tédongap, R. (2017). Asymmetries and portfolio choice. The Review of Financial Studies, 30(2), 667–702.
Deguest, R., Martellini, L., & Milhau, V. (2018). A reinterpretation of the optimal demand for risky assets in fund separation theorems. Management Science, 64(9), 4333–4347.
De Meo, E. (2021). Scenario design for macro-financial stress testing. SSRN 3493554.
DeMiguel, V., Garlappi, L., Nogales, F., & Uppal, R. (2009a). A generalized approach to portfolio optimization: Improving performance by constraining portfolio norms. Management Science, 55(5), 798–812.
DeMiguel, V., Garlappi, L., & Uppal, R. (2009b). Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? The Review of Financial Studies, 22(5), 1915–1953.
Duchin, R., & Levy, H. (2009). Markowitz versus the Talmudic portfolio diversification strategies. The Journal of Portfolio Management, 35(2), 71–74.
Dybvig, P., & Liu, F. (2018). On investor preferences and mutual fund separation. Journal of Economic Theory, 174, 224–260.
Fan, J., Zhang, J., & Yu, K. (2012). Vast portfolio selection with gross-exposure constraints. Journal of the American Statistical Association, 107(498), 592–606.
Fastrich, B., Paterlini, S., & Winker, P. (2015). Constructing optimal sparse portfolios using regularization methods. Computational Management Science, 12(3), 417–434.
Flood, M., & Korenko, G. (2015). Systematic scenario selection: Stress testing and the nature of uncertainty. Quantitative Finance, 15(1), 43–59.
Gaines, B., Kim, J., & Zhou, H. (2018). Algorithms for fitting the constrained lasso. Journal of Computational and Graphical Statistics, 27(4), 861–871.
Geyer, A., Hanke, M., & Weissensteiner, A. (2014). No-arbitrage bounds for financial scenarios. European Journal of Operational Research, 236(2), 657–663.
Gouriéroux, C., & Jouneau, F. (1999). Econometrics of efficient fitted portfolios. Journal of Empirical Finance, 6(1), 87–118.
Grover, J., & Lavin, A. (2007). Modern portfolio optimization: A practical approach using an excel solver single-index model. The Journal of Wealth Management, 10(1), 60–72.
Hakansson, N. H. (1969). Risk disposition and the separation property in portfolio selection. Journal of Financial and Quantitative Analysis, 4, 401–416.
Hastie, T., Tibshirani, R., & Wainwright, M. (2015). Statistical learning with sparsity: The lasso and generalizations. CRC Press.
Harvey, C., & Siddique, A. (2000). Conditional skewness in asset pricing tests. The Journal of Finance, 55(3), 1263–1295.
Hoerl, A., & Kennard, R. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55–67.
Huang, C., & Litzenberger, R. (1988). Foundations for financial economics. North-Holland.
Ingersoll, J. (1987). Theory of financial decision making. Rowman & Littlefield.
Israelsen, C. (2003). Sharpening the Sharpe ratio. Financial Planning, 33(1), 49–51.
Israelsen, C. (2005). A refinement to the Sharpe ratio and information ratio. Journal of Asset Management, 5(6), 423–427.
Jagannathan, R., & Ma, T. (2003). Risk reduction in large portfolios: Why imposing the wrong constraints helps. The Journal of Finance, 58(4), 1651–1683.
Jobson, J., & Korkie, B. (1981). Performance hypothesis testing with the Sharpe and Treynor measures. Journal of Finance, 36, 889–908.
Joo, Y., & Park, S. (2021). Optimal portfolio selection using a simple double-shrinkage selection rule. Finance Research Letters, 43, 102019.
Jorion, P. (1986). Bayes-Stein estimation for portfolio analysis. The Journal of Financial and Quantitative Analysis, 21, 279–292.
Jurczenko, E., & Maillet, B. (2006). The four-moment capital asset pricing model: between asset pricing and asset allocation. In Multi-moment asset allocation and pricing models, Chapter 6 (pp. 113-163). Wiley.
Kan, R., & Zhou, G. (2007). Optimal portfolio choice with parameter uncertainty. Journal of Financial and Quantitative Analysis, 42, 621–656.
Kempf, A., & Memmel, C. (2006). Estimating the global minimum variance portfolio. Schmalenbach Business Review, 58(4), 332–348.
Kolm, P., Tütüncü, R., & Fabozzi, F. (2014). 60 Years of portfolio optimization: Practical challenges and current trends. European Journal of Operational Research, 234(2), 356–371.
Kremer, P., Lee, S., Bogdan, M., & Paterlini, S. (2020). Sparse portfolio selection via the sorted -norm. Journal of Banking and Finance, 110, 105687.
Laws, J. (2003). Portfolio analysis using excel. Applied quantitative methods for trading and investment, 293.
Ledoit, O., & Wolf, M. (2008). Robust performance hypothesis testing with the Sharpe ratio. Journal of Empirical Finance, 15(5), 850–859.
Ledoit, O., & Wolf, M. (2011). Robust performances hypothesis testing with the variance. Wilmott, 2011(55), 86–89.
Lintner, J. (1965a). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. The Review of Economics and Statistics, 47(1), 13–37.
Lintner, J. (1965b). Security prices, risk, and maximal gains from diversification. The Journal of Finance, 20(4), 587–615.
Lo, A. W. (2002). The statistics of Sharpe ratios. Financial Analysts Journal, 58(4), 36–52.
Lobo, M., Fazel, M., & Boyd, S. (2007). Portfolio optimization with linear and fixed transaction costs. Annals of Operations Research, 152(1), 341–365.
MacKinlay, A., & Pástor, Ľ. (2000). Asset pricing models: Implications for expected returns and portfolio selection. The Review of Financial Studies, 13(4), 883–916.
Mahalanobis, P. (1927). Analysis of race-mixture in Bengal. Journal of the Asiatic Society of Bengal, 23, 301–333.
Mahalanobis, P. (1936). On the generalized distance in statistics. National Institute of Science of India.
Mardia, K., Kent, J., & Bibby, J. (1979). Multivariate analysis. Academic Press.
Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77–91.
Markowitz, H. (1959). Portfolio selection: Efficient diversification of investments. Wiley.
Markowitz, H. M. (1999). The early history of portfolio theory: 1600–1960. Financial Analysts Journal, 55(4), 5–16.
Markowitz, H. (2014). Mean-variance approximations to expected utility. European Journal of Operational Research, 234(2), 346–355.
McNeil, A., Frey, R., & Embrechts, P. (2015). Quantitative risk management: Concepts, techniques and tools. Princeton University Press.
Memmel, C. (2003). Performance hypothesis testing with the Sharpe ratio. Finance Research Letters, 1, 21–23.
Merton, R. (1973). An intertemporal capital asset pricing model. Econometrica, 41(5), 867–887.
Meucci, A. (2009). Risk and asset allocation. Springer.
Michaud, R. (1989). The Markowitz optimization enigma: Is ‘optimized’ optimal? Financial Analysts Journal, 45(1), 31–42.
Michaud, R., & Michaud, R. (2008). Estimation error and portfolio optimization: A resampling solution. Journal of Investment Management, 6(1), 8–28.
Mossin, J. (1966). Equilibrium in a capital asset market. Econometrica, 34, 768–783.
Opdyke, J. (2007). Comparing Sharpe ratios: So where are the p-values? Journal of Asset Management, 8(5), 308–336.
Pye, G. (1967). Portfolio selection and security prices. The Review of Economics and Statistics, 49(1), 111–115.
Roll, R. (1977). A critique of the asset pricing theory’s tests. Journal of Financial Economics, 4, 129–176.
Ross, S. (1978). Mutual fund separation in financial theory—The separating distributions. Journal of Economic Theory, 17(2), 254–286.
Samuelson, P. (1967). General proof that diversification pays. Journal of Financial and Quantitative Analysis, 2(1), 1–13.
Schanbacher, P. (2015). Averaging across asset allocation models. Jahrbücher Für Nationalökonomie Und Statistik, 235(1), 61–81.
Sharpe, W. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. The Journal of Finance, 19(3), 425–442.
Stevens, G. (1998). On the inverse of the covariance matrix in portfolio analysis. The Journal of Finance, 53(5), 1821–1827.
Tobin, J. (1958). Liquidity preference as behavior towards risk. The Review of Economic Studies, 25(2), 65–86.
Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (methodological), 58(1), 267–288.
Tu, J., & Zhou, G. (2011). Markowitz meets Talmud: A combination of sophisticated and naive diversification strategies. Journal of Financial Economics, 99(1), 204–215.
Turlach, B., & Wright, S. (2015). Quadratic programming. Wiley Interdisciplinary Reviews: Computational Statistics, 7(2), 153–159.
Vieira, E., & Filomena, T. (2020). Liquidity constraints for portfolio selection based on financial volume. Computational Economics, 56, 1055–1077.
Vinod, H., & Morey, M. (1999). Confidence intervals and hypothesis testing for the Sharpe and Treynor performance measures: A bootstrap approach. Computational Finance, 99, 25–40.
Woodside-Oriakhi, M., Lucas, C., & Beasley, J. (2011). Heuristic algorithms for the cardinality constrained efficient frontier. European Journal of Operational Research, 213(3), 538–550.
Yang, Y. (2000). Combining different procedures for adaptive regression. Journal of Multivariate Analysis, 74(1), 135–161.
Yang, Y. (2001). Adaptive regression by mixing. Journal of the American Statistical Association, 96(454), 574–588.
Yang, Y. (2004). Aggregating regression procedures to improve performance. Bernoulli, 10(1), 25–47.
Yen, Y., & Yen, T. (2014). Solving norm constrained portfolio optimization via coordinate-wise descent algorithms. Computational Statistics & Data Analysis, 76, 737–759.
Zhao, Z., Ledoit, O., & Jiang, H. (2020). Risk reduction and efficiency increase in large portfolios: leverage and shrinkage. University of Zurich, Department of Economics, Working Paper, No. 328, 34 p.
Zou, H., & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (statistical Methodology), 67(2), 301–320.
