Covariance Matrix for Portfolio Selection on Vietnam Stock Market
Author(s)
Thu Trang Dang , Thi Thu Ha Pham , Thi Thu Huong Do ,
Download Full PDF Pages: 204-212 | Views: 650 | Downloads: 122 | DOI: 10.5281/zenodo.4572842
Abstract
The objective of this dissertation is to investigate that whether the investors can improve the performance of minimum – variance optimized portfolios by altering the estimators of covariance matrix input. Besides, based on the results of out – of – sample portfolio performance metrics, the dissertation is going to select the suitable estimators of covariance matrix for portfolio optimization on Vietnam stock market.
Keywords
Covariance matrix, Vietnam stock market
References
i. Bai, J., and Shi, S. (2011). Estimating high dimensional covariance matrices and its applications. Annals of Economics and Finance, 12: 199–215.
ii. Broadie, M. (1993). Computing efficient frontiers using estimated parameters. Annals of operations research, 45:21-58.
iii. Best, J., and Grauer, R. (1991). Sensitivity analysis for mean-variance portfolio problems. Management Science, 37(8):980–989.
iv. Bengtsson, C., and Holst, J. (2002). On portfolio selection: Improved covariance matrix estimation for Swedish asset returns. Journal of Portfolio Management, 33(4): 55-63.
v. Chan, L., Jason, K., and Josef, L.(1999). On portfolio optimization: Forecasting covariances and choosing the risk model. The Review of Financial Studies, 12(5):937–974.
vi. Chandra, S.(2003). Regional Economy Size and the Growth-Instability Frontier: Evidence from Europe. J. Reg. Sci., 43(1): 95-122. doi:10.1111/1467-9787.00291.
vii. Chekhlov, A., and Uryasev, S. (2005). Drawdown measure in portfolio optimization. International Journal of Theoretical and Applied Finance, 8(1):13-58.
viii. Chen, Y., Ami W., Yonina E., and Alfred, H. (2010). Shrinkage algorithms for MMSE covariance estimation. IEEE Transactions on Signal Processing, 58: 5016–29.
ix. Chopra, V., and Ziemba, W.(1993). The effect of errors in means, variances, and covariances on optimal portfolio choice. Journal of Portfolio Management, 19(2):6- 11.
x. Clarke, Roger G., Harindra De Silva, and Steven Thorley. (2006). Minimum-variance portfolios in the U.S. equity market. Journal of Portfolio Management, 33: 10–24.
xi. Cohen, J., and Pogue, J. (1967). An empirical evaluation of alternative portfolio selection models. The Journal of Business, 40(2):166–193.
xii. De Nard, G., Ledoit, O., and Wolf, M. (2019). Factor models for portfolio selection in large dimensions: The good, the better and the ugly. Journal of Financial Econometrics. Forthcoming.
xiii. DeMiguel, V., and Francisco N., (2009). Portfolio selection with robust estimation. Operations Research, 57(3):560–577.
xiv. Efron, B., R. Tibshirani. (1993). An Introduction to the Bootstrap. Chapman and Hall, New York.
xv. Edwin, J., Martin, G., and Manfred, P. (1997). Simple rules for optimal portfolio selection: the multi group case. Journal of Financial and Quantitative Analysis, 12(3):329–345.
xvi. Elton, Edwin J., and Martin J Gruber. (1973). Estimating the dependence structure of share prices: implications for portfolio selection. The Journal of Finance, 28(5):1203– 1232.
xvii. Elton, Edwin J., Martin J Gruber., Stephen B., and William N Goetzmann.(2009). Modern portfolio theory and investment analysis. John Wiley & Sons.
xviii. Ernest, Chan P. (2009). Quantitative trading: How to Build Your Own Algorithmic Trading Business. John Wiley & Sons.
xix. Ernest, Chan P. (2013). Algorithmic Trading: Winning Strategies and Their Rationale. John Wiley & Sons.
xx. Fabozzi, F., Gupta, F., and Markowitz, H.(2002). The legacy of modern portfolio theory. The Journal of Investing, 11(3): 7–22.
xxi. Fama, E., and French, K. (1993). Common risk factors in the returns on stocks and bonds. The Journal of Financial Economics, 33: 3–56.
xxii. Fama, E., and French, K. (2015). A five-factor asset pricing model. Journal of Financial Economics, 16: 1–22.
xxiii. Fama, E., and French, K. (2016). Dissecting Anomalies with a Five-Factor Model. Review of Financial Studies, 29: 69–103.
xxiv. Fernández, A., and Gómez, S. (2007). Portfolio selection using neural networks. Computers and Operations Research, 34: 1177–91.
xxv. Frankfurter, G., Phillips, H., and Seagle, J. (1971). Portfolio Selection: The Effects of Uncertain Means, Variances, and Covariances. Journal of Financial and Quantitative Analysis, 6(5):1251 – 1262.
xxvi. George Derpanopoulos (2018). Optimal financial portfolio selection. Working paper.
xxvii. Haugen, Robert A., and Nardin L. Baker. (1991). The efficient market inefficiency of capitalization-weighted stock portfolios. Journal of Portfolio Management, 17: 35– 40.
xxviii. Huber, P. J. (2004). Robust Statistics. John Wiley & Sons, New York.
xxix. Ikeda, Y., and Kubokawa, T. (2016). Linear shrinkage estimation of large covariance matrices using factor models. Journal of Multivariate Analysis, 152: 61–81.
xxx. Iyiola, O., Munirat, Y., and Christopher, N.(2012). The modern portfolio theory as an investment decision tool. Journal of Accounting and Taxation, 4(2):19-28.
xxxi. Jagannathan, R., and Ma, T., (2003). Risk reduction in large portfolios: Why imposing the wrong constraints helps. The Journal of Finance, 58(4):1651–1683.
xxxii. James, W. and Stein, C. (1961). Estimation with quadratic loss. In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability 1, pages 361– 380.
xxxiii. Jensen, M.(1968). The performance of mutual funds in the period 1945 – 1964. Journal of Finance, 23(2):389-416.
xxxiv. Jobson, J., Korkie, B. (1980). Estimation for Markowitz efficient portfolios. Journal of the American Statistical Association, 75(371): 544 – 554.
xxxv. Jorion, P. (1985). International Portfolio Diversification with Estimation Risk. Journal of Business, 58: 259–78.
xxxvi. Jorion, P. (1986). Bayes-Stein estimation for portfolio analysis. Journal of Financial and Quantitative Analysis, 21(3):279–292.
xxxvii. Kwan, Clarence C.Y. (2011). An introduction to shrinkage estimation of the covariance matrix: A Pedagogic Illustration. Spreadsheets in Education (eJSiE), 4(3): article 6.
xxxviii. Kempf, A., and Memmel, C. (2006). Estimating the global minimum variance portfolio. Schmalenbach Business Review, 58:332-48.
xxxix. Konno, Y. (2009). Shrinkage estimators for large covariance matrices in multivariate real and complex normal distributions under an invariant quadratic loss. Journal of Multivariate Analysis, 100: 2237–53.
xl. Lam, C. (2016). Nonparametric eigenvalue-regularized precision or covariance matrix estimator. Annals of Statistics, 44(3):928–953.
xli. Liagkouras, K., and Kostas M. (2018). Multi-period mean-variance fuzzy portfolio optimization model with transaction costs. Engineering Applications of Artificial Intelligence, 67: 260–69.
xlii. Ledoit, O. and Peche, S. (2011). Eigenvectors of some large sample covariance matrix ensembles. Probability Theory and Related Fields, 150(1–2):233–264.
xliii. Ledoit, O. and Wolf, M. (2003a). Honey, I shrunk the sample covariance matrix. Journal of Portfolio Management, 30(4):110–119.
xliv. Ledoit, O. and Wolf, M. (2003b). Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. Journal of Empirical Finance, 10(5):603–621.
xlv. Ledoit, O. and Wolf, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis, 88(2):365–411.
xlvi. Ledoit, O. and Wolf, M. (2008). Robust performance hypothesis testing with the Sharpe ratio. Journal of Empirical Finance, 15(5):850–859.
xlvii. Ledoit, O. and Wolf, M. (2012). Nonlinear shrinkage estimation of large-dimensional covariance matrices. Annals of Statistics, 40(2):1024–1060.
xlviii. Ledoit, O. and Wolf, M. (2015). Spectrum estimation: A unified framework for covariance matrix estimation and PCA in large dimensions. Journal of Multivariate Analysis, 139(2):360–384.
xlix. Ledoit, O. and Wolf, M. (2017a). Nonlinear shrinkage of the covariance matrix for portfolio selection: Markowitz meets Goldilocks. Review of Financial Studies, 30(12):4349–4388.
l. Ledoit, O. and Wolf, M. (2017b). Numerical implementation of the QuEST function.
li. Computational Statistics & Data Analysis, 115:199–223.
lii. Ledoit, O. and Wolf, M. (2018b). Optimal estimation of a large-dimensional covariance matrix under Stein’s loss. Bernoulli, 24(4B). 3791–3832.
liii. Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7:77–91.
liv. Martin, D., Clark, A., and Christopher G. (2010). Robust portfolio construction. Handbook of Portfolio Construction. Springer, 337–380.
lv. Merton, R. (1969). Life time portfolio selection under uncertainty: The continuous-time case. The review of Economics and Statistics, 51: 247–57.
lvi. Merton, R. (1971). Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 3: 373–413.
lvii. Merton, R. (1972). An analytic derivation of the efficient portfolio frontier. Journal of Financial and Quantitative Analysis, 7: 1851–72.
lviii. Merton, C. (1980). On estimating the expected return on the market: An exploratory investigation. Journal of financial economics, 8(4):323–361.
lix. Michaud, Richard O. (1989). The Markowitz optimization enigma: Is ”optimized” optimal. Financial Analysts Journal, 45(1):31–42.
lx. Michaud, Richard O., Esch, D., and Michaud, R. (2012). Deconstructing Black- Litterman: How to get the Portfolio you already knew you wanted. Available at SSRN 2641893.
lxi. Nick Radge (2006). Adaptive analysis for Australian stocks. Wrightbooks.
lxii. Nguyen, Tho. (2010). Arbitrage Pricing Theory: Evidence from an Emerging Stock Market, Working Papers 03, Development and Policies Research Center (DEPOCEN), Vietnam.
lxiii. Okhrin, Yarema, and Wolfgang Schmid. (2007). Comparison of different estimation techniques for portfolio selection. Asta Advances in Statistical Analysis, 91: 109–27.
lxiv. Pogue, A. (1970). An extension of the Markowitz portfolio selection model to include variable transactions’ costs, short sales, leverage policies and taxes. The Journal of Finance, 25: 1005–27.
lxv. Ross, S. A. (1976). The arbitrage theory of capital asset pricing. Journal of Economic Theory, 13(3):341–360.
lxvi. Samuelson, A. (1969). Life time portfolio selection by dynamic stochastic programming. The Review of Economics and Statistics, 51: 239–46.
lxvii. Sch¨afer, J. and Strimmer, K. (2005). A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Statistical Applications in Genetics and Molecular Biology, 4(1). Article 32.
lxviii. Soleimani, H., Golmakani, H., and Mohammad S. (2009). Markowitz-based portfolio selection with minimum transaction lots, cardinality constraints and regarding sector capitalization using genetic algorithm. Expert Systems with Applications, 36: 5058– 63.
lxix. Sharpe, William F. (1963). A simplified model for portfolio analysis. Management science, 9(2):277–293.
lxx. Sharpe, William F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. The journal of finance, 19(3):425–442.
lxxi. Stein, C. (1956). 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, pages 197–206. University of California Press.
lxxii. Stein, C. (1986). Lectures on the theory of estimation of many parameters. Journal of Mathematical Sciences, 34(1):1373–1403.
lxxiii. Taleb, N. (2007). The Black Swan: The Impact of the Highly Improbable, Random House, 80-120.
lxxiv. Truong, L., and Duong, T. (2014). Fama and French three-factor model: Empirical evidences from the Ho Chi Minh Stock Exchange. Journal of Science Can Tho University, 32:61 – 68.
lxxv. Vo, Q., and Nguyen, H. (2011). Measuring risk tolerance and establishing an optimal portfolio for individual investors in HOSE. Economic Development Review, 33-38.
lxxvi. Xue, Hong-Gang, Cheng-Xian Xu, and Zong-Xian Feng. (2006). Mean-variance portfolio optimal problem under concave transaction cost. Applied Mathematics and Computation, 174: 1–12.
lxxvii. Yang, L., Romain, C., and Matthew, M. (2014). Minimum variance portfolio optimization with robust shrinkage covariance estimation. Paper presented at 2014 48th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA, November 2–5; pp. 1326–30.
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