DOI QR코드

DOI QR Code

Investment Performance of Markowitz's Portfolio Selection Model over the Accuracy of the Input Parameters in the Korean Stock Market

한국 주식시장에서 마코위츠 포트폴리오 선정 모형의 입력 변수의 정확도에 따른 투자 성과 연구

  • 김홍선 (연세대학교 경영대학 경영학과) ;
  • 정종빈 (연세대학교 경영대학 경영학과) ;
  • 김성문 (연세대학교 경영대학 경영학과)
  • Received : 2013.09.29
  • Accepted : 2013.12.02
  • Published : 2013.12.31

Abstract

Markowitz's portfolio selection model is used to construct an optimal portfolio which has minimum variance, while satisfying a minimum required expected return. The model uses estimators based on analysis of historical data to estimate the returns, standard deviations, and correlation coefficients of individual stocks being considered for investment. However, due to the inaccuracies involved in estimations, the true optimality of a portfolio constructed using the model is questionable. To investigate the effect of estimation inaccuracy on actual portfolio performance, we study the changes in a portfolio's realized return and standard deviation as the accuracy of the estimations for each stock's return, standard deviation, and correlation coefficient is increased. Furthermore, we empirically analyze the portfolio's performance by comparing it with the performance of active mutual funds that are being traded in the Korean stock market and the KOSPI benchmark index, in terms of portfolio returns, standard deviations of returns, and Sharpe ratios. Our results suggest that, among the three input parameters, the accuracy of the estimated returns of individual stocks has the largest effect on performance, while the accuracy of the estimates of the standard deviation of each stock's returns and the correlation coefficient between different stocks have smaller effects. In addition, it is shown that even a small increase in the accuracy of the estimated return of individual stocks improves the portfolio's performance substantially, suggesting that Markowitz's model can be more effectively applied in real-life investments with just an incremental effort to increase estimation accuracy.

Keywords

References

  1. 김성문, 김홍선, "한국 주식시장에서 비선형계획법을 이용한 마코위츠의 포트폴리오 선정 모형의 투자 성과에 관한 연구", 경영과학, 제 26권, 제2호(2009), pp.19-35.
  2. 박경찬, 정종빈, 김성문, "지수가중이동평균법과 결합된 마코위츠 포트폴리오 선정 모형 기반 투자 프레임워크 개발 : 글로벌 금융위기 상황하 한국 주식시장을 중심으로", 한국경영과학회지, 제38권, 제2호(2013), pp.75-93. https://doi.org/10.7737/JKORMS.2013.38.2.075
  3. 최재호, 정종빈, 김성문, "마코위츠 포트폴리오 선정 모형을 기반으로 한 투자 알고리즘 개발 및 성과평가 : 미국 및 홍콩 주식시장을 중심으로", 경영과학, 제30권, 제1호(2013), pp. 73-89. https://doi.org/10.7737/KMSR.2013.30.1.073
  4. Best, M.J. and R.R. Grauer, "On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means : Some Analytical and Computational Results," The Review of Financial Studies, Vol.4, No.2(1991), pp. 315-342. https://doi.org/10.1093/rfs/4.2.315
  5. Black, F. and R. Litterman, "Global Portfolio Optimization," Financial Analysts Journal, Vol.48, No.5(1992), pp.28-43.
  6. Broadie, M., "Computing Efficient Frontiers Using Estimated Parameters," Annals of Operations Research, Vol.45(1993), pp.21-58. https://doi.org/10.1007/BF02282040
  7. Chopra, V.K. and W.T. Ziemba, "The Effect of Errors in Means, Variances, and Covariances on Optimal Portfolio Choice," Journal of Portfolio Management, (1993) pp.6-11.
  8. DeMiguel, V., L. Garlappi, and R. Uppal, "Optimal Versus Naive Diversification : How Inefficient is the 1/N Portfolio Strategy?," Review of Financial Studies, Vol.22, No.5 (2009), pp.1915-1953. https://doi.org/10.1093/rfs/hhm075
  9. DeMiguel, V. and F.J. Nogales, "Portfolio Selection with Robust Estimation," Operations Research, Vol.57, No.3(2009), pp.560-577. https://doi.org/10.1287/opre.1080.0566
  10. Duchin, R. and H. Levy, "Markowitz Versus the Talmudic Portfolio Diversification Strategies," The Journal of Portfolio Management, Vol.35, No.2(2009), pp.71-74. https://doi.org/10.3905/JPM.2009.35.2.071
  11. Elton, E.J., M.J. Gruber, and M.W. Padberg, "Optimal Portfolios from Simple Ranking Devices," The Journal of Portfolio Management, (1978) pp.15-19.
  12. Frankfurter, G.M., H.E. Phizzips, and J.P. Seaqlze, "Portfolio Selection : The Effects of Uncertain Means, Variances, and Covariances," The Journal of Financial and Quantitative Analysis, Vol.6, No.5(1971), pp.1251-1262. https://doi.org/10.2307/2329859
  13. Hillier, F.S., M.S. Hillier, K. Schmedders, and M. Stephens, Introduction to Management Science-A Modeling and Case Studies Approach with Spreadsheets, 3rd ed. New York : McGraw-Hill, 2008.
  14. Hillier, F.S. and G.J. Liberman, Introduction to Operations Research, 9th ed. New York : McGraw-Hill, 2010.
  15. Horst, J.R., F.A. De Roon, and B.J.M. Werker, "An Alternative Approach to Estimation Risk," in Advances in Corporate Finance and Asset Pricing, I.L. Renneboog, Ed. Amsterdam : Elsevier, 2006.
  16. Jagannathan, R. and T. Ma, "Risk Reduction in Large Portfolios : Why Imposing the Wrong Constraints Helps," The Journal of Finance, Vol.58, No.4(2003), pp.1651-1683. https://doi.org/10.1111/1540-6261.00580
  17. Jorion, P., "International Portfolio Diversification with Estimation Risk," The Journal of Business, Vol.58, No.3(1985), p.259. https://doi.org/10.1086/296296
  18. Kan, R. and G. Zhou, "Optimal Portfolio Choice with Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Vol.42, No.3(2007), pp.621-656. https://doi.org/10.1017/S0022109000004129
  19. Klein, R.W. and V.S. Bawa, "The Effect of Estimation Risk on Optimal Portfolio Choice," Journal of Financial Economics, Vol.3(1976), pp.215-231. https://doi.org/10.1016/0304-405X(76)90004-0
  20. Konno, H. and H. Yamazaki, "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, Vol.37, No.5(1991), pp. 519-531. https://doi.org/10.1287/mnsc.37.5.519
  21. Markowitz, H., "Portfolio selection," Journal of Finance, Vol.7(1952), pp.77-91.
  22. Merton, R.C., "On Estimating the Expected Return on The Market," Journal of Financial Economics, Vol.8(1980), pp.323-361. https://doi.org/10.1016/0304-405X(80)90007-0
  23. Michaud, R.O., "The Markowitz Optimization Enigma : Is 'Optimized' Optimal?," Financial Analysts Journal, Vol.45, No.1(1989), pp.31-42. https://doi.org/10.2469/faj.v45.n1.31
  24. Ong, C.S., J.J. Huang, and G.H. Tzeng, "A Novel Hybrid Model for Portfolio Selection," Applied Mathematics and Computation, Vol. 169, No.2(2005), pp.1195-1210. https://doi.org/10.1016/j.amc.2004.10.080
  25. Pastor, L. and R.F. Stambaugh, "Comparing Asset Pricing Models : An Investment Perspective," Journal of Financial Economics, Vol.56(2000), pp.335-381. https://doi.org/10.1016/S0304-405X(00)00044-1
  26. Sharpe, W.F., "A Linear Programming Algorithm for Mutual Fund Portfolio Selection," Management Science, Vol.13, No.7(1967), pp. 499-510. https://doi.org/10.1287/mnsc.13.7.499
  27. Xia, Y., B. Liu, S. Wang, and K. K. Lai, "A Model for Portfolio Selection with Order of Expected Returns," Computers and Operations Research, Vol.27(2000), pp.409-422. https://doi.org/10.1016/S0305-0548(99)00059-3