Journal of the Korean Operations Research and Management Science Society (한국경영과학회지)

The Korean Operations Research and Management Science Society (한국경영과학회)
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Developing an Investment Framework based on Markowitz's Portfolio Selection Model Integrated with EWMA : Case Study in Korea under Global Financial Crisis

지수가중이동평균법과 결합된 마코위츠 포트폴리오 선정 모형 기반 투자 프레임워크 개발 : 글로벌 금융위기 상황 하 한국 주식시장을 중심으로

  • 박경찬 (연세대학교 경영대학 경영학과) ;
  • 정종빈 (연세대학교 경영대학 경영학과) ;
  • 김성문 (연세대학교 경영대학 경영학과)
  • Received : 2013.03.02
  • Accepted : 2013.04.01
  • Published : 2013.06.30
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Abstract

In applying Markowitz's portfolio selection model to the stock market, we developed a comprehensive investment decision-making framework including key inputs for portfolio theory (i.e., individual stocks' expected rate of return and covariance) and minimum required expected return. For estimating the key inputs of our decision-making framework, we utilized an exponentially weighted moving average (EWMA) which places more emphasis on recent data than the conventional simple moving average (SMA). We empirically analyzed the investment results of the decision-making framework with the same 15 stocks in Samsung Group Funds found in the Korean stock market between 2007 and 2011. This five-year investment horizon is marked by global financial crises including the U.S. subprime mortgage crisis, the collapse of Lehman Brothers, and the European sovereign-debt crisis. We measure portfolio performance in terms of rate of return, standard deviation of returns, and Sharpe ratio. Results are compared with the following benchmarks : 1) KOSPI, 2) Samsung Group Funds, 3) Talmudic portfolio based on the na$\ddot{i}$ve 1/N rule, and 4) Markowitz's model with SMA. We performed sensitivity analyses on all the input parameters that are necessary for designing an investment decision-making framework : smoothing constant for EWMA, minimum required expected return for the portfolio, and portfolio rebalancing period. In conclusion, appropriate use of the comprehensive investment decision-making framework based on the Markowitz's model integrated with EWMA proves to achieve outstanding performance compared to the benchmarks.

Keywords

References

  1. 김성문, 김홍선, "한국 주식시장에서 비선형계획법을 이용한 마코위츠의 포트폴리오 선정 모형의 투자 성과에 관한 연구", 경영과학, 제26권, 제2호(2009), pp.19-35.
  2. 김재영, "[금융특집] '한국대표, 가장 믿을 건 너희들' 그룹주펀드에 돈이 몰린다", 동아일보, (2010).
  3. 류 정, "톱 20위 중 15개가 삼성그룹株투자 펀드", 조선일보(2012. 07. 02).
  4. 류춘호, "1차 확률적 지배를 하는 최대수익 포트폴리오 가중치의 탐색에 관한 연구", 한국경영과학회지, 제34권, 제4호(2009), pp.153-163.
  5. 엄철준, "최적자산배분이론의 유용성에 관한 연구", 산업경제연구, 제16권, 제5호(2003), pp.17-26.
  6. 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
  7. 최형석, "[펀드 따라잡기] 삼성, 펀드수익률도 '대한민국 대표선수'", 조선일보(2008).
  8. Albright, S.C. and W.L. Winston, Management Science Modeling, 3rd edition, Thomson (South-Western), 2009.
  9. Bawa, V.S., S.J. Brown, and R.W. Klein, Estimation Risk and Optimal Portfolio Choice, Amsterdam : North-Holland, 1979.
  10. Ben-Tal, A., T. Margalit, and A.N. Nemirovski, "Robust modeling of multi-stage portfolio problems," in Frenk H., K. Roos, T. Terlaky, and S. Zhang (Eds.), High performance optimization, Dordrecht : Kluwer, 2002.
  11. 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
  12. Blume, M.E., "Portfolio Theory : A Step Toward Its Practical Application," The Journal of Business, Vol.43, No.2(1970), pp.152-173. https://doi.org/10.1086/295262
  13. Bodie, Z., A. Kane, and A.J. Marcus, Investments, 9th edition, New York : McGraw-Hill, 2011.
  14. Boudoukh, J., M. Richardson, and R.F. Whitelaw, "Investigation of a class of volatility estimators," The Journal of Derivatives, Vol.4, No.3 (1997), pp.63-71. https://doi.org/10.3905/jod.1997.407973
  15. Broadie, M., "Computing efficient frontiers using estimated parameters," Annals of Operations Research, Vol.45(1993), pp.21-58. https://doi.org/10.1007/BF02282040
  16. Chan, L., J. Karceski, and J. Lakonishok, "On portfolio optimization : forecasting covariances and choosing the risk model," Review of Financial Studies, Vol.12, No.5(1999), pp. 937-974. https://doi.org/10.1093/rfs/12.5.937
  17. Chiang, T.C. and D. Zheng, "An empirical analysis of herd behavior in global stock markets," Journal of Banking and Finance, Vol.34(2010), pp.1911-1921. https://doi.org/10.1016/j.jbankfin.2009.12.014
  18. Chopra, V.K. and W.T. Ziemba, "The effect of errors in means, variances, and covariances on optimal portfolio choice," Journal of Portfolio Management, Vol.19, No.2(1993), pp.6-11.
  19. Cuthbertson, K. and D. Nitzsche, Financial Engineering : Derivatives and Risk Management, John Wiley and Sons, 2001.
  20. DeMiguel, V., L. Garlappi, F.J. Nogales, and R. Uppal, "A Generalized Approach to Portfolio Optimization : Improving Performance by Constraining Portfolio Norms," Management Science, Vol.55, No.5(2009), pp.798-812. https://doi.org/10.1287/mnsc.1080.0986
  21. 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
  22. 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
  23. 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
  24. El Ghaoui, L., M. Oks, and F. Oustry, "Worst-Case Value-At-Risk and Robust Portfolio Optimization : A Conic Programming Approach," Operations Research, Vol.51, No.4 (2003), pp.543-556. https://doi.org/10.1287/opre.51.4.543.16101
  25. Elton, E.J. and M.J. Gruber, "Modern Portfolio Theory, 1950 to Date," Journal of Banking and Finance, Vol.21, No.11(1997), pp. 1743-1759. https://doi.org/10.1016/S0378-4266(97)00048-4
  26. Fabozzi, F.J., F. Gupta, and H.M. Markowitz, "The Legacy of Modern Portfolio Theory," Journal of Investing, Vol.11, No.3(2002), pp. 7-22.
  27. Fabozzi, F.J., D. Huang, and G. Zhou, "Robust portfolios : contributions from operations research and finance," Annals of Operations Research, Vol.176, No.1(2010), pp.191-220. https://doi.org/10.1007/s10479-009-0515-6
  28. Feibel, B.J., Investment performance measurement, Hoboken, N.J. : John Wiley and Sons, 2003.
  29. Gardner Jr., E.S., "Exponential Smoothing: The State of the Art," Journal of Forecasting, Vol.4, No.1(1985), pp.1-28. https://doi.org/10.1002/for.3980040103
  30. Gardner Jr., E.S., "Exponential smoothing : The state of the art-Part II," International Journal of Forecasting, Vol.22, No.4(2006), pp.637-666. https://doi.org/10.1016/j.ijforecast.2006.03.005
  31. Goldfarb, D. and G. Iyengar, "Robust Portfolio Selection Problems," Mathematics of Operations Research, Vol.28, No.1(2003), pp.1-38. https://doi.org/10.1287/moor.28.1.1.14260
  32. Hillier, F.S., M.S. Hillier, K. Schmedders, and M. Stephens, Introduction to Management Science-A Modeling and Case Studies Approach with Spreadsheets, 3rd edition, New York : McGraw-Hill, 2008.
  33. Hillier, F.S. and G.J. Lieberman, Introduction to Operations Research, 9th edition, New York : McGraw-Hill, 2010.
  34. Horasanli, M. and N. Fidan, "Portfolio Selection by Using Time Varying Covariance Matrices. Journal of Economic and Social Research," Vol.9, No.2(2007), pp.1-22.
  35. Morgan, J.P. and Reuters, RiskMetrics : Technical Document. Risk Management, 4th edition, New York : Morgan Guaranty Trust Company, 1996.
  36. 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
  37. James, F.E., Jr., "Monthly moving averages-An effective investment tool?," Journal of Financial and Quantitative Analysis, Vol.3, No.3(1968), pp.315-326. https://doi.org/10.2307/2329816
  38. Jobson, J.D. and B. Korkie, "Estimation for Markowitz Estimation Efficient Portfolios," Journal of the American Statistical Association, Vol.75, No.371(1980), pp.544-554. https://doi.org/10.1080/01621459.1980.10477507
  39. Jobson, J.D. and B. Korkie, "Putting Markowitz theory to work," The Journal of Portfolio Management, Vol.7, No.4(1981), pp.70-74. https://doi.org/10.3905/jpm.1981.408816
  40. Jorion, P., "International Portfolio Diversification with Estimation Risk," The Journal of Business, Vol.58, No.3(1985), pp.259-278. https://doi.org/10.1086/296296
  41. Jorion, P., "Bayes-Stein Estimation for Portfolio Analysis," The Journal of Financial and Quantitative Analysis, Vol.21, No.3(1986), pp.279-292. https://doi.org/10.2307/2331042
  42. 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
  43. Larsen, G.A., Jr., and B.G. Resnick, "Parameter Estimation Techniques, Optimization Frequency, and Portfolio Return Enhancement," The Journal of Portfolio Management, Vol.27, No.4(2001), pp.27-34.
  44. Markowitz, H., "Portfolio selection," Journal of Finance, Vol.7(1952), pp.77-91.
  45. Markowitz, H., Portfolio Selection : Efficient Diversification of Investments(Cowles Foundation Monograph : No. 16). New York : John Wiley and Sons, 1959.
  46. Merton, R.C., "On Estimating the Expected Return on the Market : An Exploratory Investigation," Journal of Financial Economics, Vol.8(1980), pp.323-361. https://doi.org/10.1016/0304-405X(80)90007-0
  47. Merton, R.C., "Thoughts on the future : theory and practice of investment management," Financial Analyst Journal, Vol.59, No.1(2003), pp.17-23.
  48. 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
  49. Pantaleo, E., M. Tumminello, F. Lillo, and R.N. Mantegna, "When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators," Quantitative Finance, Vol.11, No.7(2011), pp.1067-1080. https://doi.org/10.1080/14697688.2010.534813
  50. Penza, P. and V.K. Bansalv, Measuring market risk with value at risk, New York : John Wiley, 2001.
  51. Radin, R.L., Optimization in Operations Research, Upper Saddle River, N.J. : Prentice Hall, 1988.
  52. Roy, A.D., "Safety first and the holding of assets," Econometrica, Vol.20, No.3(1952), pp.431-449. https://doi.org/10.2307/1907413
  53. Sharpe, W.F., "The Sharpe Ratio," The Journal of Portfolio Management, Vol.21, No.1 (1994), pp.49-58. https://doi.org/10.3905/jpm.1994.409501
  54. Siegel, A.F. and A. Woodgate, "Performance of Portfolios Optimized with Estimation Error," Management Science, Vol.53, No.6(2007), pp.1005-1015. https://doi.org/10.1287/mnsc.1060.0664
  55. Sullivan, W.G. and W.W. Claycombe, Fundamentals of Forecasting, Reston Publishing Company, Inc, 1977.
  56. Taylor, B.W., Introduction to Management Science, 9th edition, Prentice Hall, 2007.
  57. Taylor, J., "Volatility forecasting with smooth transition exponential smoothing," International Journal of Forecasting, Vol.20(2004), pp.273-286. https://doi.org/10.1016/j.ijforecast.2003.09.010
  58. Winston, W.L., Operations Research Applications and Algorithms, 4th edition, Thomson (Brooks/Cole), 2004.
  59. Winston, W.L. and M. Venkataramanan, Introduction Mathematical Programming, 4th edition, Thomson (Brooks/Cole), 2003.
  60. Zellner, A. and V.K. Chetty, "Prediction and Decision Problems in Regression Models from the Bayesian Point of View," Journal of the American Statistical Association, Vol. 60(1965), pp.608-616. https://doi.org/10.1080/01621459.1965.10480817