Computational Economics

, 33:237 | Cite as

Models and Simulations for Portfolio Rebalancing

  • Gianfranco Guastaroba
  • Renata Mansini
  • M. Grazia Speranza
Article

Abstract

In 1950 Markowitz first formalized the portfolio optimization problem in terms of mean return and variance. Since then, the mean-variance model has played a crucial role in single-period portfolio optimization theory and practice. In this paper we study the optimal portfolio selection problem in a multi-period framework, by considering fixed and proportional transaction costs and evaluating how much they affect a re-investment strategy. Specifically, we modify the single-period portfolio optimization model, based on the Conditional Value at Risk (CVaR) as measure of risk, to introduce portfolio rebalancing. The aim is to provide investors and financial institutions with an effective tool to better exploit new information made available by the market. We then suggest a procedure to use the proposed optimization model in a multi-period framework. Extensive computational results based on different historical data sets from German Stock Exchange Market (XETRA) are presented.

Keywords

Risk management Conditional value at risk Portfolio rebalancing Multi-period portfolio analysis Mixed integer linear programming 

References

  1. Andersson F., Rosen D., Uryasev S. (2001) Credit risk optimization with conditional value-at-risk criterion. Mathematical Programming 89: 273–291CrossRefGoogle Scholar
  2. Artzner P., Delbaen F., Eber J.-M., Heath D. (1999) Coherent measures of risk. Mathematical Finance 9: 203–228CrossRefGoogle Scholar
  3. Blume M.E., Crockett J., Friend I. (1974) Stock ownership in the United States: Characteristics and trends. Survey of Current Business 54: 16–40Google Scholar
  4. Chiodi L., Mansini R., Speranza M.G. (2003) Semi-absolute deviation rule for mutual funds portfolio selection. Annals of Operations Research 124: 245–265CrossRefGoogle Scholar
  5. Elton E.J., Gruber M.J. (1974) On the optimality of some multiperiod portfolio selection criteria. Journal of Business 47: 231–243CrossRefGoogle Scholar
  6. Gennotte G., Jung A. (1994) Investment strategies under transaction costs: The finite horizon case. Management Science 40: 385–404CrossRefGoogle Scholar
  7. Guastaroba, G., Mansini, R., & Speranza, M. G. (2005). On the use of CVaR model in a rebalancing portfolio strategy. Technical Report 2005 (number 249). Department of Quantitative Methods, University of Brescia, Italy.Google Scholar
  8. Kellerer H., Mansini R., Speranza M.G. (2000) Selecting portfolios with fixed costs and minimum transaction lots. Annals of Operations Research 99: 287–304CrossRefGoogle Scholar
  9. Konno H., Wijayanayake A. (2001) Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints. Mathematical Programming 89: 233–250CrossRefGoogle Scholar
  10. Konno H., Yamazaki H. (1991) Mean-absolute deviation portfolio optimization model and its application to Tokyo stock market. Management Science 37: 519–531CrossRefGoogle Scholar
  11. Li D., Ng W.-L. (2000) Optimal dynamic portfolio selection: multiperiod mean-variance formulation. Mathematical Finance 10: 387–406CrossRefGoogle Scholar
  12. Li Z.-F., Wang S.-Y., Deng X.-T. (2000) A linear programming algorithm for optimal portfolio selection with transaction costs. International Journal of Systems Science 31: 107–117CrossRefGoogle Scholar
  13. Li Z.-F., Li Z.-X., Wang S.-Y., Deng X.-T. (2001) Optimal portfolio selection of assets with transaction costs and no short sales. International Journal of Systems Science 32: 599–607CrossRefGoogle Scholar
  14. Mansini R., Ogryczak W., Speranza M.G. (2003) LP solvable models for portfolio optimization: A classification and computational comparison. IMA Journal of Management Mathematics 14: 187–220CrossRefGoogle Scholar
  15. Mansini R., Ogryczak W., Speranza M.G. (2005) Conditional value at risk and related linear programming models for portfolio optimization. Annals of Operations Research 152: 227–256CrossRefGoogle Scholar
  16. Mansini R., Speranza M.G. (2005) An exact approach for portfolio selection with transaction costs and rounds. IIE Transactions 37: 919–929CrossRefGoogle Scholar
  17. Markowitz H.M. (1952) Portfolio selection. Journal of Finance 7: 77–91CrossRefGoogle Scholar
  18. Markowitz H.M. (1959) Portfolio selection: Efficient diversification of investments. Wiley, New YorkGoogle Scholar
  19. Ogryczak W., Ruszczyński A. (2002) Dual stochastic dominance and related mean-risk models. SIAM Journal on Optimization 13: 60–78CrossRefGoogle Scholar
  20. Patel N.R., Subrahmanyam M.G. (1982) A simple algorithm for optimal portfolio selection with fixed transaction costs. Management Science 38: 303–314CrossRefGoogle Scholar
  21. Pflug G.C. (2000) Some remarks on the Value-at-Risk and the Conditional Value-at-Risk. In: Uryasev S. (eds) Probabilistic constrained optimization: Methodology and applications. Kluwer Academic Publisher, Dordrecht, pp 272–281Google Scholar
  22. Pogue G.A. (1970) An extension of the Markowitz portfolio selection model to include variable transaction costs, short sales, leverage policies and taxes. Journal of Finance 25: 1005–1028CrossRefGoogle Scholar
  23. Rockafellar R.T., Uryasev S. (2000) Optimization of Conditional Value-at-Risk. Journal of Risk 2: 21–41Google Scholar
  24. Smith K.V. (1967) A transition model for portfolio revision. Journal of Finance 22: 425–439CrossRefGoogle Scholar
  25. Steinbach M.C. (2001) Markowitz revisited: Mean-variance models in financial portfolio analysis. SIAM Review 43: 31–85CrossRefGoogle Scholar
  26. Yoshimoto A. (1996) The mean-variance approach to portfolio optimization subject to transaction costs. Journal of the Operation Research Society of Japan 39: 99–117Google Scholar
  27. Young M.R. (1998) A minimax portfolio selection rule with linear programming solution. Management Science 44: 673–683CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  • Gianfranco Guastaroba
    • 1
  • Renata Mansini
    • 2
  • M. Grazia Speranza
    • 1
  1. 1.Department of Quantitative MethodsUniversity of BresciaBresciaItaly
  2. 2.Department of Electronics for AutomationUniversity of BresciaBresciaItaly

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