Annals of Operations Research

, Volume 157, Issue 1, pp 3–23 | Cite as

A general framework for multistage mean-variance post-tax optimization

  • Maria A. Osorio
  • Nalan Gülpınar
  • Berç Rustem


An investor’s decisions affect the way taxes are paid in a general portfolio investment, modifying the net redemption value and the yearly optimal portfolio distribution. We investigate the role of these decisions on multistage mean-variance portfolio allocation model. A number of risky assets grouped in wrappers with special taxation rules is integrated in a multistage financial portfolio optimization problem. The uncertainty on the returns of assets is specified as a scenario tree generated by simulation/clustering based approach. We show the impact of decisions in the yearly reallocation of the investments for three typical cases with an annual fixed withdrawal in a fixed horizon that utilizes completely the option of taper relief offered by banks in UK. Our computational framework can be used as a tool for testing decisions in this context.


Post-tax optimization Mean-variance portfolio management Multistage stochastic mixed-integer quadratic programming Scenario tree 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Asea, P., & Turnovsky, S. (1997). Capital income taxation and risk-taking in a small open economy. Department of Economics, University of California, Los Angeles Working Paper 768. Google Scholar
  2. Birge, J. R., & Louveaux, F. V. (1997). Introduction to stochastic programming. New York: Springer. Google Scholar
  3. Feldstein, M. (1976). Personal taxation and portfolio composition: an econometric analysis. Econometrica, 44(4), 631–649. CrossRefGoogle Scholar
  4. Kall, P., & Wallace, S. W. (1994). Stochastic programming. New York: Wiley. Google Scholar
  5. Kouwenberg, R. (2001). Scenario generation and stochastic programming models for asset liability management. European Journal of Operational Research, 134(2), 279–293. CrossRefGoogle Scholar
  6. Hoyland, K., & Wallace, S. W. (2001). Generating scenario trees for multistage problems. Management Science, 47(2), 295–307. CrossRefGoogle Scholar
  7. Hubbard, G. (1985). Personal taxation, pension wealth, and portfolio composition. Review of Economics and Statistics, 67, 53–60. CrossRefGoogle Scholar
  8. Gulpinar, N., Rustem, B., & Settergren, R. (2003). Multistage stochastic mean-variance portfolio analysis with transaction cost. Innovations in Financial and Economic Networks, 3, 46–63. Google Scholar
  9. Gulpinar, N., Rustem, B., & Settergren, R. (2004). Optimisation and simulation approaches to scenario tree generation. Journal of Economics Dynamics and Control, 28(7), 1291–1315. CrossRefGoogle Scholar
  10. Kallberg, J. G., & Ziemba, W. T. (1983). Comparison of alternative utility functions in portfolio selection problems. Management Science, 29(11), 1257–1276. Google Scholar
  11. Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7, 77–91. CrossRefGoogle Scholar
  12. Mészáros, C. (1997). BPMPD user’s manual version 2.20. Department of Computing Research Report #97/8, July 1997. Google Scholar
  13. Osorio, M. A., Settergren, R., Rustem, B., & Gulpinar, N. (2002). Post tax optimal investments. In Financial engineering, e-commerce and supply chain (pp. 153–173). Dordrecht: Kluwer Academic. Google Scholar
  14. Osorio, M. A., Gulpinar, N., Settergren, R., & Rustem, B. (2004). Post-tax optimization with stochastic programming. European Journal of Operational Research, 157, 152–168. CrossRefGoogle Scholar
  15. Prekopa, A. (1995). Stochastic programming. Budapest: Akademiai Kiado. Google Scholar
  16. Pulley, L. B. (1981). A general mean-variance approximation to expected utility for short holding periods. Journal of Financial and Quantitative Analysis, 16, 361–373. CrossRefGoogle Scholar
  17. Stein, D. (1998). Measuring and evaluating portfolio performance after taxes. The Journal of Portfolio Management, 25(2), 117–124. Google Scholar
  18. Stein, D. (2000). Diversification in the presence of taxes. The Journal of Portfolio Management, 27(1), 61–71. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Maria A. Osorio
    • 1
    • 3
  • Nalan Gülpınar
    • 2
    • 4
  • Berç Rustem
    • 2
  1. 1.Chemical Engineering DepartmentUniversidad Autonoma de PueblaSan Manuel PueblaMexico
  2. 2.Department of ComputingImperial College LondonLondonUK
  3. 3.School of Computer SciencesUniversidad Autonoma de PueblaPueblaMexico
  4. 4.Warwick Business SchoolThe University of WarwickCoventryUK

Personalised recommendations