Computational Economics

, Volume 29, Issue 3–4, pp 333–354 | Cite as

Portfolio optimization when risk factors are conditionally varying and heavy tailed

Original Paper

Abstract

Assumptions about the dynamic and distributional behavior of risk factors are crucial for the construction of optimal portfolios and for risk assessment. Although asset returns are generally characterized by conditionally varying volatilities and fat tails, the normal distribution with constant variance continues to be the standard framework in portfolio management. Here we propose a practical approach to portfolio selection. It takes both the conditionally varying volatility and the fat-tailedness of risk factors explicitly into account, while retaining analytical tractability and ease of implementation. An application to a portfolio of nine German DAX stocks illustrates that the model is strongly favored by the data and that it is practically implementable.

Keywords

Multivariate stable distribution Index model Portfolio optimization Value-at-risk Model adequacy 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akgiray V., Booth G.G. (1988). The stable law model of stock returns. Journal of Business and Economics Statistics, 6: 51–57CrossRefGoogle Scholar
  2. Bawa V.S., Lindenberg E.B. (1977). Capital market equilibrium in a mean-lower partial moment framework. Journal of Financial Economics, 5: 189–200CrossRefGoogle Scholar
  3. Belkacem, L., Lèvy-Vèhel, J., & Walter, C. (1995). Generalized market equilibrium: Stable CAPM, unpublished manuscript.Google Scholar
  4. Belkacem L., Lèvy-Vèhel J., Walter C. (2000). CAPM, risk and portfolio selection in α-stable markets. Fractals, 8: 99–116Google Scholar
  5. Blattberg R., Sargent T.J. (1971). Regression with non-gaussian stable disturbances: Some sampling results. Econometrica, 39: 501–510CrossRefGoogle Scholar
  6. Bollerslev T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31: 307–327CrossRefGoogle Scholar
  7. Christoffersen P.F. (2003). Elements of financial risk management. London, Academic PressGoogle Scholar
  8. DeGroot, M. H. (1986). Probability and statistics. 2nd edn. Reading, Massachusetts, Addison-WesleyGoogle Scholar
  9. Doganoglu T., Mittnik S. (1998). An approximation procedure for asymmetric stable densities. Computational Statistics, 13: 463–475Google Scholar
  10. Doganoglu, T., & Mittnik, S. (2004). The Estimation of Multivariate Stable Paretian Index Models, unpublished manuscript.Google Scholar
  11. Elton E.J., Gruber M.J., Bawa V.S. (1979). Simple rules for optimal portfolio selection in stable paretian markets. Journal of Finance, 34: 1041–1047CrossRefGoogle Scholar
  12. Engle R.F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica 50(4): 987–1007CrossRefGoogle Scholar
  13. Fama E.F. (1965a). The behavior of stock market prices. Journal of Business, 38: 34–105CrossRefGoogle Scholar
  14. Fama E.F. (1965b). Portfolio analysis in a stable paretian market. Management Science, 11: 404–419CrossRefGoogle Scholar
  15. Fama E.F. (1971). Risk, return and equilibrium. Journal of Political Economy, 77: 31–55Google Scholar
  16. Gamrowski B., Rachev S.T. (1999). A testable version of the pareto-stable CAPM. Mathematical and Computer Modelling, 29: 61–82CrossRefGoogle Scholar
  17. Harlow W.V., Rao R.K.S. (1989). Asset pricing in a generalized mean-lower partial moment framework: Theory and evidence. Journal of Financial and Quantitative Analysis, 24: 394–419CrossRefGoogle Scholar
  18. Kurz-Kim, J.-R., Rachev, S. T., Samorodnitsky, G. (2004). Asymptotic distribution of unbiased linear estimators in the presence of heavy-tailed stochastic regressors and residuals. mimeo.Google Scholar
  19. McCulloch J. H. (1997). Measuring Tail Thickness to Estimate the Stable Index α: A Critique. Journal of Business and Economics Statistics, 15: 74–81CrossRefGoogle Scholar
  20. McCulloch, J. H. (1998). Numerical approximation of the symmetric stable distribution and densitiy. In R.J. Adler, R. Feldman, M.S. Taqqu, (Eds.), A practical guide to heavy tails, Boston, MA: Birkhauser.Google Scholar
  21. Mittnik S., Doganoglu T., Chenyao D. (1999). Computing the probability density function of the stable paretian distribution. Mathematical and Computer Modelling, 29: 235–240CrossRefGoogle Scholar
  22. Mittnik S., Rachev S.T. (1993). Modeling stock returns with alternative stable distribution. Econometric Reviews, 12: 261–330Google Scholar
  23. Mittnik S., Rachev S.T., Doganoglu T., Chenyao D. (1999). Maximum likelihood estimation of the stable paretian models. Mathematical and Computer Modelling, 29: 275–293CrossRefGoogle Scholar
  24. Nolan J.P. (1999). An algorithm for evaluating stable densities in Zolotarev’s (M) parameterization. Mathematical and Computer Modelling, 29: 229–233CrossRefGoogle Scholar
  25. Panorska A., Mittnik S., Rachev S. (1995). Stable ARCH modles for financial time series. Applied Mathematic Letters, 8(4): 33–37CrossRefGoogle Scholar
  26. Rachev S.T., Mittnik S. (2000). Stable paretian models in finance. Chichester, WileyGoogle Scholar
  27. RiskMetrics Group (1996). RiskMetrics—Technical Document. 4th edition. http://www.riskmetrics.com/research/techdoc/index.cgiGoogle Scholar
  28. Samorodnitsky G., Taqqu M.S. (1994). Stable non-gaussian random processes. New York, Chapman & HallGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Toker Doganoglu
    • 1
    • 2
  • Christoph Hartz
    • 3
  • Stefan Mittnik
    • 3
    • 4
    • 5
    • 6
  1. 1.Center for Information and Network EconomicsUniversity of MunichMunichGermany
  2. 2.Faculty of Arts and SciencesSabanci UniversityIstanbulTurkey
  3. 3.Department of StatisticsUniversity of MunichMunichGermany
  4. 4.Ifo Institute for Economic ResearchMunichGermany
  5. 5.Center for Financial StudiesFrankfurtGermany
  6. 6.Institute of StatisticsLudwig-Maximilians-Universität MünchenMünchenGermany

Personalised recommendations