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A general approach to Bayesian portfolio optimization

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  • Alexander Bade
  • Gabriel Frahm
  • Uwe Jaekel

Abstract

We develop a general approach to portfolio optimization taking account of estimation risk and stylized facts of empirical finance. This is done within a Bayesian framework. The approximation of the posterior distribution of the unknown model parameters is based on a parallel tempering algorithm. The portfolio optimization is done using the first two moments of the predictive discrete asset return distribution. For illustration purposes we apply our method to empirical stock market data where daily asset log-returns are assumed to follow an orthogonal MGARCH process with t-distributed perturbations. Our results are compared with other portfolios suggested by popular optimization strategies. Copyright Springer-Verlag 2009

Suggested Citation

  • Alexander Bade & Gabriel Frahm & Uwe Jaekel, 2009. "A general approach to Bayesian portfolio optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(2), pages 337-356, October.
  • Handle: RePEc:spr:mathme:v:70:y:2009:i:2:p:337-356
    DOI: 10.1007/s00186-008-0271-4
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    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    3. Vasiliki Plerou & Parameswaran Gopikrishnan & Bernd Rosenow & Luis A. Nunes Amaral & H. Eugene Stanley, 1999. "Universal and non-universal properties of cross-correlations in financial time series," Papers cond-mat/9902283, arXiv.org.
    4. Ole Barndorff-Nielsen & Elisa Nicolato & Neil Shephard, 2002. "Some recent developments in stochastic volatility modelling," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 11-23.
    5. Klein, Roger W. & Bawa, Vijay S., 1976. "The effect of estimation risk on optimal portfolio choice," Journal of Financial Economics, Elsevier, vol. 3(3), pages 215-231, June.
    6. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    7. Frahm, Gabriel & Jaekel, Uwe, 2007. "Tyler's M-estimator, random matrix theory, and generalized elliptical distributions with applications to finance," Discussion Papers in Econometrics and Statistics 2/07, University of Cologne, Institute of Econometrics and Statistics.
    8. Lorenzo Garlappi & Raman Uppal & Tan Wang, 2007. "Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach," The Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 41-81, January.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 279-292, September.
    11. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    12. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    13. Frahm, Gabriel, 2007. "Linear statistical inference for global and local minimum variance portfolios," Discussion Papers in Econometrics and Statistics 1/07, University of Cologne, Institute of Econometrics and Statistics.
    14. Polson, Nicholas G & Tew, Bernard V, 2000. "Bayesian Portfolio Selection: An Empirical Analysis of the S&P 500 Index 1970-1996," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 164-173, April.
    15. Kalymon, Basil A., 1971. "Estimation Risk in the Portfolio Selection Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(1), pages 559-582, January.
    16. Alexander Kempf & Christoph Memmel, 2006. "Estimating the global Minimum Variance Portfolio," Schmalenbach Business Review (sbr), LMU Munich School of Management, vol. 58(4), pages 332-348, October.
    17. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    18. Frost, Peter A. & Savarino, James E., 1986. "An Empirical Bayes Approach to Efficient Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 293-305, September.
    19. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September.
    20. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    21. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    3. Dimitrios Bisias & Andrew W Lo & James F Watkins, 2012. "Estimating the NIH Efficient Frontier," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-10, May.

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