Bayesian Portfolio Selection with Gaussian Mixture Returns

Qian, Hang (2009): Bayesian Portfolio Selection with Gaussian Mixture Returns.

Abstract

Markowitz portfolio selection is challenged by huge implementation barriers. This paper addresses the parameter uncertainty and deviation from normality in a Bayesian framework. The non-normal asset returns are modeled as finite Gaussian mixtures. Gibbs sampler is employed to obtain draws from the posterior predictive distribution of asset returns. Optimal portfolio weights are then constructed so as to maximize agents’ expected utility. Simple experiment suggests that our Bayesian portfolio selection procedure performs exceedingly well.

• Item Type: MPRA Paper
• Language: English
• Keywords: portfolio selection; Gaussian mixtures; Bayesian
• Subjects: G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General

References

Black, F., and Litterman, R., 1992. Global portfolio optimization. Financial Analysts Journal, 48:28–43.

Bawa, V., Brown, S. and Klein, R. Estimation Risk and Optimal Portfolio Choice. Amsterdam: North Holland Publishing, 1979.

Celeux, G., Hurn, M., Robert, C.P., 2000. Computational and inferential difficulties with mixture posterior distributions. Journal of American Statistics Association, 95, 957–970.

Chib, S., 1995. Marginal likelihood form the Gibbs samper. Journal of the American Statistical Association, 90, 1313-1321.

Chopra, V. K., and Ziemba, W. T., 1993. The Effect of Errors in Means, Variances, and Covariances on Optimal Portfolio Choice. Journal of Portfolio Management, Vol. 19, 2, 6-11.

Dickinson, J., 1974. The reliability of estimation procedures in portfolio analysis. Journal of Financial and Quantitative Analysis 9, 447–462.

Fama, E. 1965. The behavior of stock market prices. Journal of Business. 38. pp. 34-105.

Frost, P. A., and Savarino, J. E. ,1986. An Empirical Bayes Approach to Efficient Portfolio Selection. Journal of Financial and Quantitative Analysis, 21, 293-305.

Frühwirth-Schnatter, S., 2001. Markov chain Monte Carlo estimation of classical and dynamic switching and mixture models. Journal of American Statistics Association ,96, 194–209.

Jasra, A., Holmes, C.C., Stephens, D.A., 2005. Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modeling. Statistists Science, 20, 50–67.

Jobson, J., Korkie, B., 1980. Estimation for Markowitz efficient portfolios. Journal of the American Statistical Association 75, 544–554.

Jorion, P., 1986. Bayes–Stein estimation for portfolio analysis. Journal of Financial and Quantitative Analysis 21, 279–291.

Geweke, J., 2007. Interpreatation and inference in mixture models: simple MCMC works. Computatinal Statistics and Data Analysis, 51, 3529-3550.

Goldfarb, D., and Iyengar, G. 2003. Robust portfolio selection problems. Mathematics of Operations Research, 28(1):1–38.

Greyserman, A., Jones, D., Strawderman, W., 2006. Portfolio selection using hierarchical Bayesian analysis and MCMC methods. Journal of Banking & Finance 30, 669–678.

Harvey, C. R., and Siddique, A., 2000. Conditional Skewness in Asset Pricing Tests, Journal of Finance, 55, 1263-1295.

Klein, R. W., and Bawa, V. S. ,1976. The Effect of Estimation Risk on Optimal Portfolio Choice. Journal of Financial Economics, 3, 215-231.

Kon, S.J., 1984. Models of Stock Returns--A Comparison. Journal of Finance, Vol. 39, 1, pp. 147-165.

Kraus, A., and Litzenberger, R., 1976. Skewness Preference and the Valuation of Risk Assets, Journal of Finance, 31, 1085-1100.

Lindley, D. V., Smith, A., 1972. Bayes Estimates for the Linear Model, Journal of the Royal Statistical Society, Vol. 34, No. 1, 1-41.

Markowitz, H. M. , 1952. Portfolio Selection: Efficient Diversification of Investments, New York: Wiley.

Newcomb, S., 1886. A generalized theory of the combination of observations so as to obtain the best result. American Journal of Mathematics, 8, 343–366.

Michaud, R. O. 1998. Efficient Asset Management: A Practical Guide to Stock Portfolio Management and Asset Allocation, Financial Management Association, Survey and Synthesis Series. HBS Press, Boston, MA.

Peiro, A. ,1994. The distribution of stock returns: Intemational evidence, Applied Financial Economics, v. 4. pp. 431-439.

Polson, N. G., Tew, B. V., 2000. Bayesian Portfolio Selection: An Empirical Analysis of the S&P 500 Index 1970-1996, Journal of Business & Economic Statistics, Vol. 18, 2, 164-173.

Praetz, P., 1972. The distribution of share price changes, Journal of Business., 45, pp. 49-55.

Rachev,S., Hsu,J., Bagasheva,B., Fabozzi,F. , 2008.Bayesian Methods in Finance. John Wiley & Sons. Scherer, B. 2002. Portfolio resampling: Review and critique. Financial Analysts Journal, 58(6):98–109.

Weigand, A.S., Shi, S.M., 2000. Predicting daily probability distributions of S&P 500 returns. Journal of Forecasting 19, 375–392.