Bayesian Portfolio Selection in a Markov Switching Gaussian Mixture Model

Qian, Hang (2011): Bayesian Portfolio Selection in a Markov Switching Gaussian Mixture Model.

Abstract

Departure from normality poses implementation barriers to the Markowitz mean-variance portfolio selection. When assets are affected by common and idiosyncratic shocks, the distribution of asset returns may exhibit Markov switching regimes and have a Gaussian mixture distribution conditional on each regime. The model is estimated in a Bayesian framework using the Gibbs sampler. An application to the global portfolio diversification is also discussed.

• Item Type: MPRA Paper
• Language: English
• Keywords: Portfolio; Bayesian; Hidden Markov Model; Gaussian Mixture
• 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

Ane, T., Geman, H., 2000. Order flow, transaction clock, and normality of asset returns. Journal of Finance 55 (5), 2259-2284.

Baum, L. E., Eagon, J. A., 1967. An inequality with applications to statistical estimation for probabilistic functions of markov processes and to a model for ecology. Bulletin of American Mathematical Society 73, 360-363.

Baum, L. E., Petrie, T., 1966. Statistical inference for probabilistic functions of finite state markov chains. The Annals of Mathematical Statistics 37 (6), 1554-1563.

Baum, L. E., Petrie, T., Soules, G., Weiss, N., 1970. A maximization technique occurring in the statistical analysis of probabilistic functions of markov chains. The Annals of Mathematical Statistics 41 (1), 164-171.

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

Blattberg, R. C., Gonedes, N. J., 1974. A comparison of the stable and student distributions as statistical models for stock prices. The Journal of Business 47 (2), 244-80.

Buckley, I., Saunders, D., Seco, L., 2008. Portfolio optimization when asset returns have the gaussian mixture distribution. European Journal of Operational Research 185 (3), 1434-1461.

Calvet, L. E., Fisher, A. J., 2004. How to forecast long-run volatility: Regime switching and the estimation of multifractal processes. Journal of Financial Econometrics 2 (1), 49-83.

Celeux, G., Hurn, M., Robert, C. P., 2000. Computational and inferential diδculties with mixture posterior distributions. Journal of the American Statistical Association 95 (451), 957-970.

Chib, S., 1996. Calculating posterior distributions and modal estimates in markov mixture models. Journal of Econometrics 75 (1), 79-97.

Chopra, V. K., Ziemba, W. T., 1993. The effect of errors in means, variances, and covariances on optimal portfolio choice. Journal of Portfolio Management 19, 6-11.

Dickinson, J. P., 1974. The reliability of estimation procedures in portfolio analysis. Journal of Financial and Quantitative Analysis 9 (03), 447-462.

Fama, E. F., 1965. The behavior of stock-market prices. The Journal of Business 38 (1), pp. 34-105.

Fruhwirth-Schnatter, S., 2001. Markov chain monte carlo estimation of classical and dynamic switching and mixture models. Journal of the American Statistical Association 96 (453), 194-209.

Geweke, J., 2007. Interpretation and inference in mixture models: Simple mcmc works. Computational Statistics and Data Analysis 51 (7), 35293550.

Hamilton, J., 2005. Regime-switching models. URL: dss.ucsd.edu/ jhamilto/palgrav1.pdf.

Hamilton, J. D., 1989. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57 (2), 357-384.

Harvey, C., Liechty, J., Liechty, M., Muller, P., 2010. Portfolio selection with higher moments. Quantitative Finance 10 (5), 469-485.

Harvey, C. R., Siddique, A., 2000. Conditional skewness in asset pricing tests.Journal of Finance 55 (3), 1263-1295.

Jasra, A., Holmes, C. C., Stephens, D. A., 2005. Markov chain monte carlo methods and the label switching problem in bayesian mixture modeling. Statistical Science 20 (1), 50-67.

Jobson, J. D., Korkie, B., 1980. Estimation for markowitz efficient portfolios. Journal of the American Statistical Association 75 (371), 544-554.

Jondeau, E., Rockinger, M., 2006. Optimal portfolio allocation under higher moments. European Financial Management 12 (1), 29-55.

Kim, C.-J., Piger, J., Startz, R., 2008. Estimation of markov regimeswitching regression models with endogenous switching. Journal of Econometrics 143 (2), 263-273.

Kraus, A., Litzenberger, R. H., 1976. Skewness preference and the valuation of risk assets. Journal of Finance 31 (4), 1085-1100.

Krolzig, H.-M., 1997. Markov-switching vector autoregressions : modelling, statistical inference, and application to business cycle analysis. Springer.

Lucas, R. E., 1978. Asset prices in an exchange economy. Econometrica 46 (6), 1429-1445.

Markowitz, H., 1952. Portfolio selection. Journal of Finance 7, 77-91.

Michaud, R. O., Michaud, R. O., 2008. Efficient asset management: A practical guide to stock portfolio optimization and asset allocation.

Peiro, A., 1999. Skewness in financial returns. Journal of Banking and Finance 23 (6), 847 - 862.

Rabiner, L. R., 1989. A tutorial on hidden markov models and selected applications in speech recognition. In: Proceedings of the IEEE. 257-286.

Roman, D., Mitra, G., Spagnolo, N., 2010. Hidden markov models for financial optimization problems. IMA Journal of Management Mathematics 21 (2), 111-129.

Scherer, B., 2002. Portfolio resampling: Review and critique. Financial Analysts Journal 58 (6), 98-109. Sims, C. A., Zha, T., 2006. Were there regime switches in u.s. monetary policy? American Economic Review 96 (1), 54-81.

Turner, C. M., Startz, R., Nelson, C. R., 1989. A markov model of heteroskedasticity, risk, and learning in the stock market. Journal of Financial Economics 25 (1), 3-22.