Application of Bootstrap Method for Portfolio Analysis

Aneta Zglińska-Pietrzak

doi:https://doi.org/10.59139/ps.2012.03.3

Aneta Zglińska-Pietrzak Uniwersytet Łódzki Przegląd Statystyczny. Statistical Review, vol. 59, 2012, 3, pages: 246-258 Published online: 30 September 2012 DOI https://doi.org/10.59139/ps.2012.03.3

529 Views 27 Downloads

ARTICLE

(Polish) PDF

ABSTRACT

This paper presents Markowitz’s mean-variance portfolio optymalization theory with and without bootstrap simulations. It is assumed that means and covariances of the assets returns are known and the variance with respect to a fixed expected return is minimized. It is concluded that there are significant differences between portfolios with and without bootstrap method and that the resampling data leads to asset allocations that are less risky. This methodology is applied in the Warsaw Stock Exchange.

KEYWORDS

bootstrap simulations, portfolio analysis

REFERENCES

[1] Berkowitz J., Kilian L., (2000), Recent developments in bootstrapping time series, Econometrics Reviews, vol. 19, 1-48.

[2] Domanski Cz., Pruska K., (2000), Nieklasyczne metody statystyczne, PWE Warszawa.

[3] Efron B., (1979), Bootstrap methods: another look at the jackknife, Annals of Statistics, no. 7, 1-26.

[4] Efron B, Thbshiriani R. J., (1993), The Introduction to the Bootstrap, Chapman&Hall New York.

[5] Hall P., (1992), The Bootstrap and Edgeworth Expansion, New York, Springer-Verlag.

[6] Haugen R.A., (1996), Teoria nowoczesnego inwestowania. Obszerny podrecznik analizy portfelowej, WIG-PRESS Warszawa.

[7] Horowitz J.L., (2001), The Bootstrap and Hypothesis Tests in Econometrics, Journal of Econometrics, vol. 100, 37-40.

[8] Lai T.L., Xing H., Chen Z., (2011), Mean-Variance portfolio Optymalization when Means and Covariances are Unknown, The Annals of Applied Statistics, vol. 5, no. 2A, 798-823.

[9] Li H., Maddala G.S., (1996), Bootstrapping time series models, Ekonometric Reviews, vol. 15, 115-158.

[10] Markowitz H., (1952), Portfolio selection, Journal of Finance, vol. 7, no. 1, 77-91.

[11] Markowitz H., Usmen N., (2003), Resampled Frontiers versus Diffuse Bayes: An Experiment, Journal of Investment Management, vol. 1 no. 4, 9-25.

[12] Michaud R.O., (1998), Efficient Asset Management: A Practical Guide to Stock Portfolio Optymalization and Asset Allocation, Massachusetts: Harvard Bussiness School Press.

[13] Pascual L., Romo J., Ruiz E., (2000), Forecasting returns and volatilities in GARCH processes using the bootstrap, Working papers 00-63(31), Universidad Carlos III de Madrid, Spain.

[14] Shanken J., (1996), Statistical methods in tests of portfolio efficiency: a synthesis. In: Handbooks of Statistics: Statistical Methods in Finance, edited by G. S. Maddala and C. R. Rao, 693-711, North-Holland.

[15] Thombs L.A., Schucany W.R., (1990) Bootstrap prediction intervals for autoregressions, Journal of the American Statistical Association, 85, 486-492.

[16] Vlaar P.J.G., (2000), Value at risk models for Dutch bond portfolios, Journal of Banking&Finance, vol. 24, 1131-1154.

[17] Zhidong Bai, Huixia Liu, Wing-Keung Wrong (2009), On the Markowitz mean-variance analysis of self-financing portfolios, RMI Working Paper no. 09/02.