Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:C1L-A

Session:

Number:527

Dynamical Portfolio Theory by Nonlinear Bagging Predictors

Kiyoharu Tanaka,  Tomoya Suzuki,  

pp.527-530

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.527

PDF download (512.3KB)

Summary:
In the Markowitz's mean-variance portfolio model, the probability distribution of a future return is composed by the recent historical prices, and then a future return and a future risk are estimated as the mean value and the standard deviation of the distribution. Namely, the future return is predicted by a simple moving average, and the risk is nothing but a historical fluctuation. In this study, to improve the prediction accuracy of the future return, we apply the nonlinear prediction method following local spatial dynamics, and to estimate the future risk, we produce the probability distribution aggregating predicted values by the Bagging algorithm. Then, each risk is reduced by making a portfolio, that is, the portfolio effect. Namely, our method tries to improve the prediction accuracy and to reduce the risk of its prediction error, simultaneously. To confirm the validity of our method, we performed investment simulations. As results, we could obtain higher profit and realize lower risk of investment than the conventional method.

References:

[1] H. M. Markowitz: “Portfolio Selection,” Journal of Finance, Vol.7, No.1, pp.77-91 1952.

[2] L. Breiman: “Bagging Predictors,” Machine Learning, Vol. 24, pp. 123-140, 1996.

[3] D. Haraki, T. Suzuki, H. Hashiguchi, and T. Ikeguchi: “Bootstrap Nonlinear Prediction,” Physical Review E, Vol. 75, 056212, 2007.

[4] K. Nakata and T. Suzuki: “Evaluating the Risk of Nonlinear Prediction with the Bagging Algorithm,” Proc. of NCSP'12, pp. 748-791, 2012.

[5] W. F. Sharpe: “Capital asset prices : A theory of market equilibrium under conditions of risk,” Journal of Finance, Vol. 19, No. 3, pp. 425-442, 1964.

[6] J. D. Farmer and J. J. Sidorowich: “Predicting chaotic time series,” Physical Review Letters, Vol. 59, pp. 845-848, 1987.

[7] T. Suzuki: “Appropriate time scales for nonlinear analyses of deterministic jump systems,” Physical Review E, Vol. 83, No.6, 066203, 2011.