Stella, Fabio and Ventura, Alfonso (2010): Defensive online portfolio selection. Forthcoming in: Int. J of Financial Markets and Derivatives
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The class of defensive online portfolio selection algorithms,designed for ﬁ nite investment horizon, is introduced. The Game Constantly Rebalanced Portfolio and the Worst Case Game Constantly Rebalanced Portfolio, are presented and theoretically analyzed. The analysis exploits the rich set of mathematical tools available by means of the connection between Universal Portfolios and the Game- Theoretic framework. The empirical performance of the Worst Case Game Constantly Rebalanced Portfolio algorithm is analyzed through numerical experiments concerning the FTSE 100, Nikkei 225, Nasdaq 100 and S&P500 stock markets for the time interval, from January 2007 to December 2009, which includes the credit crunch crisis from September 2008 to March 2009. The results emphasize the relevance of the proposed online investment algorithm which signi ﬁ cantly outperformed the market index and the minimum variance Sharpe-Markowitz’s portfolio.
|Item Type:||MPRA Paper|
|Original Title:||Defensive online portfolio selection|
|Keywords:||on-line portfolio selection; universal portfolio; defensive strategy|
|Subjects:||D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty
C - Mathematical and Quantitative Methods > C0 - General
D - Microeconomics > D9 - Intertemporal Choice and Growth > D90 - General
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
|Depositing User:||F Stella|
|Date Deposited:||10. Sep 2011 14:39|
|Last Modified:||14. Feb 2013 11:00|
Acton, F. Numerical methods that work. Harper-Row, New York, 1970.
Algoet, P. H. and Cover, T. Asymptotic optimality and asymptotic equipartition properties of log-optimum investment. Annals of Probability, 2(16):876 — 898, 1988.
Auer, P. and Warmuth, M. K. Tracking the best disjunction. In 36th Annual Symposium on Foundations of Computer Science, pages 312 — 321, 1998.
Bell, R. and Cover, T. M. Competitive optimality of logarithmic investment. Mathematics of Operations Research, 5(2):161 — 166, 1980.
Blum,A. and Kalai,A. Universal portfolios with and without transaction costs. Machine Learning, 30(1):23 — 30, 1998.
Borodin, A., El-Yaniv, R. and Gogan, V. On the competitive theory and practice of portfolio selection. In Proceedings of the Latin American Theoretical INformatics (Latin), 2000.
Browne, S. The return on investment from proportional portfolio strategies. Advances in Applied Probability, 30(1):216 — 238, 1998.
Cover, T. M. Universal portfolios. Mathematical Finance, 1(1):1 — 29, 1991.
Cover, T. M. Elements of Information Theory, Chapter 15, Information Theory and the Stock Market. John Wiley, New York, 1991.
Cover, T. M. and Ordentlich, E. Universal portfolios with side information. IEEE Transactions on Information Theory, 42(2):348 — 363, 1996.
Cross, J. E. and Barron, A. R. Eﬃcient universal portfolios for past dependent target classes. Mathematical Finance, 13(2):245 — 276, 2003.
Evstigneev, I. V. and Schenk-Hoppè, K. R. From rags to riches: on constant proportions investment strategies. Journal of Theoretical and Applied Finance, 5(6):563 — 573, 2002.
Fagiuoli, E., Stella, F. and Ventura, A. Constant rebalanced portfolios and side information. Accepted for publication in Quantitative Finance, 2(7):161 — 173, 2007.
Gaivoronski,A.andStella,F. Stochastic nonstationary optimization for ﬁnding universal portfolios. Annals of Operations Research, 100:165 — 188, 2000.
Gaivoronski, A. and Stella, F. On-line portfolio selection using stochastic programming. Journal of Economic Dynamics and Control, 27(6):1013 — 1014, 2003.
Helmbold, D. P., Schapire, R. E., Singer, Y. and Warmuth, M. K. On-line portfolio selection using multiplicative updates. In International Conference on Machine Learning, pages 243 — 251, 1996.
Herbster, M. and Warmuth, M. Tracking the best expert. In Proceedings of the Twelfth International Conference on Machine Learning, pages 286 — 294, 1995.
Markowitz, H. Portfolio selection. The Journal of Finance, 7(1):77 — 91, 1952.
Merton, R.C. Continuous-Time Finance Blackwell Publishing, Malden, 1990.
Murphy, A.H. and Epstein, E.S.Veriﬁcation of probabilistic predictions: A brief review. Journal of Applied Meteorology, 80(6):748 — 755, 1967.
Shafer, G. and Vovk, V. Probability and Finance: It’s Only a Game! Wiley, New York, 2001.
Singer, Y. Switching portfolios. Journal of Neural Systems, 8(4):445 — 455, 1997.
Ventura, A. Online computational algorithms for ﬁnancial markets. PhD thesis, Universita ’ degli Studi di Milano-Bicocca, 2006.
Vovk, V. and Nouretdinov, I. and Takemura, A. and Shafer, G. Defensive forecasting for linear protocol. The Game-Theoretic Probability and Finance Project, Working Paper 10, 2005.
Vovk, V. and Takemura, A. and Shafer, G. Defensive forecasting. The Game-Theoretic Probability and Finance Project, Working Paper 8, 2005.
Vovk,V. and Watkins,C. Universal portfolio selection. In Proceedings of the 11th Annual Conference on Computational Learning Theory, pages 12 — 23, 1998.