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Universal Portfolios

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  • Thomas M. Cover
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    Abstract

    We exhibit an algorithm for portfolio selection that asymptotically outperforms the best stock in the market. Let x i= (x i, x i2 ,…, x im )-super-t denote the performance of the stock market on day i, where x ii is the factor by which the jth stock increases on day i. Let b i= ( bi1 b i2 , b im )-super-t, b; ij > 0, b ij = 1, denote the proportion b ij of wealth invested in the "j" th stock on day i. Then S n= II i-super-n= bi-super-tx i is the factor by which wealth is increased in "n" trading days. Consider as a goal the wealth S n*= max b II i-super-n= 1 b-super-tx i that can be achieved by the best constant rebalanced portfolio chosen after the stock outcomes are revealed. It can be shown that Sn * exceeds the best stock, the Dow Jones average, and the value line index at time "n." In fact, S n* usually exceeds these quantities by an exponential factor. Let x 1, x 2, be an arbitrary sequence of market vectors. It will be shown that the nonanticipating sequence of portfolios db yields wealth such that , for every bounded sequence x 1, x 2…, and, under mild conditions, achieve Copyright 1991 Blackwell Publishers.

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 1 (1991)
    Issue (Month): 1 ()
    Pages: 1-29

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    Handle: RePEc:bla:mathfi:v:1:y:1991:i:1:p:1-29

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    Cited by:
    1. Ormos, Mihály & Urbán, András & Zoltán, Tamás, 2009. "Logoptimális portfóliók empirikus vizsgálata
      [Empirical analysis of log-optimal portfolios]
      ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(1), pages 1-18.
    2. Thorsten Hens & Terje Lensberg & Klaus Schenk-Hoppé & Peter Wöhrmann, 2011. "An evolutionary explanation of the value premium puzzle," Journal of Evolutionary Economics, Springer, vol. 21(5), pages 803-815, December.
    3. MacLean, Leonard C. & Sanegre, Rafael & Zhao, Yonggan & Ziemba, William T., 2004. "Capital growth with security," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 937-954, February.
    4. Stella, Fabio & Ventura, Alfonso, 2010. "Defensive online portfolio selection," MPRA Paper 33279, University Library of Munich, Germany.
    5. Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2003. "Evolutionary Stability of Portfolio Rules in Incomplete Markets," Discussion Papers 03-03, University of Copenhagen. Department of Economics.
    6. Vajda, István & Ottucsák, György, 2006. "Empirikus portfólióstratégiák
      [Empirical portfolio strategies]
      ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 624-640.
    7. Bin Li & Steven C. H. Hoi, 2012. "Online Portfolio Selection: A Survey," Papers 1212.2129, arXiv.org, revised May 2013.
    8. Dokuchaev, N. G. & Savkin, Andrey V., 2004. "Universal strategies for diffusion markets and possibility of asymptotic arbitrage," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 409-419, June.
    9. Foster, Dean P. & Vohra, Rakesh, 1999. "Regret in the On-Line Decision Problem," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 7-35, October.
    10. Kumon, Masayuki & Takemura, Akimichi & Takeuchi, Kei, 2011. "Sequential optimizing strategy in multi-dimensional bounded forecasting games," Stochastic Processes and their Applications, Elsevier, vol. 121(1), pages 155-183, January.
    11. Gaivoronski, Alexei A. & Stella, Fabio, 2003. "On-line portfolio selection using stochastic programming," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 1013-1043, April.
    12. Bin Li & Steven C. H. Hoi, 2012. "On-Line Portfolio Selection with Moving Average Reversion," Papers 1206.4626, arXiv.org.
    13. Kei Takeuchi & Masayuki Kumon & Akimichi Takemura, 2007. "A new formulation of asset trading games in continuous time with essential forcing of variation exponent," Papers 0708.0275, arXiv.org, revised Jan 2010.
    14. A. Borodin & R. El-Yaniv & V. Gogan, 2011. "Can We Learn to Beat the Best Stock," Papers 1107.0036, arXiv.org.
    15. Parkes, David C. & Huberman, Bernardo A., 2001. "Multiagent Cooperative Search for Portfolio Selection," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 124-165, April.
    16. Soumik Pal & Ting-Kam Leonard Wong, 2013. "Energy, entropy, and arbitrage," Papers 1308.5376, arXiv.org.
    17. Masayuki Kumon & Jing Li & Akimichi Takemura & Kei Takeuchi, 2012. "Bayesian logistic betting strategy against probability forecasting," Papers 1204.3496, arXiv.org.
    18. Yoram Singer, 2013. "Switching Portfolios," Papers 1301.7413, arXiv.org.
    19. Eckhard Platen & Renata Rendek, 2010. "Approximating the Numeraire Portfolio by Naive Diversification," Research Paper Series 281, Quantitative Finance Research Centre, University of Technology, Sydney.
    20. Dokuchaev, Nikolai G. & Savkin, Andrey V., 2002. "A bounded risk strategy for a market with non-observable parameters," Insurance: Mathematics and Economics, Elsevier, vol. 30(2), pages 243-254, April.
    21. Luo, Yong & Zhu, Bo & Tang, Yong, 2014. "Simulated annealing algorithm for optimal capital growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 408(C), pages 10-18.
    22. Freund, Yoav & Schapire, Robert E., 1999. "Adaptive Game Playing Using Multiplicative Weights," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 79-103, October.

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