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Fractal Profit Landscape of the Stock Market

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  • Andreas Gronlund
  • Il Gu Yi
  • Beom Jun Kim
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    Abstract

    We investigate the structure of the profit landscape obtained from the most basic, fluctuation based, trading strategy applied for the daily stock price data. The strategy is parameterized by only two variables, p and q. Stocks are sold and bought if the log return is bigger than p and less than -q, respectively. Repetition of this simple strategy for a long time gives the profit defined in the underlying two-dimensional parameter space of p and q. It is revealed that the local maxima in the profit landscape are spread in the form of a fractal structure. The fractal structure implies that successful strategies are not localized to any region of the profit landscape and are neither spaced evenly throughout the profit landscape, which makes the optimization notoriously hard and hypersensitive for partial or limited information. The concrete implication of this property is demonstrated by showing that optimization of one stock for future values or other stocks renders worse profit than a strategy that ignores fluctuations, i.e., a long-term buy-and-hold strategy.

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    File URL: http://arxiv.org/pdf/1205.0505
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1205.0505.

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    Date of creation: May 2012
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    Publication status: Published in PLoS One (7)4 : e33960 (2012)
    Handle: RePEc:arx:papers:1205.0505

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    Web page: http://arxiv.org/

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    1. Andrew W. Lo & Harry Mamaysky & Jiang Wang, 2000. "Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation," NBER Working Papers 7613, National Bureau of Economic Research, Inc.
    2. Toth, Bence & Scalas, Enrico & Huber, Juergen & Kirchler, Michael, 2006. "The value of information in a multi-agent market model," MPRA Paper 341, University Library of Munich, Germany.
    3. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    5. Brad M. Barber & Terrance Odean, 2000. "Trading Is Hazardous to Your Wealth: The Common Stock Investment Performance of Individual Investors," Journal of Finance, American Finance Association, vol. 55(2), pages 773-806, 04.
    6. Stephan Schulmeister, 2007. "The Profitability of Technical Stock Trading has Moved from Daily to Intraday Data," WIFO Working Papers 289, WIFO.
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    Cited by:
    1. Zhong, Li-Xin & Xu, Wen-Juan & Ren, Fei & Shi, Yong-Dong, 2013. "Coupled effects of market impact and asymmetric sensitivity in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2139-2149.

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