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Fractal Profit Landscape of the Stock Market

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  • Andreas Gronlund
  • Il Gu Yi
  • Beom Jun Kim

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.

Suggested Citation

  • Andreas Gronlund & Il Gu Yi & Beom Jun Kim, 2012. "Fractal Profit Landscape of the Stock Market," Papers 1205.0505, arXiv.org.
    • Handle: RePEc:arx:papers:1205.0505
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    Cited by:

    1. Wiktor Kolwzan & Agnieszka Skowronek-Gradziel & Teresa Kupczyk & Jozef Ledzianowski, 2022. "Study of the Nature and Dynamics of Processes in Terms of Fractals on the Example of Selected Joint Stock Companies," European Research Studies Journal, European Research Studies Journal, vol. 0(2), pages 172-197.
    2. 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.
    3. repec:ers:journl:v:xxvi:y:2023:i:3:p:78-103 is not listed on IDEAS
    4. Ioana-Andreea Boboc & Mihai-Cristian Dinică, 2013. "An Algorithm for Testing the Efficient Market Hypothesis," PLOS ONE, Public Library of Science, vol. 8(10), pages 1-11, October.

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