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Fractal statistical measure and portfolio model optimization under power-law distribution

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  • Wu, Xu
  • Zhang, Linlin
  • Li, Jia
  • Yan, Ruzhen

Abstract

An effective portfolio selection model is constructed on the premise of measuring accurately the risk and return on assets. According to the reality that the tail of returns on assets obey power-law distribution, this paper firstly builds two fractal statistical measures, fractal expectation and fractal variance, to measure the asset returns and risks, inspired by the method of measuring curve length in the fractal theory. Then, by incorporating the fractal statistical measure into the return-risk criterion, a portfolio selection model based on fractal statistical measure is established, namely the fractal portfolio selection model, and the closed-form solution of the model is given. Finally, through empirical analysis we find that the fractal portfolio selection model is effective and can improve investment performance.

Suggested Citation

  • Wu, Xu & Zhang, Linlin & Li, Jia & Yan, Ruzhen, 2021. "Fractal statistical measure and portfolio model optimization under power-law distribution," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).
    • Handle: RePEc:eee:ecofin:v:58:y:2021:i:c:s1062940821001169
    DOI: 10.1016/j.najef.2021.101496
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    Cited by:

    1. Wu, Xu & Wang, Pei-Yu & Wang, Kun, 2023. "The effect of stabilization fund to rescue stock market based on expected return-capita circulation equation," Socio-Economic Planning Sciences, Elsevier, vol. 87(PB).
    2. Xi Zhang & Xu Wu & Linlin Zhang & Zhonglu Chen, 2022. "The Evaluation of Mean-Detrended Cross-Correlation Analysis Portfolio Strategy for Multiple risk Assets," Evaluation Review, , vol. 46(2), pages 138-164, April.
    3. Wang, Xiantao & Zhu, Yuanguo & Tang, Pan, 2024. "Uncertain mean-CVaR model for portfolio selection with transaction cost and investors’ preferences," The North American Journal of Economics and Finance, Elsevier, vol. 69(PA).

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    More about this item

    Keywords

    Portfolio selection model; Power-law distribution; Fractal expectation; Fractal variance;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G19 - Financial Economics - - General Financial Markets - - - Other
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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