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An outperforming investment strategy under fractional Brownian motion

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  • Liu, Qiang
  • Xiang, Yun
  • Zhao, Yonghong

Abstract

Kelly criterion, equivalent to Merton’s lifetime portfolio selection with the Bernoulli utility, maximizes the expected return of investments. This paper derives the Kelly optimal fraction of investment under fractional Brownian motions (fBM), which intriguingly depends on the investing horizon, and uses it to gain superior investment performance. The proposed strategy invests in the risky asset according to the Kelly fraction when the fBM increments are positively correlated, but otherwise holds the risk-free asset instead. For the major stock indices in the US, Hong Kong, and China as well as both a small-cap stock and a large-cap stock in the US, the new Kelly strategy outperforms empirically the original strategy under Brownian motions. The interesting result implies that fBM can be a model of asset returns, and the Kelly fraction under fBM provides fund managers with an alternative method for asset allocations.

Suggested Citation

  • Liu, Qiang & Xiang, Yun & Zhao, Yonghong, 2019. "An outperforming investment strategy under fractional Brownian motion," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 505-515.
    • Handle: RePEc:eee:ecofin:v:47:y:2019:i:c:p:505-515
    DOI: 10.1016/j.najef.2018.06.009
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    Cited by:

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    More about this item

    Keywords

    Kelly fraction; Fractional Brownian motion; Investing-horizon dependence; Kelly investing strategy; Lifetime portfolio selection;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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