An outperforming investment strategy under fractional Brownian motion

Qiang Liu, Yun Xiang and Yonghong Zhao

The North American Journal of Economics and Finance, 2019, vol. 47, issue C, 505-515

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.

Keywords: Kelly fraction; Fractional Brownian motion; Investing-horizon dependence; Kelly investing strategy; Lifetime portfolio selection (search for similar items in EconPapers)
JEL-codes: G10 G11 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecofin:v:47:y:2019:i:c:p:505-515

DOI: 10.1016/j.najef.2018.06.009

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