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.
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