ABSTRACT
In this paper, Magnus Holm and Hans-Peter Bermin revisit the foundational Kelly trading strategy in the context of modern financial markets where asset prices can experience discrete jumps—sudden changes in value that are not captured by traditional continuous models. While classical results show that the Kelly strategy (which aims to maximize long-term capital growth) coincides with the portfolio that maximizes the Sharpe ratio when prices evolve smoothly, the authors reveal that this connection breaks down once price jumps are introduced.
They demonstrate that with jumps:
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The growth-optimal Kelly strategy no longer sits on the local efficient frontier defined by the instantaneous Sharpe ratio.
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However, for realistic jump magnitudes (e.g., up to ±25%), the practical differences between Kelly-optimal and Sharpe-optimal allocations remain small.
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A Kelly trader’s allocations tend to react differently to crash risk and asset selection: Kelly strategies are more cautious in the face of crash scenarios and more adventurous when picking high-potential assets compared to Sharpe-based allocations.
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Standard jump models—such as Merton’s—may misestimate bankruptcy risk, especially under leverage, highlighting the need for refined jump frameworks in risk analysis.
Overall, the work extends classical portfolio theory by quantifying how jumps influence long-run growth seekers vs risk-return maximizers, offering both theoretical insights and practical implications for dynamic trading under real-world price discontinuities.