Kelly Trading When Asset Prices Have Jumps

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 maximise long-term capital growth) coincides with the portfolio that maximises the Sharpe ratio when prices evolve smoothly, the authors reveal that this connection breaks down once price jumps are introduced.

The growth-optimal Kelly strategy no longer sits on the local efficient frontier defined by the instantaneous Sharpe ratio.

However, for realistic jump magnitudes (e.g., up to ±25%), the practical differences between Kelly-optimal and Sharpe-optimal allocations remain small.

Kelly-optimal allocations respond differently to crash risk and jump dynamics than allocations derived from instantaneous Sharpe considerations.

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 clarifying how price jumps affect the relationship between growth-optimal and Sharpe-optimal strategies, offering both theoretical insight and practical implications for trading under real-world price discontinuities.

Kelly trading when asset prices have jumps

https://link.springer.com/article/10.1007/s10203-025-00561-6