Kelly trading when asset prices have jumps

Abstract If asset prices have no jumps it is known that the growth optimal Kelly strategy lies on the local efficient frontier, that is has maximal instantaneous Sharpe ratio. In this paper we show that, when asset prices have jumps, this property ceases to hold. However, the discrepancy is small for jumps with magnitude less than 25%. Our results further indicate that a Kelly trader fears market crashes but favors stock picking more than a maximal Sharpe trader. We also explain why Merton’s approach to jump modeling is not well suited to study the risk of bankruptcy associated with leverage.