Kelly trading and expected utility

We study intertemporal hedging of parameter risk in a continuous-time portfolio problem with stochastic investment opportunities. Under Brownian uncertainty, we derive conditions under which an optimal expected power-utility strategy has a maximal instantaneous Sharpe ratio, or equivalently is a Kelly strategy. In general, the optimal power-utility strategy is not a Kelly strategy, because it contains an intertemporal hedge against fluctuations in the maximal instantaneous Sharpe ratio. Nevertheless, under relevant collinearity or diagonal conditions, each component of the optimal strategy can be expressed as a scaling of the corresponding component of the growth-optimal Kelly strategy. In this sense, the power-utility strategy provides a parsimonious modification of Kelly leverage, although the adjustment need not be economically small in multi-asset environments. The modification is consistent with time-diversification and provides a possible channel through which relative risk aversion inferred from observed leverage may depend on the investment horizon.