Kelly investing with downside risk control in a regime-switching market

The optimal capital growth strategy or Kelly strategy has many desirable properties, such as maximizing the asymptotic long-run growth of capital. However, it is aggressive and can have the considerable short-run risk of losing much of the invested wealth. In this paper, we provide a method to obtain the maximum growth while staying above a specified downside wealth threshold with high probability, where shortfalls below the threshold are penalized with a convex function of shortfall. The financial market is characterized by regimes, where the dynamics of the stochastic regime process is Markovian. Within a regime, the asset prices are lognormal. With the additional model features of regimes and downside risk control, the optimal strategy has a modified Kelly format. The modification requires the assignment of weights to each regime, with the weights incorporating the risk control. The multi-asset problem is reduced to determining the regime weights and the fraction of investment capital allocated to risky assets. The estimation risk is controlled by regime switching and the decision risk is controlled by the downside threshold. The methods are applied to the problem of investing in select sector exchange-traded funds.