Exploring the use of the Kelly criterion for Basel capital requirement: An optimal and countercyclical approach

Abstract

The Basel capital is a ‘margin’ requirement imposed by regulators to cushion banks against extreme losses, and is a function of value-at-risk. The way banks adjust their balance sheets to maintain the requirement is equivalent to leverage targeting that has been shown to cause procyclical risk. The 2008 crisis revealed that Basel 2 capital was insufficient but the industry believes the current Basel III requirements are too high for sustainable business. Is there an optimal capital? Balance sheet rebalancing with a target leverage can be described by a multiplicative game/process. Most players will lose even if the game has a positive expectation because excessive leverage brings the majority to ruin over time and the system achieves a ‘winner takes all’ effect. Fortunately, the Kelly criterion provides an optimal leverage that prevents this. Using empirical data for simulation, we show that the Kelly criterion gives an optimal capital vis-à-vis Basel 2, Basel 2.5 and expected shortfall. This framework provides the best survival strategy over the economic cycle. The article suggests how this can be applied for an actual bank. Moreover, a Kelly-based capital is potentially countercyclical, which addresses procyclical risks and could also reinforce the central bank's monetary policy transmission mechanism.