Exploring the Use of 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 falls in prices of assets held, and is often a function of value-at-risk (VaR). 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 to protect banks against crisis losses, but the industry believes the current Basel 3 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 or process. Most players will lose money even if the game has a positive expectation because excessive leverage causes the majority to get wiped out over time and the system achieves a “winner takes all” effect. Fortunately, the Kelly criterion provides an optimal leverage that prevents this. By using empirical data for balance sheet simulation, we show that the Kelly criterion gives an optimal capital vis-a-vis Basel 2, Basel 2.5 and expected shortfall. This capital approach provides the best survival strategy over the economic cycle. The article suggests how this can be computed in practice for an actual bank. Also the Kelly-based capital is potentially countercyclical, which addresses procyclical risks and could also reinforce the central bank monetary policy transmission mechanism.