The financial crisis and the shadow price of bank capital

We employ parametric forms of directional distance functions to obtain shadow prices of bank equity capital for listed and unlisted banks. We exploit cost, revenue and profit maximisation as the optimisation criteria to derive pricing rules, which allow us to find shadow prices for both inputs and outputs by explicitly accounting for the bank’s capital structure choices and hence risk-taking behaviour. We show how knowledge of one input price can be used to price outputs and how knowledge of one output price can be used to price inputs along with information on input and output quantities. We also show how information on total cost or revenue can be used to shadow price inputs and outputs, respectively. We obtain some striking results highlighting the perils of overambitious balance sheet expansions supported by excessive leverage. More specifically, we show that shadow prices for equity capital had reached abnormally high levels in the years leading up to the subprime crisis in the US indicative of excessive risk-taking behaviour.