Staff Reports

Procyclical Leverage and Value-at-Risk

Previous title: “Financial Intermediary Leverage and Value-at-Risk”
July 2008Number 338
Revised August 2013
JEL classification: G21, G32

Authors: Tobias Adrian and Hyun Song Shin

The availability of credit varies over the business cycle through shifts in the leverage of financial intermediaries. Empirically, we find that intermediary leverage is negatively aligned with the banks' value-at-risk (VaR). Motivated by the evidence, we explore a contracting model that captures the observed features. Under general conditions on the outcome distribution given by Extreme Value Theory (EVT), intermediaries maintain a constant probability of default to shifts in the outcome distribution, implying substantial deleveraging during downturns. For some parameter values, we can solve the model explicitly, thereby endogenizing the VaR threshold probability from the contracting problem.

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