Financial intermediary leverage and value-at-risk

We study a contracting model of leverage and balance sheet size for financial intermediaries that fund their activities through collateralized borrowing. Leverage and balance sheet size increase together when measured risks decrease. When the loss distribution is exponential, the behavior of intermediaries conforms to the Value-at-Risk (VaR) rule, in which exposure is adjusted to maintain a constant probability of default. In a system context, increased risk reduces the debt capacity of the financial system as a whole, giving rise to amplified de-leveraging by institutions through the chain of repo transactions.