Stress tests and risk capital

Paul H. Kupiec

Journal of Risk

Abstract: ABSTRACT For many financial institutions, "stress tests" are an important input into processes that set risk capital allocations. In the current regulatory environment, two distinct model-based approaches for setting regulatory capital requirements include stress test components. The Basle internal models approach used by US banking regulators requires stress tests to augment VaR-based capital requirements. The US Congress has mandated that the regulatory risk-based capital requirements of the government-sponsored housing enterprises be based upon a stress test alone. This paper investigates the formal link between stress tests and risk capital in the context of an equilibrium model of a firm's capital structure. Two common approaches used to allocate capital under a stress test are examined. The results demonstrate that the stress testing approaches do not solve for an equity capital allocation that protects against default in stress scenarios. One approach produces biased estimates of the optimal debt-equity funding mix. The alternative approach estimates the minimum value of a portfolio of risk-free bonds that will "hedge" or fully insure stress scenario exposures. Neither approach estimates the equity component of an optimal capital structure. Because stress test procedures do not estimate the optimal debt-equity funding mix, stress test and VaR-based estimates of risk capital are not comparable. A modified stress test procedure can be used to set optimal equity capital allocations using stress test techniques that are comparable with VaR-based capital measures.

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