Conditional coverage and its role in determining and assessing long-term capital requirements

We define the vector of conditional coverage values generated over the business cycle by a constant capital figure. Using a convenient analytical framework, we explore its properties and propose two applications based on it. For the former, we state a result that links the concepts of conditional and unconditional solvency and offers an alternative interpretation of the unconditional capital. For the latter, we propose using the minimum of the conditional coverage vector in the determination of long-term capital requirements, as well as using its minimum and its standard deviation in the long-term assessment of a given capital figure. Both applications are illustrated empirically. The entire analysis can be understood as an attempt to recognize and incorporate capital cyclicality into the measurement and analysis of default risk.