Modeling Diversification and Spillovers of Loan Portfolios’ Losses by LHP Approximation and Copula

Abstract This paper suggests a top-down method for aggregating the economic capital of an entire banking system and decomposing it into loan sectors according to their risk contributions. We model the individual losses of loan sectors by large homogeneous portfolio (LHP) approximation based on multi-factor skew normal credit worthiness and combine them by applying static and dynamic copulas to reflect diversification effects and spillovers across loan sectors. Our method is more efficient and practically useful than typical multi-factor models using numerical integration due to the latency of risk factors in that losses are directly generated by Monte Carlo simulation using copula without knowing any risk factors. As a result of our empirical study on charge-off rates of the U.S. commercial banking system, we find that the residential real estate loan sector is the most affecting as its default risk spills over to the rest of the banking system, and hence its risk contribution to the entire banking system is large. However, the commercial real estate loan and business loan sectors are revealed to be affected sectors whose risk contributions are large, but the losses are mainly due not only to their large exposure size, but also to default contagion from others. The risk contributions of credit cards and other consumer loans as default risk affecting sectors become larger in terms of the recent conditional dependence. Lastly, using time-varying correlation analysis, we find that the subprime mortgage crisis is a systemic event that affects the entire-banking-system, while the commercial real estate and the dotcom bubble crises are sector-wide systemic events.