Impact of Factor Models on Portfolio Risk Measures: A Structural Approach

Abstract

This paperanalyzes the impact of several popular factor models on the calculation of value-at-risk (VaR) for the loss of a credit portfolio with many obligors. The study covers linear and nonlinear factor models focusing on the importance of tail dependence. The financial crisis, which was an example of an extreme tail event, showed the need for models other than the Gaussian model. We show that, even when controlling for correlation and fat marginal tails among models, the tail dependence has an important impact on VaR and asset allocation. We use the central limit theorem to approximate the loss distribution conditional on the common factors. The efficient frontier and portfolio allocation are provided by optimizing a portfolio of corporate loans. We give evidence that the Gaussian factor model can lead to portfolios with a misleading optimal risk–return trade- off because it does not capture extreme events adequately.