Dependence Models and the Portfolio Effect

This paper describes efforts to estimate the "portfolio effect" -- the diversification benefit from assembling a portfolio - by simulating the implied portfolio-level capital safety standard for various contract-level capital safety standards. The results showed that apparently aggressive contract-level capital standards still implied conservative portfolio-level capital safety standards. Taken at face value, this would have had a dramatic impact on pricing decisions. However, the method used to generate the simulated contract outcomes -- the Normal copula -- was found to generate asymptotically independent tail samples, thus understating the tail of the portfolio outcome distribution. Tail-based risk measures were, therefore, understated as well.