Michel Dacorogna, Tail-Dependence an Essential Factor for

Influence of Correlation on RACLet us take the same risk twice (lognormally distributed, m=10 ands=1) and bundle them in a portfolio.Let us vary the correlation between the risks from 0 to 0.90.Here are the various diversification benefits, D, in percent:RACPD 1 RACwhere RAC P is theportfolio RAC andRAC i are the RAC’sof the various risks.iiDiversification Benefits40%35%30%25%20%15%10%5%0%0 0.3 0.6 0.9Correlation CoefficientTail DependenceMichel M. DacorognaETH Risk Center Workshop, Oct. 25-26, 20127Dependence is not Always LinearWe have learned to model dependence through linear correlation.The whole modern portfolio theory is based on correlation.Often dependence increases when diversification is most needed:in case of stress. It is thus non-linear.It is possible to use the copulas instead of linear correlation tomodel dependences (copula=“generalized dependence structure”as opposed to “linear dependence”=correlation).The dependence structure will influence greatly the needs for RACand the diversification benefits one can obtain.In the following, we present a statistical study of variousdependence structures and their influence on diversification.Tail DependenceMichel M. DacorognaETH Risk Center Workshop, Oct. 25-26, 20128