Hi, guys Would like to ask you a simple but confusing question? As everybody know, the default correlation affects the expected value of loss in each tranches of CDO. I would like to ask you whether the default correlation affects the total expected value of loss ? My answer is not.Thanks for your comments.Lj

I think you are right. Default correlation doesn't affect the total expected value of loss on the portfolio, because the total loss is a linear combination of the individual losses: P = \sum_i {c_i * A_i} ==> L[P] = \sum_i {c_i * L(A_i)} ==> EL[P] = \sum_i {c_i * EL (A_i)}where A_i is the i-th asset (CDS, bond etc.), L[P] is the total loss on the portfolio, L(A_i) is the loss on the i-th asset and EL[P] is the total expected loss.In more intuitive words, the total expected value doesn't depend on the shape of the loss density function (which depends on the correlation structure), but that shape affects the expected loss on a single tranche, as you can easily see: for example, supersenior and junior tranches EL will be affected by a change in the shape (change of correlation) of the right and the left tails of the loss density function respectively, while the total expected value will remain the same, given that the marginal expected losses of all the assets are unchanged.

Thanks for your comments. But I think that the unexpected loss will be affected by the correlation.LJ

Of course. Because whatever definition of unexpected loss you are using (for example the loss in excess of the mean), it will be related to the shape of the loss distribution function (second and higher moments), which in turn is related to the correlation: higher is the correlation, wider is the loss probability density function. So approximately unexpected loss of the portfolio is affected by correlation in a quite similar way to expected loss in a senior tranche.

Thanks a lot.