How is Crash Metrics deal

Question

How is Crash Metrics deal?

Answer 1

Crash Metrics deals with any number of underlying through exploiting the high degree of correlation during extreme markets among equities. We can relate the return on the ith stock to the return upon a representative index, x, in a crash by

δS_i/S_i = k_iX,

Here κ_i is a constant crash coefficient. For illustration, if the kappa for stock XYZ is 1.2 this means that while the index falls by 10% XYZ will fall by 12%. Therefore, the crash coefficient permits a portfolio with many underlyings to be interpreted during a crash as a portfolio on a single underlying, the index. Therefore we consider the worst case of

δΠ= F(δS1, ... , δS_N) = F(κ₁xS₁, ... , κ_NxS_N) like our measure of downside risk. Note that it is really just a function of the one variable x and therefore it is very easy to plot change in the portfolio against x, and the return on the index.