Morgan Stanley Interview Question
Analysts(Strange question.) The correlation matrix A = {{1, rho, rho}, {rho, 1, rho}, {rho, rho, 1}} must be symmetric PSD. In this case we can compute the eigenvalues of A directly, which are 1 - rho (twice) and 1 + 2 rho. Both of these quantities must be positive, so -1/2 <= rho <= 1. This restriction is it; if it's satisfied we take a square root E^T E = A and set {X,Y,Z} = E v, where v has a 3D Gaussian distribution.
The possible values of rho are 0 and 1.
- waterwreath February 05, 2013As we know, the correlation matrix of different assets should be positive semi-definite, which means its leading principal minor are all non-negative. Apply this in the question, and it turns out rho can only be 0 or 1.