Morgan Stanley Interview Question for Analysts






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1
of 1 vote

The possible values of rho are 0 and 1.
As 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.

- waterwreath February 05, 2013 | Flag Reply
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0
of 2 vote

(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.

- Anonymous April 04, 2010 | Flag Reply
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0
of 0 vote

Thanks for you solutions. But I don't understand your last sentence. Can you explain a little more? what do you mean by set {X,Y,Z}=Ev ?

- oceantin April 04, 2010 | Flag Reply
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0
of 0 votes

v is a random vector (Gaussian distribution). X, Y, and Z are set to the components of the matrix-vector multiplication E v.

- Anonymous April 04, 2010 | Flag


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