Portfolio Risk Question

[hershey220]

In the JAM study not in section 2, page 11, it says that "the number of covariance terms is N(N-1)/2..."

Then later on page 15, it says "This reduces the number of parameters from N(N+1)/2..."

Should these two be different or is it a typo? One says covariance and the other says parameters so it may be correct, but they just look too similar.

[campbell]

The first one is the number of pairs of different assets, which is N choose 2, (or, you have N choices for the first asset, N-1 choices for the second asset, and then divide by 2 because order doesn't matter).

The parameters are because you have the covariances AND the variances to deal with. So that's N*(N-1)/2 + N = (N^2 - N)/2 + (2N)/2 = (N^2 + N)/2 = N(N+1)/2