You are given a portfolio of two assets whose returns are jointly normally distributed with the following mean vector and covariance matrix:

Mean vector

0.20

0.10

Covariance matrix

0.08 0.04

0.04 0.06

(a) Compute the 95% VaR of the portfolio if $1 is invested in the first asset and $1 is invested in the second.

(b) Compute the risk-contribution of each asset to the VaR.

(c) Is the current portfolio weighting optimal? If not, suggest a better one.