Problem $1(30$ points$)$: $($Box method$)$

Assume you hold an equally$-$weighted portfolio of $N=100$ stocks. $($i$.$e$.).$ Variances of individual stock are the same and equal to ${}^{\text{'}}=8.$ Assume all stocks are divided into two groups: group A stocks are from $1-50$ and group B are from $51-100.$ Any pair of stocks from group A have pairwise covariances of $1.$ Any pair of stocks from group B have covariance of $1.$ Stocks from different groups are uncorrelated with each other.

a$)(10$ points$)$ Find contribution to total variance of your equally$-$weighted portfolio from stock variances

b$)(20$ points$)$ Find contribution to total variance of your equally$-$weighted portfolio from stock covariances and calculate total variance of your portfolio.