Assume that security returns are generated by the single$-$index model,

Ri $=\backslash$alpha i $+\backslash$beta iRM $+$ ei

where Ri is the excess return for security i and RM is the market$$s excess return. The risk$-$free rate is $3\%.$ Suppose also that there are three securities A$,$ B$,$ and C$,$ characterized by the following data:

Security $\backslash$beta i E$($Ri$)\backslash$sigma $($ei$)$

A $0\mathrm{.}98\%17\%$

B $1\mathrm{.}3128$

C $1\mathrm{.}71611$

Required:

If $\backslash$sigma M $=12\%,$ calculate the variance of returns of securities A$,$ B$,$ and C$.$

Now assume that there are an infinite number of assets with return characteristics identical to those of A$,$ B$,$ and C$,$ respectively. What will be the mean and variance of excess returns for securities A$,$ B$,$ and C$?$