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 $0\mathrm{.}66\%21\%$

B $0\mathrm{.}887$

C $1\mathrm{.}01016$

a$.$ If $\backslash$sigma M $=17\%,$ calculate the variance of returns of securities A$,$ B$,$ and C$.($Do not round intermediate calculations. Round your answers to the nearest whole number.$)$

Variance

Security A

$0\mathrm{.}055$

Security B

Security C

b$.$ Now assume that there are an infinite number of assets with return characteristics identical to those of A$,$ B$,$ and C$,$ respectively. If one forms a well$-$diversified portfolio of type A securities$,$ what will be the mean and variance of the portfolio$$s excess returns? What about portfolios composed only of type B or C stocks? $($Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number.$)$

Mean Variance

Security A

$6$

$\%$

Security B

$8$

$\%$

Security C

$10$

$\%$

c$.$ Is there an arbitrage opportunity in this market?

multiple choice

Yes

No