$3.3$ Stocks $($A$,$ B$,$ and C$)$ and $2$ common risk factors $(1$ and $2)$ have the following relationship:

E$($RA$)=(1\mathrm{.}0)\backslash$lambda $1+(0\mathrm{.}7)\backslash$lambda $2$

E$($RB$)=(0\mathrm{.}6)\backslash$lambda $1+(0\mathrm{.}5)\backslash$lambda $2$

E$($RC$)=(0\mathrm{.}8)\backslash$lambda $1+(0\mathrm{.}6)\backslash$lambda $2$

A$)$ If $\backslash$lambda $1=3\%$ and $\backslash$lambda $2=2\%,$ what are the prices expected next year for each of the stocks? Assume that all three stocks currently sell for $$20$ and will not pay dividend in the next year.

B$)$ Suppose that you know that next year the prices for Stocks A$,$ B$,$ and C will actually be $$42\mathrm{.}32,$ $$41\mathrm{.}91,$ and $$46\mathrm{.}61.$ Assume that you can use the proceeds from any necessary short sale. Determine the riskless, arbitrage investment to take advantage of these mispriced securities$.$

C$)$ What is the profit from your investment?