At Quantorbust Inc., you believe a statistical $2-$factor model is accurate. You can buy and sell

very large well$-$diversified portfolios like A and B$,$ with expected excess returns and factor

betas:

a$)$ Find the no$-$arbitrage values of the factor premia, P$1$ and P$2$ consistent with the APT and your

estimates

b$)$ Your active management team evaluates a large active universe $C.$ They predict $E(R_c)-RF=$

$0\mathrm{.}19$ and estimate C$\text{'}$s betas as $1=1\mathrm{.}5,2=1\mathrm{.}1?$ Should you long or short C$?$

c$)$ Construct a simple arbitrage portfolio, give the long and the short portfolio betas $1$ and $2,$

and the total portfolio betas and expected return. What is the expected return per $ invested in

the long portfolio? What is the variance of the arbitrage portfolio?

$E(R$ per $ long $)=$

$V(R)=$

d$)$ Realistically, even if the $2-$factor model is correct, name two sources of remaining risk in your

arbitrage portfolio