Problem $12-10$ APT

Assume that the returns on individual securities are generated by the following two$-$

factor model:

$R_{it}=E(R_{it})+{}_{ij}{F}_{1t}+{}_{i2}{F}_{2t}$

Here:

$R_{it}$ is the return on Security $i$ at Time $t.$

$F_1$ and $F_{2t}$ are market factors with zero expectation and zero covariance.

In addition, assume that there is a capital market for four securities$,$ and the capital

market for these four assets is perfect in the sense that there are no transaction costs

and short sales $($i$.$e$.,$ negative positions$)$ are permitted. The characteristics of the four

securities follow:

a$.$ Construct a portfolio containing $($long or short$)$ Securities $1$ and $2,$ with a return that

does not depend on the market factor, $F_1,$ in any way $($Hint$.$ Such a portfolio will have

${}_1=0.)($A negative answer should be indicated by a minus sign. Do not round

intermediate calculations.$)$

a$-1.$ Compute the expected return and $$ coefficient for this portfolio. $($Do not round

intermediate calculations and enter your expected return answer as a percent.

Leave no cells blank $-$ be certain to enter $"0"$ wherever required.$)$

b$.$ Construct a portfolio containing Securities $3$ and $4,$ with a return that does not

depend on the market factor, $F_1,$ in any way. $($A negative answer should be

indicated by a minus sign. Do not round intermediate calculations and round your

answer to $1$ decimal, e$.$g$.,32\mathrm{.}1.)$

b$-1.$ Compute the expected return and ${}_2$ coefficient for this portfolio. $($Do not round

intermediate calculations and enter your expected return answer as a percent.

Leave no cells blank $-$ be certain to enter $"0"$ wherever required.$)$

Answer is complete but not entirely correct.