Problem $12-10$ APT

Assume that the returns on Individual securitles are generated by the following two$-$

factor model:

$R_{\frac{?}{t}}$ Is the return on Security $/$ at Time $t$

$F_{1t}$ and $F_{2t}$ are market factors with zero expectation and zero covarlance.

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 $($l$.$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, $F_{1t},$ In any way $($Hint$.$ Such a portfolio will have

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

Intermedlate calculations.$)$

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

Intermedlate 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 Securitles $3$ and $4,$ with a return that does not

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

Indlcated by a minus sign. Do not round Intermedlate calculations and round your

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

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

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

Leave no cells blank $-$ be certaln to enter $"0"$ wherever requlred.$)$