Here:

Rit is the return on Security i at Time t$.$

F$1$t and F$2$t 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:

Security $\backslash$beta $1\backslash$beta $2$ E$($R$)$

$11\mathrm{.}7502\mathrm{.}25035\%$

$21\mathrm{.}5002\mathrm{.}75035$

$31\mathrm{.}7501\mathrm{.}25025$

$42\mathrm{.}1001\mathrm{.}50020$

a$.$

Construct a portfolio containing $($long or short$)$ Securities $1$ and $2,$ with a return that does not depend on the market factor, F$1$t$,$ in any way. $($Hint: Such a portfolio will have $\backslash$beta $1=0.)($Do not round intermediate calculations. A negative answer should be indicated by a minus sign.$)$

X$1$

X$2$

a$-1.$

Compute the expected return and $\backslash$beta $2$ 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.$)$

Expected return $\%$

$\backslash$beta $2$

b$.$

Construct a portfolio containing Securities $3$ and $4,$ with a return that does not depend on the market factor, F$1$t$,$ in any way. $($A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

X$3$

X$4$

b$-1.$

Compute the expected return and $\backslash$beta $2$ coefficient for this portfolio. $($Do not round intermediate calculations and enter your expected return answer as a percent. Round your answers to the nearest whole number. Leave no cells blank $-$ be certain to enter $"0"$ wherever required.$)$

Expected return $\%$

$\backslash$beta $2$