Assume that an economy has $2$ stocks: A and B$.$ Additionally, there is a risk$-$free asset with an expected return of $5\%.$ The expected return of stock A is $10\%,$ with a standard deviation of $20\%.$ The expected return of stock B is $15\%,$ with a standard deviation of $25\%.$ The correlation between both stocks is $0\mathrm{.}135.$ The market capitalization of A is $$240,000,000,$ and the market capitalization of $B$ is $$360,000,000.(10$ points$)$

a$.$ Is a portfolio that invests $40\%$ in $A,60\%$ in $B,$ and $0\%$ in the risk$-$free asset efficient?

b$.$ Is a portfolio that invests $20\%$ in $A,80\%$ in $B,$ and $0\%$ in the risk$-$free asset efficient?

c$.$ If any of the portfolios in the previous two points are inefficient, how much more expected return would we be able to obtain in an efficient portfolio with the same risk as the portfolio in question? What would be the weights in A$,$ B$,$ and the riskfree asset of this efficient portfolio? $($hint: Use the capital market line$)$

You want to create a portfolio with the same expected return as the market, and you have $$2,000$ to invest. You have the following information $(10$ points$)$

$\backslash$table$[[$Asset$,$Investment Beta$],[$Stock A$,800,1\mathrm{.}5],[$Stock B$,,2],[$Stock C$,,1\mathrm{.}2],[$Risk$-$free asset $-500,,]]$

Find the missing values in the table.

$5.$ A stock has an expected return of $10\mathrm{.}45\%,$ its beta is $0\mathrm{.}85,$ and the expected return on the market is $11\mathrm{.}8\%.$ What must the risk$-$free rate be$?(10$ points$)$