Consider two risky stocks, A and B $,$ with expected returns of $21\%$ and $7\%,$ respectively.

Stock A has a standard deviation of $19\%$; Stock B has a standard deviation of $13\%.$ The

correlation between the two stocks is $0\mathrm{.}15.$

a$.)$ Using a spreadsheet, calculate the expected portfolio return and portfolio standard

deviation for the set of portfolios that is feasible with these two stocks. Calculate these

statistics for $11$ portfolios, changing the portfolio weights in increments of $10\%.$ For

example, $0\%A,100\%B$;$10\%A,90\%B$; through $100\%A,0\%B.$ Plot this set of portfolios

on a graph where expected portfolio return is on the $y-$axis and portfolio standard deviation is

on the x $-$axis.

b$.)$ Assume there is a risk$-$free rate of $2\%.$ Solve algebraically for the portfolio weights of A

and $B$ in the optimal risky portfolio. What is the expected return and standard deviation of

this portfolio?

c$.)$ On your graph from a$.),$ draw the capital allocation line $($CAL$)$ that goes from the risk$-$free

rate through the optimal risky portfolio in b$.).$

d$.)$ Imagine an investor that wants to invest in an efficient portfolio with a target standard

deviation of $12\mathrm{.}5\%.$ What are the investor's weights in the optimal risky portfolio and the

risk$-$free rate? What is the expected return of this portfolio?