Mark Harrywitz proposes to invest in two shares, X and Y$.$ He expects a return of $12\%$ from X and $8\%$

from Y$.$ The standard deviation of returns is $8\%$ for X and $5\%$ for Y$.$ The correlation coefficient between

the returns is $0\mathrm{.}2.$

a$.$ Compute the expected return and standard deviation of the following portfolios: $(50$; $50),(25$;

$75),(75$; $25).$

b$.$ Sketch the set of portfolios composed of X and Y$.$

c$.$ Suppose that Mr$.$ Harrywitz can also borrow or lend at an interest rate of $5\%.$ Show on your

sketch how this alters his opportunities.

d$.$ Given that he can borrow or lend, what proportions of the common stock portfolio should be