There are two stocks: A and B$,$ and Treasury Bill $($TB$).$ The parameters of these securities are following:

Expected Return Standard Deviation Correlation with Stock A

Stock A $12\%15\%1$

Stock B $15\%26\%0\mathrm{.}3$

TB $3\%00$

a$.(20$ pts$)$ If you need an expected return of $13\%$ and you only have the access to the three securities above, what is your optimal portfolio composition? What is the standard deviation of your portfolio?

b$.(15$pts$)$ If you need an expected return of $13\%$ and you only have the access to the two stocks above $($but no access to TB$),$ what is your portfolio composition? What is the standard deviation of your portfolio?