$(35$ pts$)$ There are two stocks: A and B$,$ and Treasury Bill $($TB$).$ The parameters of these securities are following:

$\backslash$table$[[,$Expected Return,Standard Deviation,$\backslash$table$[[$Correlation with Stock$],[$A$]]],[$Stock A$,12\%,15\%,1],[$Stock B$,15\%,26\%,0\mathrm{.}3],[$TB$,3\%,0,0]]$

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?