Assume that your client would prefer to invest her entire wealth into a portfolio with an annual risk premium of $12\%$ and a standard deviation of $20\%.$ You have constructed a risky portfolio with an expected return of $15\%$ and a standard deviation of $26\%.$ T$-$Bills are currently yielding $2\%.$ What is the optimal allocation, $y,$ to the risky portfolio given your client's risk preferences? What is the expected return and standard deviation on your client's optimal complete portfolio?

Multiple Choice

$y=0\mathrm{.}55$;$E(r_c)=0\mathrm{.}08$;${}_C=0\mathrm{.}11$

$y=0\mathrm{.}64$;$E(r_c)=0\mathrm{.}10$;${}_c=0\mathrm{.}17$

$y=0\mathrm{.}64$;$E(r_c)=0\mathrm{.}08$;${}_c=0\mathrm{.}10$

$y=0\mathrm{.}74$;$E(r_c)=0\mathrm{.}13$;${}_c=0\mathrm{.}21$