Consider the following information about a risky portfolio that you manage and a risk$-$free asset:

$E(r_P)=11\%,{}_P=15\%,r_f=4\%.$

Required:

a$.$ Your client wants to invest a proportion of her total investment budget in your risky fund to provide an expected rate of return on

her overall or complete portfolio equal to $6\%.$ What proportion should she invest in the risky portfolio, $P,$ and what proportion in the

risk$-$free asset?

b$.$ What will be the standard deviation of the rate of return on her portfolio?

c$.$ Another client wants the highest return possible subject to the constraint that you limit his standard deviation to be no more than

$17\%.$ Which client is more risk averse?