Consider the following information about a risky portfolio that you manage and a risk$-$free asset: $E(r_P)=8\%,P=15\%,r_f=2\%.$

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 $8\%.$ 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 $12\%.$ Which client is more risk averse?

Answer is complete but not entirely correct.

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Required C

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 $8\%.$ What proportion should she invest in the risky portfolio, $P,$ and what proportion in the risk$-$free asset?

$\backslash$table$[[$Risky portfolio,$8,\%$