Consider the following information about a risky portfolio that you manage and a risk$-$free asset: $E(r_P)=12\%,{}_P=15\%,r_f=4\%.$

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 $7\%.$ What proportion should she invest in the risky portfolio, $P,$ and what proportion in the riskfree asset? $($Do not round intermediate calculations. Round your answer to $2$ decimal place.$)$

b$.$ What will be the standard deviation of the rate of return on her portfolio? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Standard deviation

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?

First client

Second client