Assume that you manage a risky portfolio with an expected rate of return of $12\%$ and a standard deviation of $47\%.$ The T$-$bill rate is $4\%$ A client prefers to invest in your portfolio a proportion $(y)$ that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio's standard deviation will not exceed $35\%.$

Required:

a$.$ What is the investment proportion, $y?$

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

Investment proportion $y$

Investment proportion y $\%$

b$.$ What is the expected rate of return on the overall portfolio?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.