You manage a risky portfolio with an expected rate of return of $13\%$ and a standard deviation of $30\%.$ The T$-$bill rate is $4\%.$

Stock A $45\%$

Stock B $35\%$

Stock C $20\%$

Suppose that your client decides to invest in your portfolio a proportion y of the total investment budget so that the overall portfolio will have an expected rate of return of $9\%.$

Required:

What is the proportion y$?$

What are your client$$s investment proportions in your three stocks and the T$-$bill fund?

What is the standard deviation of the rate of return on your client$$s portfolio?