You manage a risky portfolio with an expected rate of return of $12\%$ and a standard

deviation of $8\%.$ The T$-$bill rate is $1\%.$ Suppose that your client prefers to invest

in your fund a proportion of his wealth that minimizes the overall portfolio standard

deviation subject to the constraint that the overall portfolio's mean be at least $8\%.$

What is the proportion?

What is the standard deviation of the resulting portfolio?

What is its reward$-$to$-$variability ratio?

What is your client's risk aversion? $($Hint: Slide $4-63)$

What is the maximum level of risk aversion for which your original risky portfolio

is still preferred to T$-$bills?