You are currently only invested in the Natasha Fund $($aside from risk$-$free securities$).$ It has an expected return

of $14\%$ with a volatility of $18\%.$ Currently, the risk$-$free rate of interest is $3\mathrm{.}1\%.$ Your broker suggests that you

add Hannah Corporation to your portfolio. Hannah Corporation has an expected return of $20\%,$ a volatility of

$61\%,$ and a correlation of $0($zero$)$ with the Natasha Fund.

a$.$ Calculate the required return of Hannah stock. Is your broker right?

b$.$ You follow your broker's advice and make a substantial investment in Hannah stock so that, considering only

your risky investments, $60\%$ is in the Natasha Fund and $40\%$ is in Hannah stock. When you tell your finance

professor about your investment, he says that you made a mistake and should reduce your investment in

Hannah. Recalculate the required return on Hannah stock. Is your finance professor right?

c$.$ You decide to follow your finance professor's advice and reduce your exposure to Hannah. Now Hannah

represents $11\mathrm{.}895\%$ of your risky portfolio, with the rest in the Natasha fund. Recalculate the required return on

Hannah stock. Is this the correct amount of Hannah stock to hold?

Hint: Make sure to round all intermediate calculations to at least five decimal places.