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

$19\%.$ Currently, the risk$-$free rate of interest is $3\mathrm{.}2\%.$ Your broker suggests that you add Hannah Corporation to your portfolio. Hannah

Corporation has an expected return of $21\%,$ a volatility of $58\%,$ 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 $15\mathrm{.}029\%$ 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.