You are currently only invested in the Natasha Fund (aside from risk-free securities). It has an expected return of 15% with a volatility of 22%. Currently, the risk-free rate of interest is 3.1%. Your broker suggests that you add Hannah Corporation to your portfolio. Hannah Corporation has an expected return of 20%, a volatility of 60%, 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, 65% is in the Natasha Fund and 35% 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 16.032% 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?

d. Calculate the Sharpe ratio of each of the three portfolios. What portfolio weight in Hannah stock maximizes the Sharpe ratio?

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