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 20%. Currently, the risk-free rate of interest is 2.5%. 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.

You follow your broker's advice and make a substantial investment in Hannah stock so that, considering only your risky investments, 65.0% is invested in Hannah stock and the rest is invested in the Natasha Fund.

a. Calculate the beta of Hannah stock with the portfolio consisting of 70.0% Hannah stock and 30.0% of Natasha Fund.

The beta of Hannah stock is . (Round to two decimal places.)

b. Calculate the required return on Hannah stock. (Hint: Make sure to round all intermediate calculations to at least five decimal places.)

The required return of Hannah stock is %. (Round to two decimal places.)

c. Your finance professor suggests that you should calculate the optimal amount of Hannah stock in the portfolio assuming a risk-free rate of 2%. (Hint: use Excel's solver, define that the portfolio's Sharpe ratio shall be maximized. Consider the risk-free rate in the Sharpe ratio formula.)

The optimal weight of Hannah stock in the portfolio is %. (Round to one decimal place.)

This optimal portfolio has a Sharpe ratio of . (Round to three decimal places.)