Question

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 21%. 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 19%, a volatility of 58%, and a correlation of 0 (zero) with the Natasha Fund.

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

a. Calculate the required return of Hannah stock.

The required return of Hannah stock is ______? (Round to one decimal place.)

Is your broker right?  

___________, because the expected return of Hannah stock exceeds the required return. (Fill in "Yes" or "No")

b. You follow your broker's advice and make a substantial investment in Hannah stock so that, considering only your risky investments, 57% is in the Natasha Fund and 43% 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. (Round all intermediate values decimal places as needed.)

The required return of Hannah stock is ________? (Round to one decimal place.)

Is your finance professor right?

____________, because the expected return of Hannah stock is less than the required return. (Fill in "Yes" or "No")

c. You decide to follow your finance professor's advice and reduce your exposure to Hannah. Now Hannah represents 16.053% of your risky portfolio, with the rest in the Natasha fund. Recalculate the required return on Hannah stock. (Round all intermediate values to five decimal places as needed.)

The required return of Hannah stock is ____________ (Round to one decimal place.)

Is this the correct amount of Hannah stock to hold?

______________, because now the required and expected return are very similar. (Fill in "Yes" or "No")

Answer 1

The correlation and beta are relatively a benchmark, in this case the current portfolio. If X is Natasha Fund and Y is Hannah Stock then the portfolio is P = 0.6X + 0.4Y. If you then calculate beta for Y relative to benchmark P, you get Cov (Y, P) = Cov (Y, 0.6X + 0.4Y) = Cov (Y, 0.6X) + Cov (Y, 0.4Y) = 0 + 0.4 Cov (Y, Y) = 0.4 * 0.6 ^ 2 = 0.144. Here I have used Cov (Y, X) = 0 given in the task.

To get a beta, divide by the variance of the portfolio Cov (P, P) = 0.072.

For an optimal portfolio, the required return for the respective incoming securities relative to the portfolio should be equal to the expected return on the securities. If it is lower / higher one should increase / decrease the holding of that security.