3. \"Compute the expected return given these three economic states, their likeli

Question

3. "Compute the expected return given these three economic states, their likelihoods, and the potential returns:"

4. "If the risk-free rate is 6 percent and the risk premium is 5 percent, what is the required return?"

5. "The average annual return on the Standard and Poor's 500 Index from 1986 to 1995 was 15.8 percent. The average annual T-bill yield during the same period was 5.6 percent. What was the market risk premium during these 10 years?

6. "Hastings Entertainment has a beta of 0.24. If the market return is expected to be 11 percent and the risk-free rate is 4 percent, what is Hastings' required return?" Use the capital asset pricing model to calculate Hastings' required return.

7. Calculate the beta of your portfolio, which comprises the following items: (a) Olympic Steel stock, which has a beta of 2.9 and comprises 25 percent of your portfolio, (b) Rent-a-Center stock, which has a beta of 1.5 and comprises 35 percent of your portfolio, and (c) Lincoln Electric stock, which has a beta of 0.2 and comprises 40 percent of your portfolio.

Economic State Probability Return Fast Growth 0.30 40% Slow Growth 0.50 10% Recession 0.20 %u221225%

Explanation / Answer

Hi,

Please find the answer as follows:

Part 3:

Expected Return = 40*.30 + 10*.50 + (-25)*.20 = 12%

Part 4:

Required Return = 6 + 5 = 11% (Assuming a beta of 1)

Part 5:

Required Return = Rf + MRP (where MRP stands for Market Risk Premium)

15.8 = 5.6 + Market Risk Premium

Market Risk Premium = 15.8 - 5.6 = 10.2%

Part 6:

Required Return = Rf + B(Rm - Rf) = 4 + .24*(11 - 4) = 5.68%

Part 7:

Portfolio Beta =.25*2.9 + .35*1.5 + .40*.2 = 1.33

Thanks.

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