Problem 1. Refer to the table below to complete this question. Compute the expected return given these three economic states, their likelihoods, and the potential returns.
Problem 2. If the risk-free rate is 6 percent and the risk premium is 5 percent, what is the required return? Identify which financial security's return is typically considered the risk-free rate.
Problem 3. 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?
Problem 4. 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 and show applicable input values, computational steps, and formulas. Recalculate the required return with a change to beta, and explain the effect of a 1.0 increase in beta on the subsequent amount of change in required return.
Problem 5. 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. Determine whether the portfolio has less risk, equal risk, or more risk, compared to the overall market.
Economic State Probability Return
Fast Growth 0.30 40%
Slow Growth 0.50 10%
Recession 0.20 −25%