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Expected Return and Market Risk

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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.

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.

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?

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.

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.

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Economic State Probability Return

Fast Growth 0.30 40%
Slow Growth 0.50 10%
Recession 0.20 −25%
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The solution of expected returns and risk-free rates is provided in excel format with full calculations.

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Manal Elkhoshkhany, MBA
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  • BA, Ain Shams University, Cairo Egypt
  • MBA, California State University, Sacramento
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