# Estimating Risk and Return

1. “Why is expected return considered forward-looking? What are the challenges for practitioners to utilize expected return? ” (Cornett, Adair, and Nofsinger, 2012, p. 246). Expected return is “forward-looking” in the sense that it represents the return investors expect to receive in the future as compensation for the market risk taken. The challenge is that practitioners cannot precisely know what the future holds and thus what the expected return should be. Thus, we create methods to estimate the expected return. 2. Describe how different allocations between the risk-free security and the market portfolio can achieve any level of market risk desired. ” (Cornett, Adair, and Nofsinger, 2012, p. 246). An investor can allocate money between a risk-free security that has zero risk (? =0), and the market portfolio that has market risk (? =1). If 75% of the portfolio is invested in the market, then the portfolio will have a ? =0. 75. If only 25% is invested in the market, then the portfolio will have a market risk of ? =0. 25. The first example (? =0. 75) might be taken by a less risk averse investor while the second example (? 0. 25) illustrates the portfolio of a more risk averse investor. By allocating the investment money between 0 and 100% into the market portfolio, an investor can achieve any level of market risk desired. 3. “Compute the expected return given these three economic states, their likelihoods, and the potential returns:” Economic StateProbabilityReturn Fast Growth0. 3040% Slow Growth0. 5010% Recession0. 20? 25% Expected return = 0. 3? 40% + 0. 5? 10% + 0. 2? -25% = 12% 4. “If the risk-free rate is 6 percent and the risk premium is 5 percent, what is the required return? ” (Cornett, Adair, and Nofsinger, 2012, p. 47). Required return = 6% + 5% = 11% 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? ” (Cornett, Adair, and Nofsinger, 2012, p. 247). Average market risk premium = 15. 8% ? 5. 6% = 10. 2% 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? ” (Cornett, Adair, and Nofsinger, 2012, p. 247).

Use the capital asset pricing model to calculate Hastings’ required return. Hastings’ required return = 4% + 0. 24 ? (11% ? 4%) = 5. 68% 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. (Adapted from Cornett, Adair, and Nofsinger, p. 248. ) 0. 25? 2. 9 + 0. 35? 1. 5 + 0. 40? 0. 2 = 1. 33

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