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Chapter 8 - Risk and Rates of Return - Solutions

# Chapter 8 - Risk and Rates of Return - Solutions - Risk and...

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Old Exam Questions - Risk and Rates of Return - Solutions Page 1 of 63 Pages Risk and Rates of Return - Solutions 1. The variance of a portfolio consisting of Securities 1 through 5, with weights W 1 through W 5 , can be written as: σ P 2 = W 1 2 σ 1 2 + W 2 2 σ 2 2 + W 3 2 σ 3 2 + W 4 2 σ 4 2 + W 5 2 σ 5 2 + 2W 1 W 2 COV 12 + 2W 1 W 3 COV 13 + 2W 1 W 4 COV 14 + 2W 1 W 5 COV 15 + 2W 2 W 3 COV 23 + 2W 2 W 4 COV 24 + 2W 2 W 5 COV 25 + 2W 3 W 4 COV 34 + 2W 3 W 5 COV 35 + 2W 4 W 5 COV 45 * A. True B. False 2. The Efficient Frontier can be defined as consisting of those portfolios that offer the highest return for a given level of risk, or the least risk for a given level of return. * A. True B. False 3. A covariance matrix involving N securities will have [ (N)*(N) ] cells, [ N ] variance terms, [ (N)*(N-1) / 2 ] covariance terms, and [ (N)*(N-1) / (N-1) ] pairs of covariance terms. A. True * B. False 4. Assume that Securities A and B are expected to pay exactly the same dividend stream over time. However, Security A has a beta of -1.50, while Security B has a beta of +1.50. Because Security A has less risk than Security B (in fact, because of the negative beta it has less risk than a risk-free security), its required rate of return will be less and its price will be more than for Security B. * A. True B. False 5. Fannie Mae uses duration to manage its interest rate risk. To do so, it attempts to maximize the difference between the duration of its assets and the duration of its liabilities. This help to maximize profits while immunizing or minimizing their exposure to interest rate risk. A. True * B. False

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Old Exam Questions - Risk and Rates of Return - Solutions Page 2 of 63 Pages 6. Prices of debt (fixed income) securities are directly related to the required rate of return. As market interest rates (required rates of return) go up, the price of the security also goes up. A. True * B. False 7. If you constructed a variance/covariance matrix for the S&P 500, you would need to calculate 500 variances and 124,750 pairs of covariances. * A. True B. False 8. The variance of a 4-security portfolio can be calculated as follows: σ 2 P = W 1 2 σ 2 1 + W 2 2 σ 2 2 + W 3 2 σ 2 3 + W 4 2 σ 2 4 + W 1 W 2 σ 1 σ 2 COR 12 + W 1 W 3 σ 1 σ 3 COR 13 + W 1 W 4 σ 1 σ 4 COR 14 + W 2 W 3 σ 2 σ 3 COR 23 + W 2 W 4 σ 2 σ 4 COR 24 + W 3 W 4 σ 3 σ 4 COR 34 A. True * B. False 9. Given a risk-free rate of 5 percent and an expected return on the market of 12 percent (a market risk premium of 7 percent), a security with a beta of +2.0 will have a required rate of return of 19 percent, while a security with a beta of -2.0 will have a required rate of return of -9 percent. * A. True B. False
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