Chapter 09

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1. Award: 10.00 points Problems? Adjust credit for all students. What must be the beta of a portfolio with E ( r P ) = 18% , if r f = 6% and E ( r M ) = 14% ? Note: Do not round intermediate calculations. Round your answer to 1 decimal place. Beta of a portfolio 1.5 Explanation: E ( r P ) = r f + β P × [ E ( r M ) − r f ] 0.18 = 0.06 + β P × [0.14 − 0.06] β P = 0.12 ÷ 0.08 = 1.5 Worksheet Difficulty: 1 Basic Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 09: The Capital Asset Pricing Model > Chapter 09 Problems - Static and Algorithmic References
2. Award: 10.00 points Problems? Adjust credit for all students. The market price of a security is $50. Its expected rate of return is 14%. The risk-free rate is 6%, and the market risk premium is 8.5%. What will be the market price of the security if its correlation coefficient with the market portfolio doubles (and all other variables remain unchanged)? Assume that the stock is expected to pay a constant dividend in perpetuity. Note: Do not round intermediate calculations. Round your answer to 2 decimal places. $ Market price 31.82 Explanation: If the security’s correlation coefficient with the market portfolio doubles (with all other variables such as variances unchanged), then beta, and therefore the risk premium, will also double. The current beta is 0.94, solved from the CAPM relationship: 14% − 6% = 8% The new risk premium would be 16%, and the new discount rate for the security would be: 16% + 6% = 22% If the stock pays a constant perpetual dividend, then we know from the original data that the dividend ( D ) must satisfy the equation for the present value of a perpetuity: Price = Dividend ÷ Discount rate 50 = D ÷ 0.14 D = 50 × 0.14 = $7.00 At the new discount rate of 22%, the stock would be worth: $7 ÷ 0.22 = $31.82 The increase in stock risk has lowered its value by 36.36%. Worksheet Difficulty: 1 Basic Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 09: The Capital Asset Pricing Model > Chapter 09 Problems - Static and Algorithmic References
3. Award: 10.00 points Problems? Adjust credit for all students. Are the following true or false? Required: a. Stocks with a beta of zero offer an expected rate of return of zero. False b. The CAPM implies that investors require a higher return to hold highly volatile securities. False c. You can construct a portfolio with beta of 0.75 by investing 0.75 of the investment budget in T-bills and the remainder in the market portfolio. False Explanation: a. β = 0 implies E ( r ) = r f , not zero. b. Investors require a risk premium only for bearing systematic (undiversifiable or market) risk. Total volatility, as measured by the standard deviation, includes diversifiable risk. c. Your portfolio should be invested 75% in the market portfolio and 25% in T-bills. Then: β P = (0.75 × 1) + (0.25 × 0) = 0.75 Worksheet Difficulty: 1 Basic Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 09: The Capital Asset Pricing Model > Chapter 09 Problems - Static and Algorithmic References
4. Award: 10.00 points Problems? Adjust credit for all students. Here are data on two companies. The T-bill rate is 4% and the market risk premium is 6%. Company $1 Discount Store Everything $5 Forecasted return 12% 11% Standard deviation of returns 8% 10% Beta 1.5 1.0 What would be the fair return for each company according to the capital asset pricing model (CAPM)? Note: Do not round intermediate calculations. Round your answers to 1 decimal place. Company Expected Return $1 Discount Store 13.0 % Everything $5 10.0 % Explanation: The expected (or fair) return is the return predicted by the CAPM for a given level of systematic risk. E ( r i ) = r f + β i × [ E ( r M ) − r f ] E ( r $1 Discount ) = 0.04 + 1.5 × (0.10 − 0.04) = 0.13 = 13% E ( r Everything $5 ) = 0.04 + 1.0 × (0.10 − 0.04) = 0.10 = 10% Worksheet Difficulty: 1 Basic Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 09: The Capital Asset Pricing Model > Chapter 09 Problems - Static and Algorithmic References
5. Award: 10.00 points Problems? Adjust credit for all students. Here are data on two companies. The T-bill rate is 4% and the market risk premium is 6%. Company $1 Discount Store Everything $5 Forecasted return 12% 11% Standard deviation of returns 8% 10% Beta 1.5 1.0 Characterize each company in the above table as underpriced, overpriced, or properly priced. $1 Discount Store is overpriced Everything $5 is underpriced Explanation: The expected (or fair) return is the return predicted by the CAPM for a given level of systematic risk. E ( r i ) = r f + β i × [ E ( r M ) − r f ] E ( r $1 Discount ) = 0.04 + 1.5 × (0.10 − 0.04) = 0.13 = 13% E ( r Everything $5 ) = 0.04 + 1.0 × (0.10 − 0.04) = 0.10 = 10% According to the CAPM, $1 Discount Stores requires a return of 13% based on its systematic risk level of β = 1.5. However, the forecasted return is only 12%. Therefore, the security is currently overvalued. Everything $5 requires a return of 10% based on its systematic risk level of β = 1.0. However, the forecasted return is 11%. Therefore, the security is currently undervalued. Worksheet Difficulty: 1 Basic Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 09: The Capital Asset Pricing Model > Chapter 09 Problems - Static and Algorithmic References
6. Award: 10.00 points Problems? Adjust credit for all students. What is the expected rate of return for a stock that has a beta of 1.0 if the expected return on the market is 15%? Expected rate of return 15% Explanation: According to the CAPM, the correct answer is 15%. The expected return of a stock with a β = 1.0 must, on average, be the same as the expected return of the market which also has a β = 1.0. Worksheet Difficulty: 1 Basic Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 09: The Capital Asset Pricing Model > Chapter 09 Problems - Static and Algorithmic References
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