Capital Asset Pricing Model and Investment: Chapter 8 Solutions
Answers to Warm-Up Exercises
E8-1. Total annual return Answer: ($0 $12,000 $10,000) $10,000 $2,000 $10,000 20%
Logistics, Inc. doubled the annual rate of return predicted by the analyst. The negative net income is irrelevant to the problem. E8-2. Expected return Answer: Analyst 1 2 3 4 Total Probability 0.35 0.05 0.20 0.40 1.00 Return 5% 5% 10% 3% Expected return Weighted Value 1.75% 0.25% 2.0% 1.2% 4.70%
E8-3. Comparing the risk of two investments Answer: CV1 0.10 0.15 0.6667 CV2 0.05
0.12
0.4167
Based solely on standard deviations, Investment 2 has lower risk than Investment 1. Based on coefficients of variation, Investment 2 is still less risky than Investment 1. Since the two investments have different expected returns, using the coefficient of variation to assess risk is better than simply comparing standard deviations because the coefficient of variation considers the relative size of the expected returns of each investment. E8-4. Computing the expected return of a portfolio Answer: rp (0.45 0.038) (0.4 0.123) (0.15 0.174) (0.0171) (0.0492) (0.0261 0.0924 9.24% The portfolio is expected to have a return of approximately 9.2%. E8-5. Calculating a portfolio beta Answer: Beta (0.20 1.15) (0.10 0.85) (0.15 1.60) (0.20 1.35) (0.35 1.85) 0.2300 0.0850 0.2400 0.2700 0.6475 1.4725 E8-6. Calculating the required rate of return Answer: a. Required return 0.05 1.8 (0.10 0.05) 0.05 0.09 0.14 b. Required return 0.05 1.8 (0.13 0.05) 0.05 0.144 0.194 c. Although the risk-free rate does not change, as the market return increases, the required return on the asset rises by 180% of the change in the market’s return.
P8-1.
Solutions to Problems
Rate of return: rt = LG 1; Basic a. Investment X: Return Investment Y: Return
($21,000 $20,000 $1,500) 12.50% $20,000 ($55,000 $55,000 $6,800) 12.36% $55,000
(Pt Pt 1 Ct ) Pt 1
b. Investment X should be selected because it has a higher rate of return for the same level of risk. P8-2. Return calculations:
E8-1. Total annual return Answer: ($0 $12,000 $10,000) $10,000 $2,000 $10,000 20%
Logistics, Inc. doubled the annual rate of return predicted by the analyst. The negative net income is irrelevant to the problem. E8-2. Expected return Answer: Analyst 1 2 3 4 Total Probability 0.35 0.05 0.20 0.40 1.00 Return 5% 5% 10% 3% Expected return Weighted Value 1.75% 0.25% 2.0% 1.2% 4.70%
E8-3. Comparing the risk of two investments Answer: CV1 0.10 0.15 0.6667 CV2 0.05
0.12
0.4167
Based solely on standard deviations, Investment 2 has lower risk than Investment 1. Based on coefficients of variation, Investment 2 is still less risky than Investment 1. Since the two investments have different expected returns, using the coefficient of variation to assess risk is better than simply comparing standard deviations because the coefficient of variation considers the relative size of the expected returns of each investment. E8-4. Computing the expected return of a portfolio Answer: rp (0.45 0.038) (0.4 0.123) (0.15 0.174) (0.0171) (0.0492) (0.0261 0.0924 9.24% The portfolio is expected to have a return of approximately 9.2%. E8-5. Calculating a portfolio beta Answer: Beta (0.20 1.15) (0.10 0.85) (0.15 1.60) (0.20 1.35) (0.35 1.85) 0.2300 0.0850 0.2400 0.2700 0.6475 1.4725 E8-6. Calculating the required rate of return Answer: a. Required return 0.05 1.8 (0.10 0.05) 0.05 0.09 0.14 b. Required return 0.05 1.8 (0.13 0.05) 0.05 0.144 0.194 c. Although the risk-free rate does not change, as the market return increases, the required return on the asset rises by 180% of the change in the market’s return.
P8-1.
Solutions to Problems
Rate of return: rt = LG 1; Basic a. Investment X: Return Investment Y: Return
($21,000 $20,000 $1,500) 12.50% $20,000 ($55,000 $55,000 $6,800) 12.36% $55,000
(Pt Pt 1 Ct ) Pt 1
b. Investment X should be selected because it has a higher rate of return for the same level of risk. P8-2. Return calculations: