Chapter 11

Chapter 11 - 1 You own a portfolio that has \$2,700 invested...

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You own a portfolio that has \$2,700 invested in Stock A and \$3,800 invested in Stock B. Assume the expected returns on these stocks are 12 percent and 18 percent, respectively. Required: What is the expected return on the portfolio? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).) Expected return on the portfolio % Explanation: The expected return of a portfolio is the sum of the weight of each asset times the expected return of each asset. The total value of the portfolio is: Total value = \$2,700 + 3,800 Total value = \$6,500 So, the expected return of this portfolio is: E(R p ) = (\$2,700/\$6,500)(0.12) + (\$3,800/\$6,500)(0.18) E(R p ) = 0.1551 or 15.51% 2. Consider the following information: Rate of Return if State Occurs State of Probability of State Economy of Economy Stock A Stock B Recession 0.24 0.030 –0.39 Normal 0.59 0.110 0.29 Boom 0.17 0.280 0.52 Requirement 1: Calculate the expected return for the two stocks. (Do not include the percent signs (%). Round your answers to 2 decimal places (e.g., 32.16).) Expected return E(R A ) % E(R B ) %
Requirement 2: Calculate the standard deviation for the two stocks. (Do not include the percent signs (%). Round your answers to 2 decimal places (e.g., 32.16).) Standard deviation σ A % σ B % Explanation: 1: The expected return of an asset is the sum of the probability of each return occurring times the probability of that return occurring. So, the expected return of each stock asset is: E(R A ) = 0.24(0.030) + 0.59(0.110) + 0.17(0.28) E(R A ) = 0.1197 or 11.97% E(R B ) = 0.24(–0.39) + 0.59(0.29) + 0.17(0.52) E(R B ) = 0.1659 or 16.59% 2: To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, and then sum. The result is the variance. So, the variance and standard deviation of each stock is: σ A 2 =0.24(0.030 – 0.1197) 2 + 0.59(0.110 – 0.1197) 2 + 0.17(0.28 – 0.1197) 2 σ A 2 = 0.00635 σ A = (0.00635) 1/2 σ A = 0.0797 or 7.97% σ B 2 =0.24(–0.39 – 0.1659) 2 + 0.59(0.29 – 0.1659) 2 + 0.17(0.52 – 0.1659) 2 σ B 2 = 0.10457 σ B = (0.10457) 1/2 σ B = 0.3234 or 32.34% 3. Consider the following information: Rate of Return If State Occurs State of Probability of Economy State of Economy Stock A Stock B Stock C Boom 0.15 0.360 0.460 0.340 Good 0.45 0.130 0.110 0.180

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Poor 0.35 0.020 0.030 −0.060 Bust 0.05 −0.120 −0.260 −0.100 Requirement 1: Your portfolio is invested 30 percent each in A and C and 40 percent in B. What is the expected return of the portfolio? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).) Expected return of the portfolio % Requirement 2: (a) What is the variance of this portfolio? (Round your answer to 5 decimal places
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Chapter 11 - 1 You own a portfolio that has \$2,700 invested...

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