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# Ch13sol - H13.1 Solution to Problem 13.1 13.1 Determining...

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H13.1. Solution to Problem 13.1 13.1. Determining Portfolio Weights: What are the portfolio weights for a portfolio that has 70 shares of Stock A that sell for \$50 per share and 110 shares of Stock B that sell for \$30 per share? The portfolio weight of an asset is total investment in that asset divided by the total portfolio value. First, we will find the portfolio value, which is: Total value = 70(\$50) + 110(\$30) = \$6,800 The portfolio weight for each stock is: Weight A = 70(\$50)/\$6,800 = .5147 Weight B = 110(\$30)/\$6,800 = .4853

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H13.2. Solution to Problem 13.2 13.2. Portfolio Expected Return: You own a portfolio that has 1,200 invested in Stock A and 1,900 invested in Stock B. If the expected returns on these stocks are 10% and 17%, respectively, what is the expected return on the portfolio? 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 = 1,200 + 1,900 = 3,100 So, the expected return of this portfolio is: E(R p ) = ( 1,200/ 3,100)(0.10) + ( 1,900/ 3,100)(0.17) = .1429 or 14.29%
H13.3. Solution to Problem 13.5, 13.7 13.5. Calculating Expected Return: Based on the following information, calculate the expected return. Economy Probability Rate of return Recession .30 -.10 Boom .70 .35 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 the asset is: E(R) = .3(–.10) + .7(.35) = .2150 or 21.50%

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H13.4. Solution to Problem 13.7 13.7. Calculating Returns and Standard Deviations: Based on the following information, calculate the expected return and standard deviation for the two stocks. Economy Probability Stock A Stock B Recession .20 .06 -.20 Normal .60 .07 .13 Boom .20 .11 .33 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 ) = .20(.06) + .60(.07) + .20(.11) = .0760 or 7.60% E(R B ) = .20(–.20) + .60(.13) + .20(.33) = .1040 or 10.40% 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, then add all of these up. The result is the variance.
H13.5. Solution to Problem 13.7 (continued) So, the variance and standard deviation of each stock is: σ A 2 =.20(.06 – .0760) 2 + .60(.07–.0760) 2 + .20(.11 – .0760) 2 = .00030 σ A = (.00030)1/2 = .0174 or 1.74% σ B 2 =.20(–.2 – .1040) 2 + .60(.13–.1040) 2 + .20(.33 – .1040)2 = .029105 σ B = (.029105)1/2 = .1706 or 17.06%

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H13.6. Solution to Problem 13.9 13.9. Returns and Standard Deviations: Consider the following information: Economy Probability Stock A Stock B Stock C Boom .60 .07 .15 .33 Bust .40 .13 .03 -.06 a. What is the expected return on an equally weighted portfolio of these three stocks?
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