chapter 13 solution

chapter 13 solution - Basic 1. The portfolio weight of an...

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Basic 1. 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 = 180($45) + 140($27) = $11,880 The portfolio weight for each stock is: Weight A = 180($45)/$11,880 = .6818 Weight B = 140($27)/$11,880 = .3182 2. 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 = $2,950 + 3,700 = $6,650 So, the expected return of this portfolio is: E(R p ) = ($2,950/$6,650)(0.11) + ($3,700/$6,650)(0.15) = .1323 or 13.23% 3. The expected return of a portfolio is the sum of the weight of each asset times the expected return of each asset. So, the expected return of the portfolio is: E(R p ) = .60(.09) + .25(.17) + .15(.13) = .1160 or 11.60%
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4. Here we are given the expected return of the portfolio and the expected return of each asset in the portfolio, and are asked to find the weight of each asset. We can use the equation for the expected return of a portfolio to solve this problem. Since the total weight of a portfolio must equal 1 (100%), the weight of Stock Y must be one minus the weight of Stock X. Mathematically speaking, this means: E(R p ) = .124 = .14w X + .105(1 – w X ) We can now solve this equation for the weight of Stock X as: .124 = .14w X + .105 – .105w X .019 = .035w X w X = 0.542857 So, the dollar amount invested in Stock X is the weight of Stock X times the total portfolio value, or: Investment in X = 0.542857($10,000) = $5,428.57 And the dollar amount invested in Stock Y is: Investment in Y = (1 – 0.542857)($10,000) = $4,574.43 5. 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) = .25(–.08) + .75(.21) = .1375 or 13.75% 6. 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) = .20(–.05) + .50(.12) + .30(.25) = .1250 or 12.50% 7. 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 ) = .15(.05) + .65(.08) + .20(.13) = .0855 or 8.55% E(R B ) = .15(–.17) + .65(.12) + .20(.29) = .1105 or 11.05% 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. So, the variance and standard deviation of each stock is: σ A 2 =.15(.05 – .0855) 2 + .65(.08 – .0855) 2 + .20(.13 – .0855) 2 = .00060 σ A = (.00060) 1/2 = .0246 or 2.46%
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σ B 2 =.15(–.17 – .1105) 2 + .65(.12 – .1105) 2 + .20(.29 – .1105) 2 = .01830
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This note was uploaded on 01/29/2012 for the course MAN 4635 taught by Professor Q during the Spring '11 term at Metro State.

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chapter 13 solution - Basic 1. The portfolio weight of an...

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