CHAPTER 13,15,16

CHAPTER 13,15,16 - CHAPTER 13 RISK, RETURN, AND THE...

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CHAPTER 13 RISK, RETURN, AND THE SECURITY MARKET LINE Solutions to Questions and Problems NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem. 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 = 100($40) + 130($22) = $6,860 The portfolio weight for each stock is: Weight A = 100($40)/$6,860 = .5831 Weight B = 130($22)/$6,860 = .4169 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 = $2,300 + 3,400 = $5,700 So, the expected return of this portfolio is: E(R p ) = ($2,300/$5,700)(0.11) + ($3,400/$5,700)(0.16) = .1398 or 13.98% 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 ) = .50(.10) + .30(.16) + .20(.12) = .1220 or 12.20% CHAPTER 13 B-233 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 ) = .122 = .15w X + .10(1 – w X ) We can now solve this equation for the weight of Stock X as: .122 = .15w X + .10 – .10w X .022 = .05w X w X = 0.44 So, the dollar amount invested in Stock X is the weight of Stock X times the total portfolio value, or: Investment in X = 0.44($10,000) = $4,400 And the dollar amount invested in Stock Y is: Investment in Y = (1 – 0.44)($10,000) = $5,600
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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) = .3(–.09) + .7(.33) = .2040 or 20.40% 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) = .25(–.05) + .40(.12) + .35(.25) = .1230 or 12.30% 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(.06) + .60(.07) + .25(.11) = .0785 or 7.85% E(R B ) = .15(–.2) + .60(.13) + .25(.33) = .1305 or 13.05% 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
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CHAPTER 13,15,16 - CHAPTER 13 RISK, RETURN, AND THE...

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