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Unformatted text preview: Basic 1. The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initial price. The return of this stock is: R = [($102 91) + 2.40] / $91 = .1473 or 14.73% 2. The dividend yield is the dividend divided by price at the beginning of the period price, so: Dividend yield = $2.40 / $91 = .0264 or 2.64% And the capital gains yield is the increase in price divided by the initial price, so: Capital gains yield = ($102 91) / $91 = .1209 or 12.09% 3. Using the equation for total return, we find: R = [($83 91) + 2.40] / $91 = .0615 or 6.15% And the dividend yield and capital gains yield are: Dividend yield = $2.40 / $91 = .0264 or 2.64% Capital gains yield = ($83 91) / $91 = .0879 or 8.79% Heres a question for you: Can the dividend yield ever be negative? No, that would mean you were paying the company for the privilege of owning the stock. It has happened on bonds. 4. The total dollar return is the increase in price plus the coupon payment, so: Total dollar return = $1,070 1,040 + 70 = $100 The total percentage return of the bond is: R = [($1,070 1,040) + 70] / $1,040 = .0962 or 9.62% Notice here that we could have simply used the total dollar return of $100 in the numerator of this equation. Using the Fisher equation, the real return was: (1 + R) = (1 + r)(1 + h) r = (1.0962 / 1.04) 1 = .0540 or 5.40% 5. The nominal return is the stated return, which is 12.30 percent. Using the Fisher equation, the real return was: (1 + R) = (1 + r)(1 + h) r = (1.123)/(1.031) 1 = .0892 or 8.92% 6. Using the Fisher equation, the real returns for longterm government and corporate bonds were: (1 + R) = (1 + r)(1 + h) r G = 1.058/1.031 1 = .0262 or 2.62% r C = 1.062/1.031 1 = .0301 or 3.01% 7. The average return is the sum of the returns, divided by the number of returns. The average return for each stock was: [ ] % 7.80 or .0780 5 09 . 16 . 17 . 21 . 08 . 1 = + + + = = = N x X N i i [ ] % 60 . 14 or .1460 5 26 . 21 . 14 . 38 . 16 . 1 = + + + = = = N y Y N i i Remembering back to sadistics, we calculate the variance of each stock as: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 { } ( 29 ( 29 ( 29 ( 29 ( 29 { } 048680 . 146 . 26 . 146 . 21 . 146 . 14 . 146 . 38 . 146 . 16 . 1 5 1 020670 . 078 . 09 . 078 . 16 . 078 . 17 . 078 . 21 . 078 . 08 . 1 5 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 = + + + + = = + + + + =  = = Y X N i i X N x x The standard deviation is the square root of the variance, so the standard deviation of each stock is: X = (.020670) 1/2 = .1438 or 14.38% Y = (.048680) 1/2 = .2206 or 22.06% 8. We will calculate the sum of the returns for each asset and the observed risk premium first....
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 Spring '11
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