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Unformatted text preview: nal answer for each problem is found without rounding during any step in the problem. 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 = [($104 – 92) + 1.45] / $92 R = .1462 or 14.62% 2. The dividend yield is the dividend divided by price at the beginning of the period, so: Dividend yield = $1.45 / $92 Dividend yield = .0158 or 1.58% And the capital gains yield is the increase in price divided by the initial price, so: Capital gains yield = ($104 – 92) / $92 Capital gains yield = .1304 or 13.04% 3. Using the equation for total return, we find: R = [($81 – 92) + 1.45] / $92 R = –.1038 or –10.38% And the dividend yield and capital gains yield are: Dividend yield = $1.45 / $92 Dividend yield = .0158 or 1.58% 257 Capital gains yield = ($81 – 92) / $92 Capital gains yield = –.1196 or –11.96% Here’s 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 change in price plus the coupon payment, so: Total dollar return = $1,056 – 1,090 + 80 Total dollar return = $46 The total nominal percentage return of the bond is: R = [($1,056 – 1,090) + 80] / $1,090 R = .0422 or 4.22% Notice here that we could have simply used the total dollar return of $46 in the numerator of this equation. Using the Fisher equation, the real return was: (1 + R) = (1 + r)(1 + h) r = (1.0422 / 1.030) – 1 r = .0118 or 1.18% 5. The nominal return is the stated return, which is 11.70 percent. Using the Fisher equation, the real return was: (1 + R) = (1 + r)(1 + h) r = (1.1170)/(1.031) – 1 r = .0834 or 8.34% 6. Using the Fisher equation, the real returns for government and corporate bonds were: (1 + R) = (1 + r)(1 + h) rG = 1.061/1.031 – 1 rG = .0291 or 2.91% rC = 1.062/1.031 – 1 rC = .0301 or 3.01% 258 7. The average return is the sum of the returns, divided by the number of returns. The average return for each stock was: N [.15 + .23 − .34 + .16 + .09] = .0580 or 5.80% X = xi N = 5 i =1 ∑ N [.18 + .29 − .31 + .19 + .11] = .0920 or 9.20% Y = yi N = 5 i =1 ∑ We calculate the variance of each stock as:
N σ X 2 = ∑ ( xi − x ) 2 ( N − 1) i =1 1 ( .15 − .058) 2 + ( .23 − .058) 2 + ( − .34 − .058) 2 + ( .16 − .058) 2 + ( .09 − .058) 2 = .051970 σX2 = 5 −1 1 2 ( .18 − .092) 2 + ( .29 − .092) 2 + ( − .31 − .092) 2 + ( .19 − .092) 2 + ( .11 − .092) 2 = .054620 σY = 5 −1 { { } } The standard deviation is the square root of the variance, so the standard deviation of each stock is: σ X = (.0051970)1/2 σ X = .2280 or 22.80% σ Y = (.054620)1/2 σ Y = .2337 or 23.37% 8. We will calculate the sum of the returns for each asset and the observed risk premium first. Doing so, we get: Year 1973 1974 1975 1976 1977 1978 a. Large co. stock return –14.69% –26.47 37.23 23.93 –7.16 6.57 19.41% Tbill return 7.29% 7.99 5.87 5.07 5.45 7.64 39.31% Risk premium − 21.98% –34.46 31.36 18.86 –12.61 –1.07 –19.90% The average return for large company stocks over this period was: Large company stock average return = 19.41% /6 Large company stock average return = 3.24% 259 And the average return for Tbills over this period was: T V b. Using the equation for variance, we find the variance for large company stocks over this period was: Variance = 1/5[(–.1469 – .0324)2 + (–.2647 – .0324)2 + (.3723 – .0324)2 + (.2393 – .0324)2 + (–.0716 – .0324)2 + (.0657 – .0324)2] Variance = 0.058136 And the standard deviation for large company stocks over this period was: Standard deviation = (0.058136)1/2 Standard deviation = 0.2411 or 24.11% Using the equation for variance, we find the variance for Tbills over this period was: Variance = 1/5[(.0729 – .0655)2 + (.0799 – .0655)2 + (.0587 – .0655)2 + (.0507 – .0655)2 + (.0545 – .0655)2 + (.0764 – .0655)2] Variance = 0.000153 And the standard deviation for Tbills over this period was: Standard deviation = (0.000153)1/2 Standard deviation = 0.0124 or 1.24% c. The average observed risk premium over this period was: Average observed risk premium = –19.90% / 6 Average observed risk premium = –3.32% The variance of the observed risk premium was: Variance = 1/5[(–.2198 – (–.0332))2 + (–.3446 – (–.0332))2 + (.3136 – (–.0332))2 + (.1886 – (–.0332))2 + (–.1261 – (–.0332))2 + (–.0107 – (–.0332))2] Variance = 0.062078 And the standard deviation of the observed risk premium was: Standard deviation = (0.06278)1/2 Standard deviation = 0.2492 or 24.92% 9. a. To find the average return, we sum all the returns and divide by the number of returns, so: Arithmetic average return = (.34 +.16 + .19 – .21 + .08)/5 Arithmetic average return = .1120 or 11.20% Tbills average return = 39.31% / 6 U Tbills average return = 6.55% 260 b. Using the equation to calculate variance, we find: Variance = 1/4[(.34 – .112)2 + (.16 – .112)2 + (.19 – .112)2 + (–.21 – .112)2 + (.08 – .112...
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This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of TexasTyler.
 Spring '10
 eshmalwi
 Finance, Corporate Finance

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