C10 P8 9 14 21 - Chapter 10 Problem 8 We will calculate the...

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Unformatted text preview: Chapter 10 Problem 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 Arithmetic Average Standard Deviation Large Companies -14.69% -26.47% 37.23% 23.93% -7.16% 6.57% 3.24% 24.11% T-Bills 7.29% 7.99% 5.87% 5.07% 5.45% 7.64% 6.55% 1.24% Risk Premium -21.98% -34.46% 31.36% 18.86% -12.61% -1.07% -3.32% 24.92% a. 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% And the average return for T-bills over this period was: T-bills average return = 39.31% / 6 T-bills average return = 6.55% 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 T-bills 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 T-bills 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 = (0.062078)1/2 Standard deviation = 0.2492 or 24.92% d. Before the fact, for all assets the risk premium will be positive; investors demand compensation over and above the risk-free return to invest their money in a risky asset. After the fact, the observed risk premium can be negative if the asset’s nominal return is unexpectedly low, the risk-free return is unexpectedly high, or if some combination of these two events occurs. Problem 9 a. To find the average return, we sum all the returns and divide by the number of returns, so: Arithmetic average return = (–.24 +.13 + .29 + .02 + .21)/5 Arithmetic average return = .0820 or 8.20% b. Using the equation to calculate variance, we find: Variance = 1/4[(–.24 – .082)2 + (.13 – .082)2 + (.29 – .082)2 + (.02 – .082)2 + (.21 – .082)2] Variance = 0.042370 So, the standard deviation is: Standard deviation = (0.042370)1/2 Standard deviation = 0.2058 or 20.58% Problem 14 The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initial price. Since preferred stock is assumed to have a par value of $100, the dividend was $5.50, so the return for the year was: R = ($94.17 – 92.18 + 5.50) / $92.18 R = .0813 or 8.13% Problem 21 To calculate the arithmetic and geometric average returns, we must first calculate the return for each year. The return for each year is: R1 = ($71.05 – $64.18 + $0.57) / $64.18 = .1159 or 11.59% R2 = ($76.85 – $71.05 + $0.62) / $71.05 = .0904 or 9.04% R3 = ($63.12 – $76.85 + $0.68) / $76.85 = –.1698 or –16.98% R4 = ($72.81 – $63.12 + $0.77) / $63.12 = .1657 or 16.57% R5 = ($78.25 – $72.81 + $0.84) / $72.81 = .0863 or 8.63% The arithmetic average return was: RA = (0.1159 + 0.0904 – 0.1698 + 0.1657 + 0.0863)/5 RA = 0.0577 or 5.77% The geometric average return was: RG = [(1 + .1159)(1 + .0904)(1 – .1698)(1 + .1657)(1 + .0863)]1/5 – 1 RG = 1.27911/5 – 1 = 0.0505 or 5.05% ...
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This note was uploaded on 04/05/2011 for the course FIN 350 taught by Professor Debruinne during the Winter '11 term at Grand Valley State.

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