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Chapter 12 - Questions and Problems - 5, 7, 8, 9, 12, 13.
5. Nominal versus Real Returns:
a. In nominal terms?
b. In real terms?
a) The nominal return is 10.23% from the table.
b) To find the real return, we use the fisher equation
(1 + R) = (1 + r) (1 + h)
(1 + 0.1023) = (1 + r) (1 + 0.0406)
1.1023 = (1 + r) (1.0406)
1 + r = 1.0593
r = 1.0593 – 1
r = 0.0593 or 5.93%
7. Calculating Returns and Variability:
Returns
Year X Y
1 6% 18%
2 24 39
3 13 -6
4 -14 -20
5 15 47
Return X
Arithmetic average returns, R = [R1 +R2 + R3 + R4 + R5]/N
= [0.06 + 0.24 + 0.13 - 0.14 + 0.15]/5
= 0.44/5
= 0.088 or 8.80%
Variance = 1/ (N – 1) [(R1 – R) 2 + (R2 – R) 2 + (R3 – R) 2 + (R4 – R) 2+ (R5 – R) 2]
= 1/ (5 – 1) [(0.06 – 0.088)2 + (0.24 – 0.088)2 + (0.13 – 0.088)2 + (-0.14 – 0.088)2+ (0.15 – 0.088)2]
= ¼ [0.08148]
= 0.02037
Standard deviation = √Variance
= √0.02037
= 0.1427 or 14.27%
Return Y
Arithmetic average returns, R = [R1 +R2 + R3 + R4 + R5]/N
= [0.18 + 0.39 + (-0.06) + (-0.20) + 0.47]/5
= 0.78/5
= 0.1560 or 15.60%
Variance = 1/ (N – 1) [(R1 – R) 2 + (R2 – R) 2 + (R3 – R) 2 + (R4 – R) 2+ (R5 – R) 2]
= 1/ (5 – 1) [(0.18 – 0.156)2 + (0.39 – 0.156)2 + (-0.06 – 0.156)2 + (-0.20 – 0.156)2+ (0.47 – 0.156)2]
= ¼ [0.32732]
= 0.08183
Standard deviation = √Variance
= √0.08183
= 0.2861 or 28.61%
8. Risk Premiums:
a. Calculate the arithmetic average returns for large-company stocks and T-Bills over this period.
b. Calculate the standard deviation of the returns for large-company stocks and T-Bills over this period.
c. Calculate the observed risk premium in each year for the large-company stocks versus T-Bills. What was the average risk premium over this period? What was the standard deviation of the risk premium over this period?
d. Is it possible for the risk premium to be negative before an investment is undertaken? Can the risk premium be negative after the fact?
Year
Large stock return
T-bill return
Risk premium
1970
-3.57%
6.89
-10.46
1971
8.01
3.86
4.15
1972
27.37
3.43
23.94
1973
0.27
4.78
-4.51
1974
-25.93
7.68
-33.61
1975
18.48
7.05
11.43
Total
24.63
33.69
-9.06
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