Calculate the observed risk premium in each year for the large-company stocks versus the T-bills.

QUESTION

Risk Premiums Refer to Table 10.1 in the text and look at the period from 1973 through 1978.
1. Calculate the arithmetic average returns for large-company stocks and T-bills over this period.
2. Calculate the standard deviation of the returns for large-company stocks and T-bills over this period.
3. Calculate the observed risk premium in each year for the large-company stocks versus the T-bills. What was the arithmetic average risk premium over this period? What was the standard deviation of the risk premium over this period?
1. To calculate average returns just sum up the returns from 1973 to 1978 and divide them by 6 Years Large company stocks in % T-Bills 1973 14.69 7.22 1974 26.47 7.99 1975 37.23 5.87 1976 23.93 5.07 1977 7.16 5.45 1978 6.57 7.64 Arithmetic average Returns 19.34% 6.54% 2. To calculate the standard deviation just take a difference between large company stocks and average returns . Following that square the difference and sum them up. This way you get the standard deviation of both Stocks and T-Bills Years Large company stocks in % T-Bills Difference (Large company stocks-arithmetic average returns) Square the difference Difference (T Bills-arithmetic average returns) Square the difference 1973 14.69 7.22 -4.65 21.64 0.68 0.4624 1974 26.47 7.99 7.13 50.81 1.45 2.1025 1975 37.23 5.87 17.89 319.99 -0.67 0.4489 1976 23.93 5.07 4.59 21.05 -1.47 2.1609 1977 7.16 5.45 -12.18 148.39 -1.09 1.1881 1978 6.57 7.64 -12.77 163.12 1.1 1.21 Arithmetic average Returns 19.34 6.54 sum is 725 (This is the std deviation) sum is 7.57 (This is the standard deviation) 3. To calculate Risk Premium subtract T-Bills rate from Large company stock rates. The risk premium is obtained by summing the risk premium and dividing them by 6. Then just subtract average returns from risk premium. After that

uare the difference and add them up. Years Large company stocks in % T-Bills Difference (Large company stocks-arithmetic average returns) Square the difference Difference (T Bills-arithmetic average returns) Square the difference Risk Premium Difference (Risk Premium-Aritmetic risk premium) square the difference 1973 14.69 7.22 -4.65 21.64 0.68 0.4624 7.47 -5.33 28.43 1974 26.47 7.99 7.13 50.81 1.45 2.1025 18.48 18.48 341.51 1975 37.23 5.87 17.89 319.99 -0.67 0.4489 31.36 31.36 983.45 1976 23.93 5.07 4.59 21.05 -1.47 2.1609 18.86 18.86 355.70 1977 7.16 5.45 -12.18 148.39 -1.09 1.1881 1.71 1.71 2.92 1978 6.57 7.64 -12.77 163.12 1.1 1.21 -1.07 -1.07 1.14 Arithmetic average Returns 19.34 6.54 sum is 725 (This is the std deviation) sum is 7.57 (This is the standard deviation) Arithmetic Risk Premium=12.80 sum is 1713.16 (This is the standard deviation)

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