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Consider the following table for a period of six years
Consider the following table for a period of six years.
| Returns | ||
| Year | Large-Company Stocks | U.S. Treasury Bills |
| Year 1 | -15.89 % | 7.53 % |
| Year 2 | -26.83 | 8.11 |
| Year 3 | 37.47 | 6.11 |
| Year 4 | 24.17 | 6.27 |
| Year 5 | -7.64 | 5.57 |
| Year 6 | 6.81 | 8.00 |
1: Calculate the arithmetic average returns for large-company stocks and T-bills over this time period.
2: Calculate the standard deviation of the returns for large-company stocks and T-bills over this time period.
3: Calculate the observed risk premium in each year for the large-company stocks versus the T-bills.
(a) What was the arithmetic average risk premium over this period?
(b) What was the standard deviation of the risk premium over this period?
Expert Solution
1.
| Year | Large stock (A) (Return) | U.S treasury (B) (Return) |
|---|---|---|
| 1 | -15.89% | 7.53% |
| 2 | -26.83 | 8.11% |
| 3 | 37.47% | 6.11% |
| 4 | 24.17% | 6.27% |
| 5 | -7.64% | 5.57% |
| 6 | 6.81 | 8% |
| Average return (C) | 3.20% | 6.93% |
2.
| Year | Large stock | U.S. treasury | ||
|---|---|---|---|---|
| Deviation ((D) = (A) - (C)) | (D)^2 | Deviation ((E) = (B) - (C)) | (E)^2 | |
| 1 | -18.91% | 3.5740% | 0.60% | 0.0036% |
| 2 | -29.85% | 8.9072% | 1.18% | 0.0139% |
| 3 | 34.46% | 11.8715% | -0.82 | 0.0068% |
| 4 | 21.16% | 4.4753% | -0.66% | 0.0044% |
| 5 | -10.66% | 1.1353% | -1.36% | 0.0185% |
| 6 | 3.80% | 0.1440% | 1.07% | 0.0114% |
| Variance | 0.06021 | Variance | 0.00012 | |
For large stock:
Standard deviation = Variance0.5Standard deviation = 0.060210.5Standard deviation = 0.2454 or 24.54%Standard deviation = Variance0.5Standard deviation = 0.060210.5Standard deviation = 0.2454 or 24.54%
For U.S treasury:
Standard deviation = Variance0.5Standard deviation = 0.000120.5Standard deviation = 0.0109 or 1.09%Standard deviation = Variance0.5Standard deviation = 0.000120.5Standard deviation = 0.0109 or 1.09%
3.
(a)
| Year | Risk premium (Large stock return - U.S treasury) |
|---|---|
| 1 | -23.42% |
| 2 | -34.94% |
| 3 | 31.36% |
| 4 | 17.90% |
| 5 | -13.21% |
| 6 | -1.19% |
| Average risk premium | -3.92 |
(b)
| Year | Deviation (Risk premium - Average) | Deviation ^2 |
|---|---|---|
| 1 | -19.50% | 3.8038% |
| 2 | -31.02% | 9.6245% |
| 3 | 35.28% | 12.4444% |
| 4 | 21.82% | 4.7597% |
| 5 | -9.29% | 0.8637% |
| 6 | 2.73% | 0.0743% |
| Variance | 0.06314 |
Standard deviation = Variance0.5Standard deviation = 0.063140.5Standard deviation = 0.2513 or 25.13%
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