Suppose we have the following returns for large-company stocks and Treasury bill
ID: 2762472 • Letter: S
Question
Suppose we have the following returns for large-company stocks and Treasury bills over a six year period: Calculate the arithmetic average returns for large-company stocks and T-bitls over this period. b Calculate the standard deviation of the returns for large-company stocks and T-bills over this period. e-1 Calculate the observed risk premium in each year for the large-company stocks versus the T-bills. What was the average risk premium over this period? (Negative amount should be indicated by a minus sign. c 2 Calculate the observed risk premium in each year for the large-company stocks versus the T-bills. What was the standard deviation of the risk premium over this period?Explanation / Answer
Year
Large Company Stocks
U.S. Treasury Bills
Risk Premium
Year 1
3.88%
5.78%
-1.90%
Year 2
14.31%
2.45%
11.86%
Year 3
19.05%
3.68%
15.37%
Year 4
-14.63%
7.12%
-21.75%
Year 5
-32.12%
4.92%
-37.04%
Year 6
37.29%
4.89%
32.40%
Total
27.78%
28.84%
-1.06%
Arithmetic Average Returns for Large Company = 27.78%/6 = 4.63%
Arithmetic Average Returns for U.S. Treasury = 28.84%/6 = 4.81%
Variance for Large company = 1/5*[(.0388 – .0463)2 + (.1431 – .0463)2 + (.1905 – .0463)2 + (-.1463 – .0463)2 + (–.3212 – .0463)2 + (.3729 – .0463)2]
Variance = 0.061808
Standard Deviation for Large Company = Variance1/2 = 0.0618081/2 = 0.030904
Variance for U.S. Treasury = 1/5*[(.0578 – .0481)2 + (.0245 – .0481)2 + (.0368 – .0481)2 + (.0712 – .0481)2 + (.0492 – .0481)2 + (.0489 – .0481)2]
Variance = 0.000263
Standard Deviation for U.S Treasury = Variance1/2 = 0.0002631/2 = 0.000131
c1 & c2 : Refer to the above table for observed risk premium.
Year
Large Company Stocks
U.S. Treasury Bills
Risk Premium
Year 1
3.88%
5.78%
-1.90%
Year 2
14.31%
2.45%
11.86%
Year 3
19.05%
3.68%
15.37%
Year 4
-14.63%
7.12%
-21.75%
Year 5
-32.12%
4.92%
-37.04%
Year 6
37.29%
4.89%
32.40%
Total
27.78%
28.84%
-1.06%
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