Consider the following table for a period of six years. Returns Large-Company U.

Question

Consider the following table for a period of six years. Returns Large-Company U.S Stocks Treasury Bills Year 7.53% Year 1 15.89% 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 Requirement 1 Calculate the arithmetic average returns for large-company stocks and T-bills over this time period. (Do not include the percent signs Round your answers to 2 decimal places (e.g., 32.16).) Arithmetic average returns Large company stock 3.01 6.93 Requirement 2: Calculate the standard deviation of the returns for large-company stocks and T-bills over this time period Do not include the percent signs Round your answers to 2 decimal places (e.g., 32.16).) Standard deviation Large company stock T-bills Requirement 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? (Do not include the percent sign Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places (e.g., 32.16).) Risk premium (b) What was the standard deviation of the risk premium over this period? (Do not include the percent sign Round your answer to 2 decimal places (e.g., 32.16).) Risk premium standard deviation

Explanation / Answer

Requirement 1 :- Calculate the arithmetic average returns for large company stocks and T-bills over this time period.

Average Return for Large company stocks = 18.09 / 6 Years = 3.015%

Average Return for U.S. Treasury Bills = 41.59 / 6 Years = 6.932%

Requirement 2 :- Calculate the standard deviation of the returns for large company stocks and T-bills over this time period.

Variance for Large Company Stocks = {(-0.1589-0.03015)2 + (-0.2683-0.03015)2 + (0.3747-0.030150)2 + (0.2417-0.03015)2 + (-0.0764-0.03015)2 + (0.0681-0.03015)2}1/5 = 0.060214703

Standard Deviation for Large company stock = 0.0602147031/2= 0.2454 or 24.54%

Variance For U.S. Treasury Bills = {(0.0753-0.06932)2 + (0.0811-0.06932)2 + (0.0611-0.06932)2 + (0.0627-0.06932)2 + (0.0557-0.06932)2 + (0.08-0.06932)2}1/5 = 0.0005854884

Standard Deviation for U. S Treasury Bills = 0.00058548841/2 = 0.02420 or 2.42%

Requirement :- 3 Calculate the observed risk premium in each year for the large-company stock versus the T-bills

(A) What was the arithmetic average risk premium over this period?

Average Observed Risk Premium = -23.5 / 6 Years = -3.92%

(B) What was the standard deviation of the risk premium over this period?

Variance For Risk Premium Over this period = {(-0.2342+0.0392)2 + (-0.3494+0.0392)2 + (0.3136+0.0392)2 + (0.179+0.0392)2 + (-0.1321+0.0392)2 + (-0.019+0.0392)2}1/5 = 0.31536657

Standard Deviation of the Risk Premium = 0.315366571/2 = 0.5616 or 56.16%

Year Large company Stocks U.S. Treasury Bills Risk Premium 1 -15.89% 7.53% -23.42% 2 -26.83% 8.11% -34.94% 3 37.47% 6.11% 31.36% 4 24.17% 6.27% 17.9% 5 -7.64% 5.57% -13.21% 6 6.81% 8.00% -1.19% Total 18.09% 41.59% -23.5%

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