Suppose we have the following returns for large-company stocks and Treasury bill

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-bills over this period. (Round your answers to 2 decimal places. (e.g., 32.16))

Calculate the standard deviation of the returns for large-company stocks and T-bills over this period.(Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

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. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

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? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Suppose we have the following returns for large-company stocks and Treasury bills over a six year period:

Explanation / Answer

Part 1)

The arithmetic average returns are calculated as follows:

_________

Part B)

To determine the standard deviation, we need to calculate the variance for each type of security. The formula for calculating variance is given below:

Variance = 1/(Number of Years - 1)*[(Return for Year 1 - Arithmetic Mean)^2 + (Return for Year 2 - Arithmetic Mean)^2 + (Return for Year 3 - Arithmetic Mean)^2 + (Return for Year 4 - Arithmetic Mean)^2 + (Return for Year 5 - Arithmetic Mean)^2 + (Return for Year 6 - Arithmetic Mean)^2]

The formula for calculating standard deviation is given below:

Standard Deviation = (Variance)^(1/2)

_________

Variance (Large Company) = 1/(6-1)*[(3.97% - 4.77%)^2 + (14.34% - 4.77%)^2 + (19.23% - 4.77%)^2 + (-14.45% - 4.77%)^2 + (-31.94% - 4.77%)^2 + (37.47% - 4.77%)^2] = .061753

Variance (Treasury Bill) = 1/(6-1)*[(6.59% - 5.55%)^2 + (4.42% - 5.55%)^2 + (4.29% - 5.55%)^2 + (7.32% - 5.55%)^2 + (5.28% - 5.55%)^2 + (5.38% - 5.55%)^2] = .000144

_________

Standard Deviation (Large Company) = (.061753)^(1/2) = 24.85%

Standard Deviation (Treasury Bill) = (.000144)^(1/2) = 1.20%

_________

Part C)

The average observed risk premium is calculated as follows:

_________

Part D)

The variance and standard deviation for average risk premium are calculated below:

Variance (Average Risk Premium) = 1/5*[(-2.62% - (-.78%))^2 + (9.92% - (-.78%))^2 + (14.94% - (-.78%))^2 + (-21.77% - (-.78%))^2 + (-37.22% - (-.78%))^2 + (32.09% - (-.78%))^2] = .064278

Standard Deviation (Average Risk Premium) = (.064278)^(1/2) = 25.35%

Year Large Company US Treasury Bill 1 3.97 6.59 2 14.34 4.42 3 19.23 4.29 4 -14.45 7.32 5 -31.94 5.28 6 37.47 5.38 Total (A) 28.62 33.28 Number of Years (B) 6 6 Arithmetic Mean (A/B) 4.77% 5.55%

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