Calculate the arithmetic average returns for large-company stocks and T-bills ov

Question

Calculate the arithmetic average returns for large-company stocks and T-bills over this time period. (Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

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

What was the arithmetic average risk premium over this period? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

What was the standard deviation of the risk premium over this period? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Explanation / Answer

Answer:

1. Arithematic Average Return:

Large Company Stock = (15.59 + 26.74 + 37.41 + 24.11 + 7.52 + 6.75) / 6 =118.12 / 6 =19.6866%

US Treasury Bills = (7.47 + 8.08 + 6.05 + 5.97 + 5.54 + 7.91) / 6 = 6.8366%

2. Standard Deviation of the Returns:

Large Company Stock = [1 / 6 {(15.59 - 19.6866)2 + (26.74 - 19.6866)2 + (37.41 - 19.6866)2 + (24.11 - 19.6866)2 + (7.52 - 19.6866)2 + (6.75 - 19.6866)2}]1/2 = [1/6 {(-4.0966)2 + (7.0534)2 + (17.7234)2 + (4.4234)2 + (-12.1666)2 + (-12.9366)2}]1/2 = [1/6 {715.5997}]1/2 = 119.26661/2 = 10.9209%

US Treasury Bills = [1 / 6 {(7.47 - 6.8366)2 + (8.08 - 6.8366)2 + (6.05 - 6.8366)2 + (5.97 - 6.8366)2 + (5.54 - 6.8366)2 + (7.91 - 6.8366)2}]1/2 = [1/6 {(0.6334)2 + (1.2434)2 + (-0.7866)2 + (-0.8666)2 + (-1.2966)2 + (1.0734)2}]1/2 = [1/6 {6.1503}]1/2 = 1.02501/2 = 1.0124%

3. Calculation of Arithematic Average of Risk Premium

Risk Premium = Return on Stock - Risk Free Return

3a. Arithematic Average = {(15.59 - 7.47) + (26.74 - 8.08) + (37.41 - 6.05) + (24.11 - 5.97) + (7.52 - 5.54) + (6.75 - 7.91)} / 6 = 77.10 / 6 = 12.85%

3b. Risk Premium Standard Deviation = [1 / 6 {(8.32 - 12.85)2 + (18.66 - 12.85)2 + (31.36 - 12.85)2 + (18.14 - 12.85)2 + (1.98 - 12.85)2 + (-1.16 - 12.85)2}]1/2 = [1/6 {(-4.53)2 + (5.81)2 + (18.51)2 + (5.29)2 + (-10.87)2 + (-14.01)2}]1/2 = [1/6 {739.3182}]1/2 = 123.21971/2 = 11.10%

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