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. (Do not round intermediate calculations. Enter your answers as a percent 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 period. (Do not round intermediate calculations. Enter your answers as a percent rounded 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. Enter your answer as a percent rounded 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. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Year Large Company US Treasury Bill 1    3.98 4.56 2   14.33 4.92 3   19.17 3.84 4 –14.51 6.98 5 –32.00 5.22 6   37.41 5.36

Explanation / Answer

It is an investment problem. Two investments are large company stock ad US treasury bills. The returns for six years are availale. You have to calculate average return. Steps are:

1. Take total of returns

2. Divide total by number of years to get average value.

Calculations are shown below:

Answer:

Average return of large company stock = 4.73%

Average return of US T bills = 5.15%

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Answer (b);

Standrad deviation is the measure of scatterness of return data. Steps are as follows:

1. Take returns for different years. Deduct average retur from each yearly figure to get deviations.

2. Take sqare of such deviated results.

3. Add the suuarred figures.

3. Then take root of such value. It is standard deviation.

Calculations are shown below:

Answer:

Standard deviation of return of large corporation stock is 55.57%

Standard deviation of returns of T bills is 2.35%

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Answer of c.1:

Premium is the excess of large corporation return over the return of T bill. Calculate premium. Then ascertain average premium by following steps of answer (a). Calculations are shown below:

Answer:

Average risk premium is -0.42%

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Answer c.2.

Now consider risk premium figures of c.1. Then apply standard deviation steps of answer (b). Calculation is shown below;

Answer:

Standard deviation is 56.54%

Calculation of arithmetic average return Large US treasury Year Company Bill 1 3.98 4.56 2 14.33 4.92 3 19.17 3.84 4 -14.51 6.98 5 -32 5.22 6 37.41 5.36 Total 28.38 30.88 Arithmetic Average 4.73 5.15

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