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).)

Consider the following table for a period of six years.

Explanation / Answer

Year

Large co. stock return

U.S. Treasury Bills

Risk Premium

Year 1

-16.09%

7.57%

-23.66%

Year 2

-26.89%

8.13%

-35.02%

Year 3

37.51%

6.15%

31.36%

Year 4

24.21%

6.47%

17.74%

Year 5

-7.72%

5.59%

-13.31%

Year 6

6.85%

8.06%

-1.21%

17.87%

41.97%

-24.1%

Requirement 1:

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

Solution-

Large company stock average return:

Large company stock average return = 17.87% / 6

Large company stock average return = 2.98%

T-Bill Average return:

T-bills average return = 41.97% / 6

T-bills average return = 6.99%

Requirement 2:

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

Solution-

Variance for large company stocks:

Variance = 1/5[(–.1609 – .0298)2+ (–.2689 – .0298)2+ (.3751 – .0298)2+ (.2421 – .0298)2+ (–.0772 – .0298)2+ (.0685 – .0298)2]

Variance = 0.060568

Standard deviation for large company stocks:

Standard deviation = (0.060568)1/2

Standard deviation = 0.24611 or 24.61%

Variance for T-bills:

Variance = 1/5[(.0757 – .0699)2 + (.0813 – .0699)2 + (.0615 – .0699)2 + (.0647 – .0699)2 + (.0559 – .0699)2 + (.0806 – .0699)2]

Variance = 0.000114

Standard deviation for T-bills:

Standard deviation = (0.000114)1/2

Standard deviation = 0.01049 or 1.05%

Requirement 3:

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

Solution-

Average risk premium = –24.1% / 6

Average risk premium = –4.01%

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

Solution-

Variance = 1/5[(–.2366 – .0401)2+ (–.3502 – .0401)2+ (.3136 – .0401)2+ (.1774 – .0401)2+ (–.1331 – .0401)2+ (.0121 – .0401)2]

Variance = 0.070666

Standard deviation for large company stocks:

Standard deviation = (0.070666)1/2

Risk premium Standard deviation = 0.26584 or 26.58%

Year

Large co. stock return

U.S. Treasury Bills

Risk Premium

Year 1

-16.09%

7.57%

-23.66%

Year 2

-26.89%

8.13%

-35.02%

Year 3

37.51%

6.15%

31.36%

Year 4

24.21%

6.47%

17.74%

Year 5

-7.72%

5.59%

-13.31%

Year 6

6.85%

8.06%

-1.21%

17.87%

41.97%

-24.1%

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