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 Company Stocks

U.S. Treasury Bills

Risk Premium

Year 1

-14.89%

7.33%

-22.22%

Year 2

-26.53%

8.01%

-34.54%

Year 3

37.27%

5.91%

31.36%

Year 4

23.97%

5.27%

18.70%

Year 5

-7.24%

5.47%

-12.71%

Year 6

6.61%

7.70%

-1.09%

Total

19.19%

39.69%

-20.50%

Risk Premium = Large Company Stock’s Return – U.S. Treasury Bills’ Return

Variance for Large company = 1/5*[(–.1489 – .03198)2 + (–.2653 – .03198)2 + (.3727 – .03198)2 + (.2397 – .03198)2 + (–.0724 – .03198)2 + (.0661 – .03198)2]

Variance = 0.058478

Standard Deviation for Large Company = Variance1/2 = 0.0584781/2 = 0.029239

Variance for U.S. Treasury = 1/5*[(.0733 – .0662)2 + (.0801 – .0662)2 + (.0591 – .0662)2 + (.0527 – .0662)2 + (.0547 – .0662)2 + (.077 – .0662)2]

               Variance = 0.00014503

Standard Deviation for U.S Treasury = Variance1/2 = 0.000145031/2 = 0.000072517

The variance of the risk premium = 1/5*[(­–.222 – .03416)2 + (–.3454 – .03416)2 + (.3136 – .03416)2 +

                                        (.1870 – .03416)2 + (–.1271 – .03416)2 + (–.0109 – .03416)2]

               Variance = 0.067833142

Standard Deviation for risk premium = Variance1/2 = 0.0678331421/2 = 0.033916571

Year

Large Company Stocks

U.S. Treasury Bills

Risk Premium

Year 1

-14.89%

7.33%

-22.22%

Year 2

-26.53%

8.01%

-34.54%

Year 3

37.27%

5.91%

31.36%

Year 4

23.97%

5.27%

18.70%

Year 5

-7.24%

5.47%

-12.71%

Year 6

6.61%

7.70%

-1.09%

Total

19.19%

39.69%

-20.50%

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