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

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

Average returns of Large company stocks = Sum of returns/ number of years

= (3.96 +14.12+19.01-14.67-32.16+37.26)/6

= 27.52/6 = 4.59%

Average returns of T-bills = Sum of returns/ number of years

= (4.50+4.88+3.80+6.96+4.88+6.14)/6

= 31.16/6 = 5.19%

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

Standard deviation of large company stocks ={sum of (year’s return – average return)^2/6}

= [{(3.96- 4.59)^2+(14.12-4.59)^2+(19.01-4.59)^2+(-14.67-4.59)^2 +(-32.16-4.59)^2+(37.26-4.59)^2}/6 ]

= [3087.99/6]

=514.67

=22.69%

Standard deviation of T-bills =[{ (4.50-5.19)^2+(4.88-5.19)^2+(3.80-5.19)^2+(6.96-5.19)^2+(4.88-5.19)^2+(6.14-5.19)^2}/6]

=1.05 %

c-1 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?

The observed risk premium in each year for the large-company stocks versus the T-bills is the difference between return of large-company stock and T-bill for that year

Average risk premium = (3.96-5.50)+(14.12-4.88)+(19.01-3.80)+(-14.67-6.96)+(-32.16-4.88)+(37.26-6.14)

=-0.54+9.24+15.21-21.63-37.04+31.12

=-0.61%

c-2 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?

Standard deviation = [{(-0.54+0.61)^2+(9.24+0.61)^2+(15.21+0.61)^2+(-21.63+0.61)^2+(-37.04+0.61)^2+(31.12+0.61)^2}/6]

=22.81%  

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