Question

Consider the following rates of return:

Year	Large-Company Stocks			US Treasury Bills
1	3.99	%		4.59	%
2	14.16			4.94
3	19.25			3.86
4	–14.43			6.99
5	–31.92			5.30
6	37.49			6.20

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

	Average returns
Large-company stocks	%
T-bills	%

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

	Standard deviation
Large-company stocks	%
T-bills	%

c-1.

Calculate the observed risk premium in each year for the large-company stocks versus the T-bills. What was the arithmetic average risk premium over this period? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Average risk premium

%

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? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Standard deviation

%

Answer 1

Solution:

Calculation of the arithmetic average returns for large-company stocks and T-bills:

Year (n)	Large-Company Stocks		US Treasury Bills
1	3.99 %		4.59%
2	14.16 %		4.94%
3	19.25 %		3.86%
4	–14.43 %		6.99%
5	–31.92 %		5.30%
6	37.49 %		6.20%
Arithmetic average returns
	= [ 3.99% + 14.16%+ 19.25% + (-14.43%) + (-31.92%) + 37.49%] / 6		= [4.59% + 4.94% + 3.86% +6.99% +5.30% +6.20%] /6
	4.76%		5.31%

The arithmetic average returns for large-company stocks are 4.76% and for T-bills are 5.31%:

Solution b)

Calculate the standard deviation of the returns for large-company stocks and T-bills:

Variance =

Standard Deviation =

For small sample size, we divide by n-1 instead of n

Hence

The variance of the returns for large-company stocks

= (3.99%-4.76%)² + (14.16%-4.76%)² + (19.25%-4.76%)² + (-14.43%-4.76%)² + (-31.92%-4.76%)² + (37.49%-4.76%)²] / 6-1

= 616.77(%)²

The Standard Deviation of the returns for large-company stocks = = 24.83%

The variance of the returns for T-bills

= (5.49%-5.31%)² + (4.94%-5.31%)² + (3.86%-5.31%)² + (6.99%-5.31%)² + (5.30%-5.31%)² + (6.20%-5.31%)²] / 6-1

= 1.27(%)²

The Standard Deviation of the returns for T-bills= = 1.13%

Solution c1)

Calculation of the arithmetic average risk premium

Year	Large-Company Stocks (%)	US Treasury Bills (%)	Risk Premium (%) = Stock Returns - T Bills
1	3.99	4.59	-0.60
2	14.16	4.94	9.22
3	19.25	3.86	15.39
4	–14.43	6.99	-21.42
5	–31.92	5.30	-37.22
6	37.49	6.20	31.29
	Total Risk Premium		-3.34

The arithmetic average risk premium = Total Risk Premium / n = -3.34% / 6 = -0.56%

Solution c2)

Calculate the standard deviation of the risk premium:

Variance =

Standard Deviation =

For small sample size, we divide by n-1 instead of n

Hence

The variance of the risk premium will be

= (-0.60%-(-0.56%))² + (9.22%-(-0.56%))² + (15.39%-(-0.56%))² + (-21.42%-(-0.56%))² + (-37.22%-(-0.56%))² + (31.29%-(-0.56%))²] / 6-1

= 628.74(%)²

The Standard Deviation of the returns for large-company stocks = = 25.07%