Suppose we have the following returns for large-company stocks and Treasury bills over a six year period:

Problem 12-8 Risk Premiums [LO2, 3]

Suppose we have the following returns for large-company stocks and Treasury bills over a six year period:

Year	Large Company	US Treasury Bill
1	3.95	6.53
2	14.13	4.38
3	19.07	4.25
4	–14.61	7.30
5	–32.10	4.94
6	37.32	6.14

a.	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.)

	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. 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 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.)

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. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Standard deviation

%

 

Explanation:

We will calculate the sum of the returns for each asset and the observed risk premium first. Doing so, we get:

Year		Large Co. Stock Return				T-Bill Return				Risk Premium
1			3.95	%			6.53	%		–	2.58	%
2			14.13				4.38				9.75
3			19.07				4.25				14.82
4		–	14.61				7.30			–	21.91
5		–	32.10				4.94			–	37.04
6			37.32				6.14				31.18
			27.76				33.54			–	5.78

 
a.

The average return for large company stocks over this period was:

Large company stocks average return = 27.76% / 6 = 4.63%

And the average return for T-bills over this period was:

T-bills average return = 33.54% / 6 = 5.59%

 
b.

Using the equation for variance, we find the variance for large company stocks over this period was:

Variance = 1/5[(.0395 – .0463)2 + (.1413 – .0463)2 + (.1907 – .0463)2 + (– .1461 – .0463)2 +                   (–.3210 – .0463)2 + (.3732 – .0463)2]

Variance = .061743

And the standard deviation for large company stocks over this period was:

Standard deviation = (.061743)1/2 = .2485, or 24.85%

Using the equation for variance, we find the variance for T-bills over this period was:

Variance = 1/5[(.0653 – .0559)2 + (.0438 – .0559)2 + (.0425 – .0559)2 + (.0730 – .0559)2 +                   (.0494 – .0559)2 + (.0614 – .0559)2]

Variance = .000156

And the standard deviation for T-bills over this period was:

Standard deviation = (.000156)1/2 = .0125, or 1.25%

 
c.

The average observed risk premium over this period was:

Average observed risk premium = –5.78% / 6 = –.96%

The variance of the observed risk premium was:

Variance = 1/5[(–.0258 – (–.0096))2 + (.0975 – (–.0096))2 + (.1482 – (–.0096))2 + (–.2191 –                   (–.0096))2 + (–.3704 – (–.0096))2 + (.3118 – (–.0096))2]

Variance = .062800

And the standard deviation of the observed risk premium was:

Standard deviation = (.062800)1/2 = .2506, or 25.06%