Question

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	4.00	4.62
2	14.49	4.96
3	19.33	3.88
4	–14.35	7.00
5	–31.84	5.38
6	37.04	6.43

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

%

Answer 1

Answers first,

a. 4.78, 5.38

b. 24.72, 1.16

c. -0.60

d. 24.92

In order to calculate arithmatic average, following formula should be used

In order to calculate standard deviation, following formula should be used

Calculating both average and standard deviation together,

Year	Large Company (Xi)	[Xi- Mean (x)]^2
1	4	0.605802778
2	14.49	94.31646944
3	19.33	211.7510028
4	-14.35	365.8931361
5	-31.84	1340.902336
6	37.04	1040.815136

Average, Mean (x) = (4+14.49+19.33-14.35-31.84+37.04)%/6 = 4.78%

Standard Deviation =

= 24.72%

Year	US Treasury Bill (Yi)	[Yi- Mean (y)]^2
1	4.62	0.575069444
2	4.96	0.175002778
3	3.88	2.245002778
4	7	2.629802778
5	5.38	0.000002778
6	6.43	1.106002778

Average, Mean (y) = (4.62+4.96+3.88+7+5.38+6.43)%/6 = 5.38%

Standard Deviation =

= 1.16%

Risk premium refers to the excess return that investing in the stock market provides over a risk-free rate

Hence, here Risk premium of Large Stocks = Return on Large Stock - Return on US T-Bill

So, for different periods, Risk Premium is as follows, along with calculations for average risk premium ans standard deviation of risk premiums:

Year	Risk Premium	[Risk Premium - Mean (Rp)]^2
1	-0.62	0.0004
2	9.53	102.6169
3	15.45	257.6025
4	-21.35	430.5625
5	-37.22	1341.0244
6	30.61	974.0641

Mean (Rp) = (-0.62 + 9.53 + 15.45 - 21.35 - 37.22 +30.61)%/6 = -0.60%

Standard Deviation =

= 24.92%