Question

Assume these are the stock market and Treasury bill returns for a 5-year period:

Year		Stock Market Return (%)			T-Bill Return (%)
2011			−36.53			2.10
2012			29.10			0.60
2013			16.46			0.16
2014			1.58			0.08
2015			16.86			0.10

a. What was the risk premium on common stock in each year? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

b. What was the average risk premium? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

c. What was the standard deviation of the risk premium? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Answer 1

a) Risk Premium is calculated using the formula: R_i - R_f

T-Bill return for each year will be the Risk-free Rate for that year

Risk Premium for 2011 = -36.53%-2.10% = -38.63%

Risk Premium for 2012 = 29.1%-0.6% = 28.50%

Risk Premium for 2013 = 16.46%-0.16% = 16.30%

Risk Premium for 2014 = 1.58%-0.08% = 1.5%

Risk Premium for 2015 = 16.86%-0.10% = 16.76%

Year	Stock Market Return (%)	T-Bill return (%)	Risk Premium (%)
2011	-36.53	2.1	-38.63
2012	29.1	0.6	28.50
2013	16.46	0.16	16.30
2014	1.58	0.08	1.50
2015	16.86	0.1	16.76

b) Average Risk-premium = (-38.63%+28.50%+16.30%+1.5%+16.76%)/5 = 4.89%

Average Risk-premium = 4.89%

c) Sample standard deviation is calculated using the following formula:

where x_i is the risk premium for each year i and E[x] is the average risk premium which is 4.89%

E[x] = 4.89%

Sample size = n = 5

Year	Stock Market Return (%)	T-Bill return (%)	Risk Premium (%) - xi	(xi-E[x])2
2011	-36.53	2.1	-38.63	1893.642256
2012	29.1	0.6	28.50	557.620996
2013	16.46	0.16	16.30	130.279396
2014	1.58	0.08	1.50	11.464996
2015	16.86	0.1	16.76	140.991876

From the above table,

Therefore standard deviation = (2733.999520/4)^1/2 = 26.1438306%

Sample standard deviation can also be calculated using Excel Function =STDEV.S(Range of Risk premium - x_i)

Standard deviation of Risk premium = 26.14%