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

Year Stock Market Return (%) T-Bill Return (%)
2013 33.10 0.10
2014 12.60 0.10
2015 −3.10 0.10
2016 14.10 0.05
2017 23.20 0.07

Required:
a. What was the risk premium on common stock in each year?
b. What was the average risk premium?
c. What was the standard deviation of the risk premium? (Ignore that the estimation is from a sample of data.)

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anthougo anthougo · Answer 1 · 2022-09-01T10:36:09+02:00

a) The risk premium on the common stock each year is as follows:

Year Risk Premium (%)

2013 33.00%

2014 2.50%

2015 -3.20%

2016 14.05%

2017 23.13%

b) The average risk premium is 13.90%.

c) The standard deviation of the risk premium is 13.21%.

A risk premium is an excess return from an investment above the risk-free rate of return.

An asset's risk premium compensates investors for their risk tolerance.

The risk premium is calculated as the return on an investment minus the return on a risk-free investment.

Year Stock Market T-Bill Return Risk Premium Squared Variability

Return (%) (%) (%) from the mean

2013 33.10 0.10 33.00% 364.81

2014 2.60 0.10 2.50% 129.96

2015 −3.10 0.10 -3.20% 292.41

2016 14.10 0.05 14.05% 0.0225

2017 23.20 0.07 23.13% 85.1929

The total risk premium for 5 years 69.48% 872.3954

Average risk premium 13.9% (69.48%/5) 174.47908 (872.3954/5)

Standard Deviation = 13.21% (√174.47908)

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