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

## Question:

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

 Year Stock Market Return T-bill Return Year 1 -33.33 4.70 Year 2 32.50 1.10 Year 3 13.76 .30 Year 4 4.68 .07 Year 5 20.26 .09

a.) What was the risk premium on common stock in each year? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

 Year Risk Premium Year 1 __________ % Year 2 __________ % Year 3 __________ % Year 4 __________ % Year 5 __________ %

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

Standard deviation: __________ %

Risk premium refers to the rate of return that compensates for the level of risk in holding a certain asset such as stocks. The difference in the return of a stock against the risk-free rate is the risk premium.

#### Question (a)

Formula of calculating the yearly risk premium:

#### Question (b)

Formula in calculating the average risk premium:

{eq}\begin{align*} Average~risk~premium&=\frac{\sum stock~return}{number~of~periods}\\ &=\frac{.2863+.3140+.1346+.0398+.1936}{5}\\ &=\frac{.9683}{5}\\ &=.1937 \end{align*} {/eq}

The average risk premium is 19.37%

#### Question (c)

Formula of the standard deviation:

Solutions on calculating the standard deviation of the risk premium:

{eq}\begin{align*} \sigma=&\sqrt{\frac{(.2863-.1937)^{2})+(.3140-.1937)^{2})+(.1346-.1937)^{2})+(.0398-.1937)^{2})+(.1936-.1937)^{2})}{5-1}}\\ &=\sqrt{\frac{.0086+.0145+.0035+.0237+.0000}{4}}\\ &=\sqrt{\frac{.0502}{4}}\\ &=\sqrt{.0126}\\ &=.1121 \end{align*} {/eq}

The standard deviation of the risk premium is 11.21% 