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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.)

Average risk premium: __________

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

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.

Answer and Explanation:

Question (a)

Formula of calculating the yearly risk premium:

{eq}\begin{align*} Risk~premium&=Stock~return-T-Bill~return\\ Year~1~risk~premium&=0.3333-.0470\\ &=.2863\\ Year~2~risk~premium&=0.3250-.0110\\ &=.3140\\ Year~3~risk~premium&=0.1376-.0030\\ &=.1346\\ Year~4~risk~premium&=0.0468-.0070\\ &=.0398\\ Year~5~risk~premium&=0.2026-.0090\\ &=.1936\\ \end{align*} {/eq}

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:

{eq}\sigma =\sqrt{\frac{\sum (x-\bar{x})^{2}}{n-1}}\\ whereas:\\ x=risk~premium\\ \bar{x}=average~risk~premium\\ n=number~of~periods\\ {/eq}

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%


Learn more about this topic:

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How to Calculate Risk Premium: Definition & Formula

from Financial Accounting: Help and Review

Chapter 5 / Lesson 26
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