1. a. A stock\'s returns have the following distribution: Calculate the stock\'s
ID: 2780600 • Letter: 1
Question
1.
a.
A stock's returns have the following distribution:
Calculate the stock's expected return. Round your answer to two decimal places.
%
Calculate the stock's standard deviation. Do not round intermediate calculations. Round your answer to two decimal places.
%
Calculate the stock's coefficient of variation. Round your answer to two decimal places.
b.
A stock has a required return of 16%; the risk-free rate is 4.5%; and the market risk premium is 5%.
What is the stock's beta? Round your answer to two decimal places.
If the market risk premium increased to 7%, what would happen to the stock's required rate of return? Assume that the risk-free rate and the beta remain unchanged. :
I.If the stock's beta is greater than 1.0, then the change in required rate of return will be greater than the change in the market risk premium.
II.If the stock's beta is less than 1.0, then the change in required rate of return will be greater than the change in the market risk premium.
III.If the stock's beta is greater than 1.0, then the change in required rate of return will be less than the change in the market risk premium.
IV.If the stock's beta is equal to 1.0, then the change in required rate of return will be greater than the change in the market risk premium.
V.If the stock's beta is equal to 1.0, then the change in required rate of return will be less than the change in the market risk premium.
New stock's required rate of return will be ?%. Round your answer to two decimal places.
Company's Products Probability of This
Demand Occurring Rate of Return If
This Demand Occurs Weak 0.1 (22%) Below average 0.2 (12) Average 0.3 17 Above average 0.2 33 Strong 0.2 56 1.0
Explanation / Answer
1.
Expected return is the weighted average of individual returns
Expected return = 0.1*-0.22 + 0.2*-0.12 + 0.3*0.17 + 0.2*0.33 + 0.2*0.56 = 0.1830 = 18.30%
2.
Standard deviation is the square root of sum of squared deviaiton from the mean multiplied by probability
Std dev = [0.1*(0.183-(-0.22))^2 + 0.2*(0.183-(-0.12))^2 + 0.3*(0.183-0.17)^2 + 0.2*(0.183-0.33)^2 + 0.2*(0.183-0.56)^2]^(1/2) = 0.2596 = 25.96%
3.
Coefficient of variation = std dev/expected return = 0.2596/0.183 = 1.42
b.
Accoridng to CAPM,
Required return = risk free rate + beta*market risk premium
16% = 4.5% + beta*5%
beta = 2.3
- Option I - If the stock's beta is greater than 1.0, then the change in required rate of return will be greater than the change in the market risk premium.
Beta is the measure of change in the stock's return with change in market return.
- Required return = risk free rate + beta*market risk premium
Required return = 4.5% + 2.3*7%
Required return = 20.6%
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