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# Calculate the beta when market fluctuates

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19. Suppose the market portfolio is equally likely to increase by 30% or decrease by 10%.
a. Calculate the beta of a firm that goes up on average by 43% when the market goes up and goes down by 17% when the market goes down.
b. Calculate the beta of a firm that goes up on average by 18% when the market goes down and goes down by 22% when the market goes up.
c. Calculate the beta of a firm that is expected to go up by 4% independently of the market.

22. Suppose the market risk premium is 6.5% and the risk free interest rate is 5%. Calculate the cost of capital of investing in a project with a beta of 1.2.

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#### Solution Preview

19. Suppose the market portfolio is equally likely to increase by 30% or decrease by 10%.
Re=Rf + Beta*(Rm-Rf)
a. Calculate the beta of a firm that goes up on average by 43% when the market goes up and goes down by 17% when the market goes down.
When market portfolio is up, we have
43% = Rf + Beta*(30%-Rf) --Equation 1
When market portfolio is down, we have
-17% = Rf + Beta*(-10%-Rf) --Equation 2
From equation ...

#### Solution Summary

This post shows how to calculate the beta when market goes up n down in different percentage and calculate the cost of capital of investing in a project .

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