# Calculate the beta when market fluctuates

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 .

Beta, Cost of Equity, Style portfolios

Please see the attached file.

1. The cost of equity for Ryan Corporation is 8.4%. If the expected return on the market is 10% and the risk-free rate is 5%, then the equity beta is ___

2. The beta of a firm is more likely to be high under what two conditions?

high cyclical business activity and low operating leverage

high cyclical business activity and high operating leverage

low cyclical business activity and low financial leverage.

low cyclical business activity and low operating leverage

None of the above.

3. Beta is useful in the calculation of the

company's variance.

company's discount rate.

company's standard deviation.

unsystematic risk.

company's market rate.

4. Style portfolios are characterized by

their stock attributes; P/Es less than the market P/E are value funds.

their systematic factors, higher systematic factors are benchmark portfolios.

their stock attributes; higher stock attribute factors are benchmark portfolios.

their systematic factors, P/Es greater than the market are value portfolios.

There is no difference between systematic factors and stock attributes.

5. Comparing two otherwise equal firms, the beta of the common stock of a levered firm is ____________ than the beta of the common stock of an unlevered firm.

equal to

significantly less

slightly less

greater

None of the above.