Question

Manipulating CAPM Use the basic equation for the capital asset pricing model (CAPM) to work each of the following problems.

a. Find the required return for an asset with a beta of 1.44 when the risk-free rate and market return are 10% and 18%, respectively.
b. Find the risk-free rate for a firm with a required return of 14.530% and a befa of 1.11 when the market retum is 14%
c. Find the market return for an asset with a required return of 14.636% and a beta of 1.73 when the risk-froe rate is 5%.
d. Find the beta for an asset with a required return of 7.656% when the risk-free rate and market return are 6% and 8.4%, respectively.

Answer 1

Using the CAPM formula, we can determine the required return, risk-free rate, market return, and beta for different financial scenarios by manipulating and solving the CAPM equation accordingly.

Step-by-step explanation:

The Capital Asset Pricing Model (CAPM) is used to determine the expected return on an investment and is based on the risk and the time value of money. The formula for CAPM is:

Expected return = Risk-free rate + Beta * (Market return - Risk-free rate)

a. Required Return for an Asset:

For an asset with a beta of 1.44, the required return can be calculated as follows:

Required return = 10% + 1.44 * (18% - 10%) = 10% + 1.44 * 8% = 10% + 11.52% = 21.52%

b. Finding the Risk-free Rate:

To find the risk-free rate given a required return of 14.530% and a beta of 1.11 with a market return of 14%:

14.530% = Risk-free rate + 1.11 * (14% - Risk-free rate)

This equation can be solved for the risk-free rate.

c. Finding the Market Return:

If the required return is 14.636% and beta is 1.73 with a risk-free rate of 5%:

14.636% = 5% + 1.73 * (Market return - 5%)

This equation can be solved for the market return.

d. Finding Beta:

When the required return is 7.656% with a risk-free rate of 6% and a market return of 8.4%, we can solve for beta using the CAPM equation:

7.656% = 6% + Beta * (8.4% - 6%)

The beta can be determined from this equation.