Question

Suppose that the risk-free interest rate is 4% per year, and the expected return on the market portfolio is 10% per year. The standard deviation of the return on the market portfolio is 24% per year. A consumer products company, ACC Corp, has a standard deviation of return of 45% per year, and a correlation with the market of 0.28

a)   What is ACC’s beta?

b) If the CAPM holds, what is ACC’s required rate of return on equity?

Answer 1

Answer a.

Beta of ACC = Correlation between ACC and Market * Standard Deviation of ACC / Standard Deviation of Market
Beta of ACC = 0.28 * 0.45 / 0.24
Beta of ACC = 0.525

Answer b.

Required Return = Risk-free Rate + Beta * (Market Return - Risk-free Rate)
Required Return = 4.00% + 0.525 * (10.00% - 4.00%)
Required Return = 4.00% + 3.15%
Required Return = 7.15%