Question

A researcher has determined that a two-factor model is appropriate to determine the return on a stock. The factors are the percentage change in GNP and an interest rate. GNP is expected to grow by 4.3 percent and the interest rate is expected to be 3.8 percent. A stock has a beta of 2 on the percentage change in GNP and a beta of –.82 on the interest rate. If the expected rate of return on the stock is 11 percent, what is the revised expected return on the stock if GNP actually grows by 3.9 percent and the interest rate is 4.1 percent? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Revised expected return = ________ %

Answer 1

The expected return on the stock can be calculated by the 2 factor model as :

Re = Rf + beta ( percentage change in GNP ) + beta * (percentage change in interest rate)

11% = Rf + 2 * 4.3 - 0.82 * 3.8

11% = Rf + 8.6 - 3.116

Rf = 5.516%

So, the revised expected rate of return will be :

= Rf + beta * 11% + beta* 4.1%

= 5.516% + 2 * 3.9 % - 0.82 * 4.1%

= 13.316 - 3.362

= 9.954%

= 9.95% ( rounded off to two decimal places)

So, the revised expected rate of return is 9.95%.