A researcher has determined that a two-factor model is appropriate to determine

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 3.6 percent, and the interest rate is expected to be 3.1 percent. A stock has a beta of 1.3 on the percentage change in GNP and a beta of 2.75 on the interest rate. If the expected rate of return on the stock is 12 percent, what is the revised expected return on the stock if GNP actually grows by 3.2 percent and the interest rate is 3.4 percent?

Explanation / Answer

Two factor model

Grown rate in GNP = 3.6%

Expected interest rate = 3.1%

Beta for change in GNP = 1.3

Beta of interest rate = 2.75

Expected rate of return = 12%

Error rate is calculated below using following formula:

Required rate of return = Error + r1× bi1 + r2 × bi2

                             12% = Error + (3.6% × 1.3) + (3.1% × 2.75)

                                      = Error + 4.68% + 8.525%

                                      = Error + 13.205%

                             Error = 12% - 13.205%

                                      = -1.205%

Error value is -1.205%.

Now if

Grown rate in GNP = 3.2%

Expected interest rate = 3.4%

By using above value Expected rate of return is calculated below:

Expected rate of return = Error + r1× bi1 + r2 × bi2

                                      = -1.205% + (3.2% × 1.3) + (3.4% × 2.75)

                                      = -1.205% + 4.16% +9.35%

                                      =12.305%

Hence, Expected rate of return is 12.305%.

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