Consider the multifactor APT with two factors. Stock A has an expected return of 17.6%, a beta of 1.45 on factor 1, and a beta of .86 on factor 2. The risk premium on the factor 1 portfolio is 3.2%. The risk-free rate of return is 5%. What is the risk-premium on factor 2 if no arbitrage opportunities exist?

The risk premium on factor 2 = 9.26%.

Explanation:

Let us denote the risk premium of factor 2 as x

Below is the formula we can use to calculate the risk premium of factor 2.

Expected return on stock = (Beta (factor 1)* expected return of 1) +(beta of 2x * risk free reate)

17.6% = (1.45*3.2%) + 0.86x+5%

17.6 = 4.64 + 0.86x+5%

17.6 - 4.64 - 5= 0.86x

7.96 = 0.86x

x = 7.96/0.86 =9.2558

The risk premium on factor 2 = 9.26%.

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