Consider the multifactor APT with two factors. Stock A has an expected return of 20.70%, a beta of 1.2 on factor 1, and a beta of 0.6 on factor 2. The risk premium on the factor 1 portfolio is 4.00%. The risk-free rate of return is 8.40%. What is the risk premium on factor 2 if no arbitrage opportunities exist?

12.5%

Explanation:

expected return = 20.70%

risk-free rate of return is 8.40%

beta of on factor 1 = 1.2

risk premium on the factor 1 = 4.00%

beta of on factor 2 = 0.6

risk premium on factor 2 = x (unknown)

To calculate for the risk premium on factor 2, we use this formula

expected return = (beta of on factor 1 * premium on the factor 1) + (beta of on factor 2 * premium on the factor 2) + risk-free rate of return

20.70% = (1.2 * 4%) + (0.6 x) + 8.40%

0.207 = 0.048 + 0.6x + 0.084

0.207 = 0.132 + 0.6x

0.6x = 0.075

x = 0.125

=12.5%