Original question: Select any publicly traded company of your choice, construct or set up an equation to calculate the expected or required rate of return for the company using the APT model.

Using the answer below, how were the elements ( R_F + B_PiF_i + B_PjF_j ) to the formula obtained?

The APT model describes the expected return on securities in the financial markets subject to the movement of macroeconomic factors, and the sensitivity of the securities or asset to those factors. The expected rate of return using APT Model can be calculated using the below equation:

E(R_P) = R_F + B_PiF_i + B_PjF_j

where,

E(R_P) = Expected return on securities or asset P

R_F = Risk free rate

F_i = Factor risk premium for factor i

Fj = Factor risk premium for factor j

B_Pi = Sensitivity of the asset to factor i

B_Pj = Sensitivity of the asset to factor j

The macro economic factors which are considered mainly while application of the APT model are inflation, confidence of shareholders, GNP, etc.

Considering the case of Pepsi Company, the expected rate of return is calculated as follows:

The Risk free rate, R_F = 3.01%, The macro economic factors taken into consideration are inflation and GNP rates.

E(R_P) = R_F + B_PiF_i + B_PjF_j

F_i = 4%

Fj = 3%

B_Pi = 0.8

B_Pj = 1.1

E(R_P) = 3.01% + 0.8(4%) + 1.1(3%)

E(R_P) = 9.51%

Hence, the expected rate of return of Securities of Pepsi Company is 9.51%.