Two-factor Arbitrage Pricing Model

Macroeconomic multi factor model equations:
R_D = 0.09 + 1.0F_IS + 0.0F_BC
R_E = 0.08 + 0.0F_IS + 1.0F_BC

F_IS: surprise in investor sentiment
F_BC: surprise in the business cycle

Two-factor Arbitrage Pricing Model
E(R) = risk free rate + b_ISRP_IS + b_BCRP_BC

risk free rate = 0.05
b_IS = 1.25
b_BC = 1.10
RP_IS: risk premium associated with risk factor IS
RP_BC: risk premium associated with risk factor BC

According to the multi factor equations, the expected return (intercept) for the investor sentiment factor portfolio (D) = 9% and for the business cycle factor portfolio (E) equals 8%. Risk premiums are defined as the difference between the expected return on the appropriate factor portfolio and the risk-free rate.

Therefore,
RP_IS = 0.09 - 0.05 = 0.04
RP_BC = 0.08 - 0.05 = 0.03

The expected return for Portfolio P equals
0.05 + 1.25 * 0.04 + 1.10 * 0.03 = 0.133