R(Mytax) = 0.08 - F(INFL) + 1.2*F(GDP)+ e(Mytax)
R(Finotech) = 0.06 + 4*F(INFL) + 1.6*F(GDP) + e(Finotech)
The weight of portfolio invested in Mytax is 80% and invested in Finotech is 20%.
Why does this macroeconomic factor portfolio have zero sensitivity to a surprise in inflation?
R(Port) = 0.8[R(Mytax)] + 0.2[R(Finotech)]
= 0.8[0.08 − F(INFL) + 1.2*F(GDP) + e(Mytax)] + 0.2[0.06 + 4*F(INFL) + 1.6*F(GDP) + e(Finotech)]
= 0.064 – 0.08F(INFL) + 0.96F(GDP) + 0.8e(Mytax) + 0.012 + 0.8 F(INFL) + 0.32 F(GDP) + 0.2e(Finotech)
= (0.064 + 0.012) + (–0.08 + 0.08)F(INFL) + (0.96 + 0.32)F(GDP) + 0.8e(Mytax) + 0.2e(Finotech)
= 0.076 + (0.00)F(INFL) + 1.28F(GDP) + 0.8e(Mytax) + 0.2e(Finotech)
= 0.076 + 1.28** F(GDP) + 0.8e(Mytax) + 0.2e(Finotech)**