9Full derivation:

[ ] log 𝔼t eςφt+1(1−ρ) = (1− ρ)ςφ− (1− ρ)ςσ2∕2+ ((1− ρ)ς)2σ2∕2 r r = (1− ρ)ςφ− (1− ρ)ς(1− ς(1 − ρ))σ2r∕2 = (1− ρ)ςφ− (1− ρ)ς(1− ς)σ2∕2 − ρ(1 − ρ)ς2σ2∕2. r r