For constants > 0 and > 0, assume Mt def = et Ct C0

For constants δ > 0 and ρ > 0, assume Mt def

= e−δt

Ct C0

−ρ

is an SDF process, where C denotes aggregate consumption. Assume that dC C = α dt +θ
dB (13.56)
for stochastic processes α and θ.

(a) Apply Itô’s formula to calculate dM/M.

(b) Explain why the result of Part

(a) implies that the instantaneous risk-free rate is r = δ +ρα − ρ(ρ +1)
2 θ
θ (13.57)
and the price of risk process is λ = ρθ.

(c) Explain why the risk premium of any asset with price S is ρ
dS S dC C 
.
Note: This is a preview of the CCAPM (Section 14.6), which holds under more general assumptions.