Considering optimal physical investment a *, and substituting the equilibrium interest rate (2.8) into (2.7e) we get the equilibrium expected return on any contingent claim:
Now, applying Ito's lemma to F ( W, Y, t ), and making use of (2.5) and (2.2):
with:
Now comparing the volatility components of (2.10) and (2.3) we have:
Substitution into (2.9) gives:
which by (2.8) becomes:
So the equilibrium expected return on any contingent claim may be written as the risk-free return rF , plus a linear combination of the first derivatives of the contingent claim price with respect to wealth W , and the state variables Y . The coefficients of these derivatives are independent of the contractual specification for that claim; hence they are the same for all contingent claims. CIR [ 17 ] explain that these coefficients may be interpreted as factor risk premia [4] .
[4] Specifically from (2.11), the risk premium for the i th state variable Y i is