Stochastic inflation affects the risk characteristics, measured by the equity premium and the correlation of the equity’s return with consumption, in a fundamental way. The riskiness of a dollar-denominated asset depends on two conditional covariances: the covariance of the marginal rate of substitution (MRS) with the equity price and the covariance of the MRS with the rate of appreciation in the purchasing power of money. The second covariance may take either sign which becomes significant when the risk characteristics of the dollar-denominated asset are compared with the risk characteristics of an indexed asset constructed in a real version of the model.
The effects of stochastic inflation on the assets’ risk characteristics are studied in a parameterized version of a cash-in-advance asset- pricing model. The growth rates of the endowment and monetary transfer evolve according to a VAR. The equity price is a geometric distributed lead of log–normally distributed random variables; an algorithm to express the price as an explicit function of the state variables is described.