Equilibrium under uncertain inflation: A discrete time approach

Most research dealing with portfolio selection under uncertain inflation is carried out by assuming either one of the following two approximations: a linear or a quadratic approximation. In this paper, we analyze the general case, namely assume that the nominal return is the product of the real return and one plus the rate of inflation. We demonstrate that the general analysis leads to the following results that are not found in the two approximations: (1) even if we assume that nominal returns are independent of inflation, the nominal and real efficient sets will not necessarily coincide. Mean-Variance (M-V) analysis leads to a nominal efficient set, that is, a subset of the real M-V efficient set, whereas the opposite holds assuming investors maximize expected utility of real wealth. (2) Similar results are obtained when real returns are independent of inflation (the Fisher hypothesis). Assuming normality of nominal returns, we derive the CAPM in real terms or its zero beta counterpart.