Dynamic Portfolio Choice and Consumption Plan under Inflation with Nominal and Indexed Bonds

We solve for an intertemporal portfolio-consumption choice problem under inflation. We assume that the nominal interest rate is observable while the expected inflation rate is not. The inclusion of the indexed bond in the investor's portfolio provides the investor an opportunity to perfectly hedge against the inflation risk. While the hedging demand of the nominal bonds would be crowded out proportional to the demand of the indexed bonds. The estimation risk of the estimated inflation rate would also introduce an additional hedging demand. We also show that the direction in which the interest rate and the inflation rate affect the optimal consumption-wealth ratio would rely on the elasticity of intertemporal substitution of the investor. When the elasticity of intertemporal substitution is smaller than one, the consumption-wealth ratio is increasing in the nominal interest rate and decreasing in the inflation rate; the income effect dominates. When the elasticity of intertemporal substitution is greater than one, the consumption-wealth ratio is affected in an opposite way; the substitution effect dominates. However, the consumption-wealth ratio is not decided by the real interest rate, i.e., the difference of the nominal interest rate and the inflation rate. It also depends on the absolute levels of the nominal interest rate and the inflation rate. The nominal and real consumption growth rates are derived. The nominal consumption growth is decided by the sum of the real consumption growth rate and inflation rate