Improved Optimal Investment and Consumption Strategies under Inflation Risk with Stochastic Volatility

This paper develops and calibrates a financial market model that incorporates stochastic volatility in inflation, interest rate and equity dynamics. Traditional models typically assume constant inflation volatility, which limits investors’ responsiveness to economic shifts as a result of geopolitical tensions and events such as the COVID-19 pandemic. Our multidimensional affine model structure therefore extends the classical Brennan and Xia (2002) framework with a macroeconomic stochastic variance component that allows the model to capture the interdependence of asset price returns and inflation dynamics. Because the premium associated with macroeconomic risks is not directly observable and may vary with the level of uncertainty, we consider multiple model specifications that differ in how bond risk premia depend on this level. We make three contributions. First, we show how to determine optimal consumption and portfolio strategies for finite-horizon investors with constant relative risk aversion risk preferences, by solving the extended version of the Hamilton-Jacobi-Bellman equation numerically. Secondly, we demonstrate that taking account of stochastic volatility in these strategies yields substantial welfare gains. A key difference from strategies that do not account for a stochastic variance component is that the sensitivities of the optimal portfolio value to both inflation and equity price shocks decrease with the level of macroeconomic uncertainty. Finally, our sensitivity analyses confirm the robustness of the observed welfare gains for various model specifications and different data periods. Conditioning consumption and investment strategies on the level of macroeconomic uncertainty is welfare enhancing even when the parameters governing its dynamics cannot be perfectly estimated.