Notes on inflationary news and the equity premium puzzle in a two-asset incomplete-markets model

The paper develops a "Catch-22" model of optimal consumption and portfolio allocations in continuous time in the absence of assets enabling simultaneous insurance against potentially correlated equity returns risk and inflationary news risk. As such, no portfolio choice can attain full insurance, involving trading off exposure to equity risk for exposure to innovations against expected inflation. Based on the formulation of the problem via the Hamilton-Jacobi-Bellman equation and the reduction of the stochastic dynamic optimisation programme to a non-stochastic recursive problem, analytical results from the model highlight a critical dimension to pricing risk at the margin in the model, with implications for an analysis of the Equity premium puzzle relative to standard Mehra-Prescott environments. The paper shows that a potential (partial) answer to the equity premium puzzle, in a Catch-22 environment resulting from a combination of stochastic inflation and incomplete-markets, (i) plausibly comes down to how heavy-tailed is the distribution of inflationary news, and (ii) how heavy-tailed such distribution must be to explain a larger positive premium in turn depends on the nominal-real covariance. A combination of heavy-tailed distributions of innovations or news against the expected inflation rate and a negative nominal-real covariance, in particular, can explain large(r) Equity Premia. The findings also highlight a new nexus between monetary policy regimes and the Premium.