The return on everything and the business cycle in production economies

Abstract

Motivated by recent empirical evidence on returns on equity, bonds, and housing, we study interactions among an economy’s total net worth, consisting of housing and equity, the business cycle, and three specific types of productivity risk: standard, long-run, and disaster. Preferences include habits or follow a generalized recursive form. Procyclical housing adjustments reduce consumption risk as residential investment determines the next-period amount of housing as a fraction of the composite consumption good. The existence of an asset that is safe in real terms and has a positive supply prevents versions with habits or long-run risk from simultaneously replicating risk premia, investment volatility, and housing demand. The disaster risk version replicates these targets. In all versions, a perfectly negative correlation between equity returns and the marginal utility of consumption places the equity Sharpe ratios in the upper bound of any Sharpe ratios (the Hansen–Jagannathan bound). Consequently, replicating Sharpe ratios of housing larger than equity is impossible.