Capital Risk: Precautionary and Excess Saving

Abstract

Precautionary saving typically refers to the additional investment in a risk free asset when exogenous labor income is risky versus certain. When risky income results endogenously from the investment in a risky asset, the meaning and characterization of precautionary saving change and far less is known about this case. Capital risk is important for macro and finance models as risk often arises from the variability in asset returns, and precautionary saving plays a key role in interpreting the results. We assume KPS (Kreps-Porteus-Selden) preferences with additively separable time preferences and HARA (hyperbolic absolute risk aversion) risk preferences. Necessary and sufficient conditions are derived for saving to increase when investment is in a portfolio of risky and risk free assets versus just a risk free asset. Time preferences play an essential role whereas the frequently referenced risk preference property prudence is irrelevant. In macrofinance analyses, the equilibrium risk free rate is often shown to be less in the presence versus absence of capital risk and this is interpreted as reflecting a precautionary motive. However, this interpretation is not in consonance with the corresponding partial equilibrium demand analysis.