Precautionary Saving and Capital Risk: Saving vs Asset Reallocation

Insurance and macro models, increased capital risk results in higher risk free asset prices often attributed to precautionary saving. However at the demand level, even assuming the same preferences as in the equilibrium analysis, precautionary saving need not always hold. Assuming CES time and CRRA risk preferences, we derive conditions such that the consumer exhibits precautionary savng. Absent these conditions, a concrete example demonstrates that the consumer fails to exhibit precautionary saving. Key results are explained in terms of novel competing portfolio reallocation and saving components and portrayed by a natural extension of the canonical certainty Fisherian diagrammatic analysis.