Multiplicative Risk Prudence, Inflation Uncertainty and the Real Risk-Free Rate Puzzle
The Hong Kong Polytechnic University
Xin (Simba) Chang
Cambridge Judge Business School; Nanyang Business School
Bruce D. Grundy
University of Melbourne
May 11, 2010
Australian Centre for Financial Studies - Finsia Banking and Finance Conference 2010
We examine the optimal saving decision of individuals who face a multiplicative risk. An individual is defined to be multiplicative risk prudent if multiplying a pure risk to her future wealth raises her optimal savings. We show that convex marginal utility is not sufficient to induce multiplicative risk prudent. Instead, an individual is multiplicative risk prudent if and only if her relative prudence of future consumption uniformly exceeds two. Our results provide an explanation to the real risk-free rate puzzle. Intuitively, the presence of (or an increase in) inflation uncertainty in an economy should stengthen the aggregate precautionary motive to save, leading to a reduction in the equilibrium real risk-free rate. Thus neglecting inflation uncertainty may result in an overestimation of real risk-free rate. We also study jointly the impact of correlated additive and multiplicative risks on the optimal savings decision and demonstrate that the concept of multiplicative risk prudence is stronger than that of additive-multiplicative risk prudence. Our findings suggest one should take the condition of multiplicative risk prudence as a natural restriction on preference.
Number of Pages in PDF File: 30
Keywords: Multiplicative risk, Risk prudence, Background risk, Inflation Uncertainty, Risk-free Rate Puzzle, Precautionary savings.
JEL Classification: E21, D81
Date posted: July 27, 2010