Multiplicative Risk Prudence, Inflation Uncertainty and the Real Risk-Free Rate Puzzle

30 Pages Posted: 27 Jul 2010  

George Wong

The Hong Kong Polytechnic University

Xin (Simba) Chang

Cambridge Judge Business School; Nanyang Business School

Bruce D. Grundy

University of Melbourne

Date Written: May 11, 2010

Abstract

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.

Keywords: Multiplicative risk, Risk prudence, Background risk, Inflation Uncertainty, Risk-free Rate Puzzle, Precautionary savings.

JEL Classification: E21, D81

Suggested Citation

Wong, George and Chang, Xin (Simba) and Grundy , Bruce D., Multiplicative Risk Prudence, Inflation Uncertainty and the Real Risk-Free Rate Puzzle (May 11, 2010). Australian Centre for Financial Studies - Finsia Banking and Finance Conference 2010. Available at SSRN: https://ssrn.com/abstract=1649231 or http://dx.doi.org/10.2139/ssrn.1649231

George Wong (Contact Author)

The Hong Kong Polytechnic University ( email )

School of Accounting and Finance
Hung Hom, Kowloon, 0
Hong Kong
852 3400 3459 (Phone)
852 2330 9845 (Fax)

Xin Chang

Cambridge Judge Business School ( email )

Trumpington Street
Cambridge, CB2 1AG
United Kingdom

HOME PAGE: http://sites.google.com/site/simbachangxin/

Nanyang Business School ( email )

S3-B1B-76 Nanyang Avenue
Singapore, 639798
Singapore

HOME PAGE: http://www.ntu.edu.sg/home/changxin

Bruce D. Grundy

University of Melbourne ( email )

Faculty of Economics & Commerce
Department of Finance
Victoria, 3010
Australia
+61 3 8344 9083 (Phone)
+61 3 8344 6914 (Fax)

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