When is a Risky Asset 'Urgently Needed'?

Forthcoming, American Economic Journal: Microeconomics

30 Pages Posted: 12 Oct 2012 Last revised: 30 Jul 2013

See all articles by Felix Kubler

Felix Kubler

University of Zurich; Swiss Finance Institute

Larry Selden

Columbia University - Columbia Business School, Finance

Xiao Wei

Fudan University - School of Economics

Date Written: October 10, 2012

Abstract

The demand for commodities in standard applications typically is increasing in income, whereas the demand for the risk free asset in the classic portfolio problem often decreases with income. The latter is shown to occur if and only if the consumer’s uncertainty preferences over assets satisfy the condition that the risk free asset is more readily substituted for the risky asset as the quantity of the risky asset increases. In this case, the risky asset is said to be "urgently needed" following the terminology of Johnson in his classic 1913 certainty analysis. The asset and certainty settings differ in critical ways which result in a much greater likelihood for the urgently needed preference property to be satisfied in the portfolio problem. We provide several sufficient conditions for when the risky asset will be urgently needed and a surprisingly simple, complete characterization for widely popular members of the HARA (hyperbolic absolute risk aversion) class. For more general preferences, two examples are given where it is possible to fully describe the region of asset space in which the risky asset is urgently needed. Finally, using a standard representative agent model we show that the risky asset being urgently needed is equivalent to the equilibrium (relative) price of the risky asset increasing with its own supply.

Suggested Citation

Kubler, Felix E. and Selden, Larry and Wei, Xiao, When is a Risky Asset 'Urgently Needed'? (October 10, 2012). Forthcoming, American Economic Journal: Microeconomics, Available at SSRN: https://ssrn.com/abstract=2160968 or http://dx.doi.org/10.2139/ssrn.2160968

Felix E. Kubler

University of Zurich ( email )

Rämistrasse 71
Zürich, CH-8006
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Larry Selden (Contact Author)

Columbia University - Columbia Business School, Finance ( email )

3022 Broadway
New York, NY 10027
United States

Xiao Wei

Fudan University - School of Economics ( email )

600 GuoQuan Road
Shanghai, 200433
China

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