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Annuitization and asset allocation with HARA utility

Published online by Cambridge University Press:  06 October 2005

GEOFFREY KINGSTON
Affiliation:
School of Economics, University of New South Wales, Sydney (email: g.kingston@unsw.edu.au
SUSAN THORP
Affiliation:
School of Finance and Economics, University of Techonology, Sydney (email: susan.thorp@uts.edu.au

Abstract

A new explanation for the well-known reluctance of retirees to buy life annuities is due to Milevsky and Young (2002, 2003): Since the decision to purchase longevity insurance is largely irreversible, in uncertain environments a real option to delay annuitization (RODA) generally has value. Milevsky and Young analytically identify and numerically estimate the RODA in a setting of constant relative risk aversion. This paper presents an extension to the case of HARA (or GLUM) preferences, the simplest representation of a consumption habit. The precise date of annuitization can no longer be ascertained with certainty in advance. This paper derives an approximation whereby the agent precommits. The effect of increasing the subsistence consumption rate on the timing of annuity purchase is similar to the effect of increasing the curvature parameter of the utility function. As in the CRRA case studied by Milevsky and Young, delayed annuitization is associated with optimistic predictions of the Sharpe ratio and divergence between annuity purchaser and provider predictions of mortality.

Type
Research Article
Copyright
© 2005 Cambridge University Press

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Footnotes

We thank Hazel Bateman, Henry Jin, Moshe Milevsky, Sachi Purcal, Mike Sherris, Emil Valdez, Virginia Young, anonymous referees and conference participants at the 3rd IFID Centre Conference on Asset Allocation and Mortality, University of Toronto, the 11th Australian Colloquium of Superannuation Researchers, University of New South Wales, and the Australasian meeting of the Econometric Society 2004, for comments and advice. Plan for Life responded generously to our requests for data. Financial assistance from the Australian Research Council is gratefully acknowledged.