Income Drawdown Schemes for a Defined-Contribution Pension Plan

Journal of Risk and Insurance, Vol. 75, No. 3, pp. 739-761

Posted: 11 Jul 2008

See all articles by Paul Emms

Paul Emms

King's College London

Steven Haberman

City University London - Faculty of Actuarial Science

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Date Written: July 11, 2008

Abstract

In retirement a pensioner must often decide how much money to withdraw from a pension fund, how to invest the remaining funds, and whether to purchase an annuity. These decisions are addressed here by introducing a number of income drawdown schemes, which are relevant to a defined-contribution personal pension plan. Rather than assume that drawdown is at a constant rate fixed at retirement, we describe pension schemes which maintain the expected level of the pension fund over the drawdown period, whilst investing the fund in a portfolio of a risky and riskless asset. Since the pensioner takes on investment risk, we find the optimal asset allocation which minimises the expected loss of the pensioner as measured by the performance of the pension fund against a benchmark. Two benchmarks are considered: a risk-free investment and the price of an annuity. If income drawdown is proportional to the fund performance then the optimal fund performance has positive drift. The fair-value drawdown rate is defined so that the fund performance is a martingale under the objective measure. Annuitisation should occur if the expected fair-value drawdown rate falls below the annuity rate available at retirement. Since the pensioner takes on investment risk, the annuitisation age depends on the risk preferences of the individual. As an illustration, the annuitisation age is calculated for a Gompertz mortality distribution function and a power law loss function.

Keywords: Income drawdown, defined contribution pension scheme

JEL Classification: H55, G23

Suggested Citation

Emms, Paul and Haberman, Steven, Income Drawdown Schemes for a Defined-Contribution Pension Plan (July 11, 2008). Journal of Risk and Insurance, Vol. 75, No. 3, pp. 739-761 . Available at SSRN: https://ssrn.com/abstract=1158386

Paul Emms (Contact Author)

King's College London ( email )

Strand
London, England WC2R 2LS
United Kingdom

Steven Haberman

City University London - Faculty of Actuarial Science ( email )

London
United Kingdom

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