Academic journal article Journal of Risk and Insurance

Income Drawdown Schemes for a Defined-Contribution Pension Plan

Academic journal article Journal of Risk and Insurance

Income Drawdown Schemes for a Defined-Contribution Pension Plan

Article excerpt


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. The optimal asset allocation is defined so that it minimizes 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. The fair-value income drawdown rate is defined so that the fund performance is a martingale under the objective measure. Annuitization is recommended if the expected fair-value drawdown rate falls below the annuity rate available at retirement. As an illustration, the annuitization age is calculated for a Gompertz mortality distribution function and a power law loss function.


A defined-contribution (DC) pension scheme provides an income for a pensioner after retirement from a fund built up from investing a series of contributions during their period of employment. The financial risk is taken by the member of the scheme since the fund is associated with an individual and there is no guarantee of a fixed benefit level at retirement. The pension scheme is split into two phases. During the accumulation (or preretirement) phase, scheme members and/or their employer contribute to the pension fund, which is invested in a portfolio of assets with a particular risk profile. In the distribution (or postretirement) phase pensioners receive periodic income from the fund in order to provide support in old age. There are a number of mechanisms operating in different countries for distributing the pension fund (Lunnon, 2002).

In some countries, the retirement income is provided by an annuity, which (according to regulations) must be bought at retirement and provides an income for the lifetime of the pensioner. In the United States there is no such requirement, and an individual can choose whether to withdraw from the DC pension fund subject to certain restrictions. For example, in the 401(k) DC pension plan the pensioner must begin to withdraw the required minimum distribution (RMD) from the fund by the age of 70.5. In the United Kingdom the pensioner has the option to defer the purchase of the annuity and instead receive income direct from the pension fund. This is called the income drawdown option. However, irrespective of the details of distribution phase of a particular DC plan, the pensioner faces the problem of how much money to withdraw in retirement, how to invest the remaining funds and whether to purchase an annuity. These are the problems that we address here.

There is a growing literature on investment decisions in the accumulation phase of the DC pension scheme (Blake, Cairns, and Dowd, 2001, and cited references). There is less literature on the distribution phase and the income drawdown option (Milevsky, 1998; Lunnon, 2002; Blake, Cairns, and Dowd, 2003; Gerrard et al., 2004; Gerrard, Haberman, and Vigna, 2004, 2006).

Milevsky (1998) finds the optimal time to annuitize based on a deterministic model, and a more sophisticated stochastic model incorporating stochastic interest rate, asset and mortality models. For the deterministic model, the optimal time to annuitize is when the fund is unable to provide an income stream comparable to an annuity. For the stochastic model, Milevsky finds the probability that the attainable consumption is greater than the initial consumption. If one sets a threshold for this probability, then one can determine the optimal time to annuitize. Milevsky and Young (2000) fix the income drawdown rate and invest the fund in a single risky asset. They find the eventual probability of ruin, and find an approximation in order to determine if ruin occurs before the time of death; that is, the pensioner outlives his or her funds. …

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