Con Keating is currently in hospital with a poorly foot. He is a caged tiger on the ward, but the surfeit of energy has been dispelled by his putting his mind to what Bill Sharpe called the nastiest hardest problem in finance.
This is the result of Con Keating’s cogitations in hospital – drawdown is not for the faint hearted
The nastiest hardest problem.
It is a recurrent theme of many blogs that the conversion of a pension “pot” to an income in retirement is a very hard problem. The nature of the problem is simple to illustrate. It is that our life expectation does not decline linearly with elapsed time.
In this note, for simplicity, we will work with a unit fixed nominal pension, payable annually in arrears, with interest rates of zero. We use the ONS 2014-2016 life tables.
Suppose we have a fund equal to the sum of the expected annual pension payments, £22.73. In the first year of retirement, we pay £1 of pension and the fund is now worth £21.73. However, we find that our life expectation is now 21.9 years, and we will not have sufficient funds to pay pensions to this average age of death. The problem repeats and grows as every year passes. After 23 years we have exhausted all of the funds available to us, but still have a life expectation of a further 6.8 years.
The cumulative effect of this conditional cost is illustrated below.
It is worth considering the position when this problem is collectivised, as is the case with insured annuities, or as proposed in CDC. The diagram below shows the annual payments under these collective arrangements; pension payments now follow the survival curve.
One of the great attractions of drawdown is the fact that that if death occurs prior to the average life expectation, there will be funds remaining which form part of the deceased’s estate. Unlike annuities these sums are not lost. Of course, there would also be a corresponding shortfall if death does not occur until some age after the expectation. This is illustrated below.
The total cost of a drawdown pension is the member survives to age 100 years is £40, 166% of the cost of collective annuitisation. This would require an excess return from the investment of the fund of 1.28% pa to offset this shortfall. If survival is to age 90, the cost is 132% and the excess return required would be 93 basis point per annum. This is a very considerable hurdle for drawdown management to achieve.
If we alter the basic set up to reflect pensions in reality, adding indexation and other real-world features, the hurdle illustrated grows in magnitude and significance. This is illustrated below for pension indexation of 2.5% pa. The capital deficit at year 40 has increased from 17.7 to 46.36.
Drawdown really is not for the faint-hearted, or those without other resources from which to replace the pension income.
This note has not considered the problem of realising asset values to pay pensions. That brings with it a further set of problems. Among these are the sensitivity of the fund to the stochastic variation of market prices and the dependence of the pension upon early realisations. Glide paths and similar de-risking strategies are one attempt to minimise these issues, though they usually come at the expense of returns.
About the author
Con Keating is an adviser to AgeWage and on the board of Warwick Business School. He lives in Leamington Spa and is currently recovering from a foot infection in a local hospital- we wish him a speedy recovery!