That sounds pretty encouraging but sadly the real world is not so simple. Although real investment returns have averaged 3.1pc a year over the past 125 years, over 20-year periods they have varied from -2.7pc to +9.8pc.

All we can say with certainty about the future is that the latter figure will not be matched because gilt yields – a benchmark for the financial markets – are now at historic lows. 

Our 65-year-old woman is predicted to live to 90. However, she might be unlucky enough to die just one day after her 65th birthday but also has a one-in-four chance of reaching 95. In fact, the odds are probably higher than that because rich people live longer than the poor and life expectancy has been rising by about a year every decade.

Changing the investment return assumption to -2.7pc a year and life expectancy to 30 years reduces the maximum withdrawal rate to 2.2pc, with the value of the fund falling by 60pc after 15 years. Hardly a comfortable prospect. 

And that’s not all: investment returns will not be even, but volatile from year to year. When you withdraw money from a portfolio you are vulnerable to “pound cost ravaging”, the opposite of “pound cost averaging”, a known bonus for regular savers. The essence is that when prices are low you have to sell more units to get the same amount of cash.

As a result of all these factors, I don’t believe there is a safe fixed rate of withdrawal. Does that mean that everyone should buy an annuity? 

Definitely not. An annuity may be the only way to insure against the risk of living longer than average but right now could be the worst time in history to buy one. Bond yields are at record lows, which has a direct negative impact on annuity terms. 

In addition, an unintended consequence of pensions freedom has been that many people with low life expectancy who were previously forced to buy annuities no longer need to do so. With less of a windfall from annuity-holders who die early, insurance companies have had to lower their rates even further. 

I reckon it’s probably better at the moment to keep a pool of cash on one side to maintain flexibility and then review the situation regularly. How about just withdrawing income, leaving your capital intact?

A typical UK equity income fund currently yields about 4pc. Dividends usually rise at least in line with inflation, so surely that’s a better solution than playing roulette with your capital, or buying an annuity while gilt yields are at rock bottom? 

It probably is but there are no guarantees. Go back to the Thirties and dividends from British shares more than halved within six years. If you were totally reliant on that income, that would be a problem.

The optimal course of action will depend on your individual circumstances and preferences, but there are a few general guidelines that I’d recommend.

First, split your expenditure into two groups. The first covers core essentials and emergencies: include all items that are needed to have a moderately comfortable lifestyle.

Take steps to ensure that you will have enough income and capital to cover these costs in all circumstances plus enough liquid cash to cover 12 months’ spending.

The second group is discretionary spending: on holidays, asset purchases, etc. Be prepared to be flexible with these so you can reduce spending during tough times and minimise the impact of pound cost ravaging.

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