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Luck of the drawdown

Pension City, UK, the gambling capital of the world, has a new game. The punter pays a stake of, say, £100,000. At each turn, a card from a normal deck is turned over and the pot is increased by £1,000 times the value of the card (an ace counts as one and the jack, queen and king as 11, 12 and 13 respecti vely). So, if a six comes up first time, the £100,000 is inc reased to £106,000.

After each turn, the gambler chooses whether to stay in the game or leave it. If he stops, his pot is reduced by an amount depending on the length of time he has played for. After the first turn, the reduction is £25,000. But this figure increases each time by £1,000 times the number of the turn. So, after two turns, the reduction is £27,000 (£25,000 plus £2,000), after three turns £30,000 (£27,000 plus £3,000) and so on. By the seventh turn, the reduction has reached £52,000.

If you play this game, you must be prepared to keep going for a reasonable time. If you stop after the third turn, the reduction is £30,000, which means you need to have averaged at least 10 to break even. Although gamblers are eternal optimists, most would agree they could not rely on averaging 10 or more over three turns.

It is quite easy to calculate what number of turns gives the lowest average req uired to break even. It is seven, when the average return needed is £7,429. Unless the gambler is confident he can achieve this, he should not play the game.

In fact, the long-term average return is £7,000 and a total of £52,000 or more will only be achieved about twice out of every five times. But many consider this a worthwhile bet.

The real-life equivalent of this game is income drawdown and the equivalent average is known as the “type A critical yield”. This is the average investment return needed over the drawdown period to match the income from the conventional annuity that could be bought at the start.

Like the average in our game, the type A critical yield depends on how long you continue drawdown and the pattern is also similar.

If drawdown continues for just a few years, the critical yield is high because the initial charges have to be offset by investment returns spread over a short period. The yield falls fairly rapidly, though, and typically bottoms out after seven to 10 years. It then rises because the effect of mortality drag becomes significant.

A typical pattern, based on a 60-year-old single male, is illustrated by the red line in the chart below.

The key point is that you must believe there is a good chance of matching the lowest critical yield on the graph unless you have another compelling reason for drawdown. For example, death benefits or income flexibility may be very important.

Another risk with income drawdown is that annuity rates could worsen. This is like adding a feature to our game where the final reduction is not fixed but dep ends on the turn of a card.

This risk is not allowed for in the critical yield calculation and it is prudent to make an allowance for it when deciding whether the critical yield is realistic. Indeed, mortality improvements are regularly reducing annuity rates and there is an argument for add ing 0.5 per cent to the critical yield just to allow for this.

Returning to our game, let us assume that the gambler has broken even by the seventh turn and must now dec ide whe ther he should con tinue and, if so, for how long. To maintain or increase his pot, he needs an eight or better on the next turn, then a nine or better and so on. Even tually, he will decide the risk of continuing is too great and quit the game. Exactly when that happens will depend on how lucky he is feeling but probably few will continue beyond the 10th turn.

There is a similar feature with income drawdown. We have looked so far at the critical yield at the start of drawdown but once the initial inv estment decision has been made your client needs to dec ide every year whether to continue. Again, it is possible to calculate a return needed over the next year to break even and that is shown by the blue line in the chart.

A key feature here is that the yield starts low after the first year but in later years it increases quite rapidly bec ause of mortality drag. This means a positive decision is needed each year on whether to continue drawdown or buy an annuity.

Do not automatically ass ume that all clients will continue drawdown until age 75. For our single male, annuity purchase by about age 71 might be sensible. After that, the year-on-year return nee ded is over 8 per cent, which repre sents a fairly high level of risk. For females and married couples, drawdown can generally continue for longer.

Used properly, the critical yield can be a valuable tool in making decisions on drawdown. The type A yield we have looked at here gives a useful indication of whether drawdown is a sensible opt ion and when it would be wise to buy an annuity.

However, it does not help much in deciding what level of income is sustainable. For that, we need a type B yield, which we will look at next week.

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