# Mortality: deal or no deal? It depends if you’re a couple

Investors in retirement regularly need to decide whether it’s the right time to annuitise. There are many factors in this decision, but a key issue investors should keep an eye on is ‘mortality drag’ – an ominous and mysterious term.

In this blog, I explain what this is, how it can differ for singles and couples, and when it might indicate the time has come for investors to rid themselves of longevity risk.

### Mortality drag – what is it?

To understand mortality drag, consider – just for illustration – a 70-year-old individual who (according to mortality tables) has a 1% chance of dying over the next year.

An insurance company can pool many ‘similar’ lives (in terms of estimated lifespan) alongside this individual. If they know that one in every 100 such people will die between 70 and 71, they can reflect that in cheaper[1] annuity rates for everyone at age 70. It will be roughly 1% cheaper than delaying for a year because the surviving annuitants effectively get a subsidy. This can be attributed to the sharing of the pots of those customers who die.

Someone who delays annuitising can’t benefit from that subsidy. This lack of subsidy is the mortality drag. Of course if they died during the year, their estate would have received their money instead of an insurance company, but if they have no-one to bequeath the money to that fact might not concern them.

This drag can be hard to beat. Early in retirement, mortality rates (i.e. the chances of death each year) are low so there is normally relatively little drag to worry about. But later in retirement it can become difficult to justify remaining in income drawdown, since expected returns on assets net of mortality drag can be low or negative.

### Couples

That explanation assumes the individual is single. But if they’re in a couple, does mortality drag change? Intuitively, pooling assets means longevity risk should be mitigated, there should be less drag, and so they can delay annuitising for longer. But how much longer?

Unfortunately, mortality drag is more complicated in those circumstances because it also comes with uncertainty. If the individual is single and they survive the year, then they *know* their mortality drag for that year. But if they’re in a couple and they survive the year, *two* things could have happened:

A) Their spouse survived. In that case, there is a mortality drag of 1% again (if we use the same example as above).

B) Their spouse passed way. That’s obviously a horribly sad event, but purely from a financial perspective there’s a mortality gain, since their pot (or share of the combined pot) doubles. The mortality *gain* in this case turns out to be 98%.[2]

The *expected *mortality drag over the year is very low, equal to the chance that both the individual and their spouse die.[3] However, it is also uncertain because it can take two very different values. So the question is: what should an appropriate ‘risk-adjusted’ mortality drag be?

### Deal or no deal? Risk-adjusting mortality drag

It’s possible to calculate a risk-adjusted drag consistent with the investor’s choice of investment strategy in drawdown. The basic idea is that the choice of income drawdown fund reveals information about their risk tolerance. We can use that to convert uncertain mortality drag into a certain but higher ‘risk-adjusted’ drag that the investor would be equally (un)happy with.

This is rather like a contestant on ‘Deal or No Deal’ choosing to accept an offer from ‘The Banker’ – a known amount as opposed to an uncertain one. Logically they should take a lower offer from The Banker if the average remaining box amount is lower, the remaining boxes are more variable, or if they are more risk averse. The same idea applies here: the more uncertain mortality drag is, the worse the risk-adjusted drag. The extent to which it is worse depends on how cautious the individual is.

### Delaying annuitisation

The results of my calculations are shown below.

These calculations assume all investors are exposed to the same mortality rates[4] (for simplicity) and they’re invested in a fairly typical income-drawdown strategy.[5]

From our graph we can deduce that if (for example) the most risk-adjusted mortality drag the individual will tolerate is 1.75%[6], then the right age to annuitise[7] is about 76 if single but two years later – aged 78 – if in a couple.[8]

Conversely, if someone becomes single through bereavement or divorce, risk-adjusted mortality drag increases (jumping up to the red line). This could act as a trigger to annuitise based on the logic above. However, there may be other factors at play – the fact that their share of the pot has just doubled may make them less risk averse, for example.

In future blogs, I’ll explain in greater depth how knowledge of your mortality drag can help you choose the right investment strategy in retirement – when, like Deal or No Deal, you should take that offer from The Banker (here an insurance company). But unlike Deal or No Deal, we’ll also see how annuitisation doesn’t have to be an ‘all or nothing’ decision, and that mixing with income drawdown can help. Watch this space!

[1] Here I am assuming no guarantees are purchased.

[2] Calculated as 2 x 99% - 1. I’ve assumed the individual and their spouse have the same chance of death over the year of 1%.

[3] i.e. 1% times 1% = 0.01%. You can check this equals to the probability-weighted drags from possibilities A and B: 99% x 1% - 1% x 98% = 0.01%.

[4] These are purely illustrative mortality rates, broadly consistent with annuity pricing.

[5] For illustration I assumed a geometric risk premium of 3.5% pa and volatility of 8% pa.

[6] Under some assumptions you can show that if mortality drag exceeds half the growth risk premium of the income-drawdown strategy, then the individual would be better off annuitising, ignoring bequest motives.

[7] Gradual annuitisation is a good idea in theory, but for simplicity I assume annuitisation happens all at once.

[8] You can calculate results for larger groups. For example, the result is age 86 if pooling with your seven siblings! This is purely theoretical, although a messier version can happen in real life when families pool their resources and is one explanation for the annuity puzzle. The more people there are, the less uncertainty there is in mortality drag.