Do level annuities hedge enough longevity risk?

In this blog I investigate two questions that should be of interest to investors in decumulation. Why might they choose a level annuity over an inflation-linked one? And could this choice influence the ideal age to purchase an annuity?

This follows on from a couple of previous blogs (please see here) and (please see here), which explore how big an issue longevity risk can be in retirement, and the potential influence of pooling resources with a spouse.

Erosive inflation

Purchasing an annuity, regardless of its precise form, benefits investors in the sense that survivors are effectively subsidised by those that die. This rids them of what is known as ‘mortality drag’. However, longevity uncertainty can still matter if the annuity payments don’t line up with spending needs.

The most straightforward example of this is a level annuity: if the investor lives a long life, their annuity income is likely to be heavily eroded (in ‘real terms’ i.e. spending power) by inflation. The chart below shows how annual payments from the same investment (here £100,000) at age 66 might compare between level and inflation-linked annuities. 

The inflation-linked annuity starts at a lower level but is expected to increase (in nominal terms) over time. A level annuity is comparatively risky in terms of spending power. This is largely because the investor may live longer than anticipated. As you can see from the ‘Real annuity payments’ chart, the longer the investor lives, the more that spending power falls. We say that their real retirement income is ‘front-end loaded’. A further risk, of course, stems from the fact that inflation itself is uncertain, i.e. it may not evolve in line with expectations.

Spending patterns

There could be some good reasons for investors to front-end load their real retirement income from their DC savings. These include the following:

• They plan to spend more in the earlier parts of their retirement, in their more ‘active’ years
• They don’t expect the prices of the things they plan to spend on to go up as fast as the RPI index
• The generous triple lock on their state pension, which they expect to continue, compensates to some extent
• Negative real interest rates are incentivising them to spend more now
• They view breakeven inflation levels in the UK as expensive, perhaps due to structural supply and demand issues in the UK.

However, in this blog I assume that really their spending needs would be best suited by an inflation-linked annuity, but they’ve chosen a level one for psychological reasons. Such reasons might include:

• Money illusion i.e. neglect of inflation
• An optically more attractive headline rate
• A tendency to underestimate their future lifespan
• Neglect of the risk of high care costs in old age
• Neglect that even if a falling real income suits them better, there is no guarantee it will fall at the same pace as inflation.

Under this (admittedly strong!) assumption the questions are: how bad is this potential ‘mistake’? And what are the implications for when to purchase an annuity?

Horrible haircuts

To understand how ‘bad’ the choice was (i.e. spending too much early in retirement relative to later) I calculated how much lower payments from the inflation-linked income stream would need to be so the two options generate equal utility in retirement, assuming they spend all their income each year. These steps are somewhat technical and given at the end of the blog. My results are below:

For someone purchasing an annuity at age 66, the haircut is large - close to 25%. The haircut drops with for investors who choose to do so later. This is partly because people who choose to purchase an annuity later are less risk averse (so less sensitive to uneven real spending in retirement), and partly because inflation will have less time to erode future income.

Unsurprisingly, the haircuts are sensitive to the level of inflation. I used market inflation expectations as at 31 March 2021 but if expected inflation were 1% lower per year, the haircut at age 66 would only be 13%. If it were 1% higher, the haircut would be a very worrying 41%!

Delay annuitisation?

The other interesting question is how the ideal age at which to purchase an annuity might be impacted by restricting to level annuities. Level annuities are front-end loaded in real terms, which I’ve assumed is a bad thing, but this matters less if they’re purchased later. There is therefore some benefit to delaying the purchase of level annuity that partially offsets the influence of mortality drag (which incentivises earlier purchases). This allowed me to calculate the following:  

This says, for example, that someone who would buy an inflation-linked annuity age 66 should delay around 8 years, until 74, if restricting themselves to level annuities. At higher ages there’s relatively little delay, however.

Level with me

To wrap up, our first conclusion is that investors should consider carefully whether a level annuity really suits them better than an increasing one. Despite eliminating mortality drag, longevity uncertainty may still pose problems for a level annuity: should the pensioner reach old age, the spending power of their retirement income is likely to be substantially weaker.

Our second conclusion is that if they do decide to go for a level annuity for psychological (rather than rational) reasons, it may make sense to delay annuitisation. The size of the delay, however, is highly age dependent, with relatively long delays if they plan to purchase an annuity early in retirement but much shorter ones if they plan to do so later.

Method for calculating haircuts:

• Use the age the investor has chosen to annuitise to imply their risk appetite. The younger they’ve chosen to annuitise, the more risk averse they should be. This takes the form of a quadratic utility function.
• Calculate expected utility for the level annuity stream and for the increasing one. I assume that the utility in any year is just as important as the utility in any other. This involves calculating the utility of spending in each year (using our function) and then combining all years, allowing for survival chances.
• Finally, calculate how much lower, as a percentage haircut, payments from the increasing income stream would need to be so the two options have equal expected utility.