Retirement: Visualising the risk of different outcomes
Understanding the risks and rewards of different investment and spending decisions in retirement is hugely important. This is very difficult, however, and (in our view) critical aspects are often missed in simplistic approaches.
For example, uncertainty over longevity may be left out of projections, or the longterm consequences of decisions may be neglected. At the same time, any illustrations need to be relatively straightforward to interpret.
In this blog, I introduce our latest visualisation technique, which we believe can help. The basic idea is to illustrate the possible range of retirement outcomes where “retirement outcome” can easily be understood as an average income level.
The steps are:
1) Assume a sensible spending strategy.[1] We assume spending is linked to pension pot size and future life expectancy.
2) For a simulation of investment returns and lifespan, calculate how much is spent each year. We represent how good retirement is overall as the average[2] spending per year over the whole of retirement, allowing for inflation.
3) Also calculate how much, in inflationadjusted terms, is left behind on the investor’s death (as there might be bequest motives).
4) Repeat these calculations for many different simulations of the future.[3]
5) Finally, draw frequency plots of the amounts. This allows us to see how likely different outcomes are for a given strategy, and to compare different strategies.
That all might sound a little abstract, but it should become much clearer with examples!
Illustration: annuities become more appealing with age
As our first example, the charts below compare income drawdown with annuitisation, projecting from age 66. For simplicity, I’ve assumed these are level singlelife annuities with no guarantee. Further details of the case study, including how income drawdown was modelled, are given at the bottom of the blog.
As you can see, income drawdown leads to moderately better spending outcomes on average. It also leaves the possibility of bequests. However, there’s a higher chance of a poor spending outcome.
(You might note that a level annuity doesn’t result in certain outcomes. This is because our spending outcomes are adjusted to allow for inflation.[4] Buying an annuity also doesn’t have to be an allornothing decision: partial annuitisation could help individuals strike a balance with which they’re comfortable. This would result in plots that lie between the red and blue lines.)
The charts above were based on projections from age 66, but what if we do the same calculations from age 75? The results are shown below.
From a spending perspective, income drawdown now looks unfavourable with a lower median outcome than from an annuity and greater uncertainty. This is because longevity uncertainty increases with age and is consistent with increasing mortality drag. It therefore becomes more important to protect against it. We’ve also written about this here.
Multiple applications
The plots above demonstrate that although annuities have taken somewhat of a backseat since the introduction of ‘freedom and choice’ to those retiring, they can still form a very useful component in individuals’ retirement planning, particularly in old age. However, one can also use this framework to demonstrate:
• The potential benefits of replacing bonds with annuities (annuities can be thought of as like owning bonds but with longevity insurance on top).
• The benefits of dynamic (i.e. nonstatic) strategies, for example where you use income drawdown up to age 75 and then annuitise.
• The potential perils of holding too much in cash.
• The theoretical benefits that a growthlinked annuity could offer.
The bottom line is that we believe this offers a powerful framework for making intuitive comparisons. Deciding how to invest in retirement is challenging. But the easier it is to quantify and illustrate the impact of choices on ultimate member outcomes, the better.
Case study details
Age 
66 or 75 years old 
DC pot 
£200,000 
DB income 
£9,300 pa (state pension) 
Annuity form 
Level, single life, with no guarantee period 
Spending rule 
Proportional to pot size, inversely proportional to future life expectancy 
Success measure 
Average annual income (spending) in retirement, adjusted for inflation, gross of tax. 
Other measures 
Bequest motives: size of remaining pot at death, adjusted for inflation, gross of tax 
Arithmetic risk premium over cash, net of costs 
Geometric risk premium over cash, net of costs 
Volatility 

Income drawdown fund 
3.2% 
2.9% 
8.0% 
Annuity pricing: in line with gilts.
Spending rule:
Age 
Proportion of remaining pot to spend over next year 
101 
34.7% 
96 
24.2% 
91 
17.3% 
86 
12.7% 
81 
9.6% 
76 
7.5% 
71 
6.0% 
66 
5.0% 
[1] For nonannuitised assets.
[2] In previous research we have used a geometric average and called the resulting number ‘welfare’. Here we use an arithmetic average for simplicity.
[3] Using a Monte Carlo simulation process.
[4] Inflation uncertainty is partly to blame here, but the main culprit is that if the individual lives much longer the income from a level annuity is likely to be heavily eroded by inflation. In a future blog, I’ll discuss level versus inflationlinked annuities and how they may or may not fit into spending patterns.