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The Actuary The magazine of the Institute & Faculty of Actuaries

Measuring longevity risk

Howard Kearns introduces LE01: a measure of longevity risk that puts it in context with other risks and mitigating factors over time. 


Introducing LE01, a new way to measure longevity risk ©Ikon
Introducing LE01, a new way to measure longevity risk ©Ikon

“The metric has been designed so that it places more weight on longer-dated liability cashflows”

Over the last decade, pension schemes have taken steps to hedge increasing interest rates and inflation risks in their liabilities, leaving longevity risk as the dominant liability-related risk for many schemes. It is therefore increasingly important for schemes to quantify the extent of their longevity risk so that they are able to put it into context with other risk measures, examine the impact of hedging the risk and monitor those hedges through time. 

To this end, with input from industry experts, we have developed the concept of LE01, a measure of liability exposure that enables pension schemes to understand the impact of a sustained change in future longevity improvements. 

Defining the measure

Similar in concept to PV01 and IE01 (the industry standard measures of sensitivity to a 0.01% change in interest rates and inflation, respectively), we define LE01 as the increase in liability value that results from a 0.01% rise in all future longevity improvement rates. For example, consider a pension scheme using a simplistic longevity improvement assumption of 1% per annum. In order to calculate the LE01, we additionally project the future liability cashflows using a longevity improvement assumption of 1.01% per annum. The LE01 is then the difference in present value between this set of liability cashflows and the original cashflows. 

This definition of LE01 reflects a belief that measuring longevity risk through the lens of future improvements is more relevant for most pension schemes than considering the impact of an immediate reduction in current mortality rates. Current mortality rates can be estimated relatively well, based on either historical scheme experience or a socio-economic model, and are therefore unlikely to unexpectedly vary materially from one year to the next. Longevity improvements are far more subjective as they reflect the actuarial profession’s current view on the continuation of historic longevity trends and the potential impact of a range of factors, such as advances in medical technology, the availability of healthcare and changes in lifestyle.

The LE01 metric has been designed so that it places more weight on longer-dated liability cashflows, capturing the fact that the level of uncertainty inherent within a longevity projection increases with time.

The size and shape of LE01

The figures below show the LE01 profile for an example pension scheme with £1bn of liabilities split equally between deferred and pensioner members. In the case of both the LE01 and PV01 charts, each point on the curve shows the contribution to the overall LE01 or PV01 coming from the cashflow falling in the corresponding year. The area between the curve and the horizontal axis can be thought of as representing the magnitude of the overall LE01 or PV01. 

Figure 1 & 2
Fig-1 & 2
Figure 3

Figures 1, 2 & 3. Pension scheme has liabilities of £1bn, with the deferred and pensioner members having durations of 29 years and 16 years respectively. Pre-retirement revaluations are assumed to be in line with full Retail Prices Index (RPI) and post-retirement increases in line with RPI capped at 5% p.a. For comparison, we also show the shape of the underlying cashflows and the corresponding PV01 profiles.

For our example scheme, the overall magnitude of the LE01 is roughly half that of the corresponding PV01, with the ratio for pensioners being higher than that for deferreds. We would expect most pension schemes to exhibit similar ratios, although the relationship between PV01 and LE01 is in fact quite complex. If we had defined LE01 as a 0.01% per annum reduction to each future mortality rate, it would be similar in magnitude to PV01 
for most schemes. However, the chosen definition of LE01 reduces mortality rates in the early years by less than 0.01% and those in later years by more than 0.01%, with the precise reduction depending on the underlying mortality rates. For the vast majority of schemes, the impact of this varying change in mortality rates will be less than if we had simply reduced all mortality rates by 0.01% per annum.

This also explains why we see the ratio of LE01 to PV01 falling as liability duration increases. For example, a 10% increase in duration will lead to a 10% increase in the magnitude of PV01 for all schemes, but the corresponding increase in LE01 would typically be in the 6% to 7% range.

The relationship between PV01 and LE01 is also affected by pension increases and revaluations, with higher increases leading to higher LE01-to-PV01 ratios. 

Figures 1 and 2 also show that for our example pension scheme, the LE01 profile is more skewed towards the longer-dated maturities than the PV01 profile. We would generally expect this to be the case because at longer-dated maturities the LE01 calculation not only applies a more significant longevity improvement stress, but also applies it to a higher aggregate mortality rate.

Putting it into context

To make LE01 a useful metric, it is beneficial to put it into the context of other longevity risk measures. Below are two ways in which this can be done:

  1. Longevity stress tests Under Solvency II insurance rules, the default 1-in-200 longevity stress test equates to an immediate 20% reduction in current mortality rates. Applying this longevity stress to our example pension scheme leads to a 10% increase in the liabilities. The LE01 metric equated to 0.13% of the liability value, meaning that the Solvency II longevity stress is equivalent to roughly 80 units of LE01. Similarly, a 1-in-20 stress test, which pension schemes typically consider, would equate to roughly 50 units of LE01. 

  2. Current longevity improvement assumptions In the case of our example pension scheme, removing all future longevity improvement assumptions reduces the liability value from £1bn to £795m. Given the scheme’s LE01 of £1.25m, this reduction in value of £205m means that the current longevity improvement assumptions are equivalent to roughly 160 units of LE01.

Uses of LE01

We believe that analysis of LE01 allows a pension scheme to develop a more detailed understanding of its longevity exposure. This should, in turn, facilitate a more informed discussion of the risk, its potential impact on the scheme and the efficacy of hedging solutions. The benefits of measuring and monitoring LE01 include:

  • It becomes possible to understand the contribution to overall longevity risk arising from a specific group of members
  • LE01 serves as a benchmark for discussing the impact of new longevity improvement assumptions
  • It enables longevity risk to be more easily put into the context of other scheme risks.


Knowledge of LE01 may also enable schemes to more easily determine an appropriate amount of assets to be held, or the investment returns to be targeted, as a buffer against the potential impact of longevity risk. For example, a scheme may decide that it is appropriate to hold a longevity buffer equivalent to 50 units of LE01. 

For a scheme considering a longevity hedge, the LE01 can be used as a way of putting the cost of the hedge into perspective. For example, the present value of the longevity hedging fee might equate to 35 units of LE01, whereas the longevity risk being removed may be equivalent to 50 units. The scheme, therefore, has a framework under which it can decide whether the cost of the hedge is attractive in the context of the risk being removed.

In the case of a pension scheme that has already implemented a longevity hedge, the LE01 metric can be used in a number of ways:

  • To monitor the progress of the longevity hedge ratio over time; as the lives underlying the longevity hedge age, their contribution to overall scheme longevity risk will fall and therefore the longevity hedge ratio will fall
  • By monitoring the extent of the unhedged pensioner LE01, the scheme is able to understand when it might be time to implement an additional longevity hedge
  • The LE01 can be used to determine the extent of the asset buffer that must be set aside to meet potential collateral calls associated with the longevity hedge.


As pension schemes continue to hedge more of their liability-related interest rate and inflation exposure, longevity is becoming an increasingly dominant risk. By working with industry experts to develop the concept of LE01, we hope to provide schemes with a metric that enables them to develop a better understanding of their longevity risk and the potential mitigants of that risk.

Howard Kearns is a longevity director at Insight Investment