“Is your pension fund a Sweden or a Colombia?”

Longevity is widely recognised as a key risk. Hewitt's recent global risk survey, carried out in the fourth quarter of 2008, recognised that improvements in longevity appear high on the list of risk factors concerning companies - more so in the UK than equity market risk. But how many schemes are fully aware of the extent to which a few high earners can skew risk?

This article looks at how pension schemes might measure their exposure through the use of the ‘Gini coefficient' - a commonly used measure for comparing income inequality between different countries, and explores the options available to schemes for hedging the risk.

Simply put, is a scheme more like Sweden, a country with one of the most equal distributions of income in the world, or more like Colombia with significant pockets of risk hidden within its membership?

Imagine a corporate final salary pension fund tasked with paying a pension to just one member until they die. A simple task you might think? The member, Bob, aged 60, receives an annual pension of €500,000 for the rest of his life. Actuaries estimate that Bob is expected to live for another 28 years, and given a prudent and conservative investment strategy, the scheme should hold assets of €7.5m to back this liability on a ‘best estimate' basis.

As 28 years pass, it turns out that Bob is still alive, unlike others. This is not because mortality rates are different from those estimated by the actuary at the outset, but that Bob has been lucky. Unfortunately, the pension scheme has just run out of money as Bob reached 88, and there is nothing left to pay any further pension.

In practice, schemes with only one member do not really exist and would probably have been bought-out with an insurer once the number of members seriously dwindled. This example illustrates a typical blind spot for many pension schemes, technically known as ‘idiosyncratic longevity risk'. This is the random variation in longevity. Even if the ‘correct' mortality rate is known, the experience can differ for individual members. Although on average a scheme may be able to predict the life expectancies of its members, in practice the scheme doesn't know which members will live longer or shorter than expected. The risk can be very significant if a small number of members account for a large proportion of the total scheme liability.

How can a pension scheme manage or reduce this longevity risk? The answer is having a scheme with lots of ‘Bobs' in it rather than just one.

Actuaries can calculate that the expected cost of providing a pension to a single Bob would be around €7.5m. However, assuming the expected rates of death provided by the actuary are correct on average, there is a 5% chance that Bob could live more than 43 years. Therefore, there is a 5% chance that the scheme would need to hold more than €900,000 in assets today to pay the same benefits, as compared with the expected cost of only €7.5m. The ‘idiosyncratic longevity value-at-risk' of providing this benefit in liability terms is the ratio by which the cost under the 5% scenario (€900,000) exceeds the expected cost (€7.5m); 18% in this example.

In a scenario of a scheme with two Bobs - each with a pension this time of €250,000 - then the expected cost of providing the benefit is still €7.5m. However, this time we can be 95% sure that the amount of money we need to hold to pay the benefits should be no more than €860,000 - an idiosyncratic longevity value-at-risk of 17%. Therefore, doubling the number of members from one to two has reduced the risk by only 1%.

However, as the number of identical members increases, the news does get better. With 20 members, the idiosyncratic longevity risk halves, and 100 such members halves it again to 4%. This process is ‘diversification' - holding a larger number of perils (in this case, the pension scheme member living longer than expected) where the likelihood of each peril occurring does not affect the likelihood of any other event occurring.

While corporate pension funds are often large, some with staggeringly huge numbers of members, idiosyncratic risk can still pose a problem. What needs to be considered is how ‘alike' the members of a scheme are. For example, consider a pension scheme with 100 members which has an idiosyncratic longevity value-at-risk of 4% from the above example. If this is changed so that rather than all members having equal pensions, 99 have a pension of €1,000 per year, and the remaining member has a pension of €401,000 (to make up our €500,000 pension payroll as before), the risk more than trebles to 15%. The member with a €401,000 pension makes a vast contribution to the risk of the scheme.

The risk presented to the scheme by any single member is linked to how big their pension is compared with that of fellow members. How many pension schemes in the UK today have a small number of ex-chief executives with very large pensions compared with the other members in the scheme and how much risk exists in those schemes?

UK pension schemes and even large FTSE 100 pension schemes carry a surprisingly large level of idiosyncratic risk. Statistics like "10% of the liability resides with 1% of the membership" are common-place. As schemes close and mature, this type of longevity risk will only get ever larger.

A simple but effective tool to determine whether a particular scheme might be susceptible to significant idiosyncratic longevity risk is to determine a Gini coefficient for the scheme. It is the inequality of income (in our case pension amount) that is the key driver behind whether a scheme might have significant idiosyncratic risk. There are published league tables ranking countries by their Gini score. The lower the score, the more equally distributed that country's income is through the population and the higher up the table you are. Top of the league table is Sweden with a Gini score of only 23 while at the other end of the spectrum are countries like Colombia and Brazil with scores in the mid-50s.

To translate that into the world of pension schemes - if the Gini score for a scheme looks a lot like Colombia then pension amounts are distributed unevenly through the membership and there is a high chance that there may be a high level of idiosyncratic longevity risk for that scheme. Conversely, if the scheme is up near Sweden in the league table, then this type of longevity risk may not be such a large factor.

If a scheme finds itself to be a ‘Colombia', how can it control or reduce the risk? There are two types of solutions in the market to help schemes control this risk - insured annuities for the most risky members and customised longevity swaps.

The first of these solutions is probably the most familiar to readers. The pension scheme can purchase an annuity from an insurer on the lives of members who present the most idiosyncratic risk to the scheme. In return for an initial premium, the annuity promises to pay the benefits to those members until they die, effectively removing all risk relating to those members from the scheme. The true value in this type of solution is that the insurer can absorb the idiosyncratic risk into its large portfolios of other, similar risks. As such, it does not need to charge particularly high premiums to the scheme. In effect, it is cheaper for the insurer to run the risk and the scheme - a risk-pricing arbitrage if you like.

The second potential solution, which is growing in popularity, is to purchase a bespoke longevity swap on the members of the scheme. It is likely the swap would have to be taken out on a larger group of members than just those who present the highest level of risk (the ones with big pensions) as the market in this type of product requires a certain deal size (€100m of underlying liability or so) in order to make the transaction worthwhile. However, once you purchase a longevity swap on this larger group of members, you have locked in to an expected rate of mortality for each and every member. Now if some members live longer than expected, the scheme receives extra money from the swap to pay off those additional, unexpected benefits, protecting the scheme from the idiosyncratic risk. Under this type of contract, the scheme is also protected from a myriad of other longevity-related risks on the whole portfolio, such as uncertainty in future mortality trends, overnight shocks to mortality rates due to medical advances and so forth.

Changing the social issues that define if you are a Sweden or a Colombia are clearly the really tough ones to address. But if you are pension scheme with these levels of income inequality then it's time to address the risk posed by the diversity in longevity of your members.

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