Hedging or betting?

(Sep 27, 2018)

Last week I presented at Longevity 14 in Amsterdam.  A recurring topic at this conference series is index-based approaches to managing longevity risk.  Indeed, this topic crops up so reliably, one could call it a hardy perennial.

For a long time insurers and pension schemes were sceptical of derivatives-based solutions to managing longevity risk.  Part of this scepticism was due to basis risk - why enter into a contract based on population mortality when a portfolio has very specific mortality characteristics?  In particular, most portfolios tend to have a concentration of risk in a relatively small subset of lives.  Another reason for scepticism was price - it was often cheaper to reinsure the entire risk…

Read more

Tags: basis risk, concentration risk, model risk

Socio-economic differentials: convergence and divergence

(Jun 18, 2018)

Many western countries, including the UK, have recently experienced a slowdown in mortality improvements.  This might lead to the conclusion that the age of increasing life expectancies is over.  But is that the case for everyone?  Or are there some groups in the UK who are still experiencing mortality improvements?  The short answer is that mortality rates are still falling for the least deprived half of the population in England, while mortality improvements since 2011 have been virtually zero for the most deprived third.  This has important consequences for reserving for pensions and annuities, so let us explore in a bit more detail.  The findings in this blog are based on some early results of research…

Read more

Tags: mortality convergence, mortality improvements, concentration risk, basis risk

How much data do you need?

(Aug 30, 2017)

There are two common scenarios when an actuary has to come up with a mortality basis for pensioners or annuitants:

  1. For a portfolio of liabilities already owned, e.g. an insurer's existing annuities in payment or a pension scheme's pensions in payment.
  2. For a portfolio of liabilities where the risk is to be transferred, e.g. an insurer or reinsurer looking to price a buy-out or longevity swap.

Leaving aside questions of data quality, in each case the actuary is faced with the same question: is the portfolio's experience data large enough to rely on? And if there isn't enough experience data, what does the actuary do instead?

At one extreme consider a pension scheme with a hundred pensioners. With an average of around…

Read more

Tags: credibility, basis risk, concentration risk

Risk and models under Solvency II

(Aug 21, 2011)

Insurers need to have internal models for their major risks. Indeed, both the Individual Capital Assessment (ICA) regime in the UK and the pending Solvency II rules in the EU demand that insurers have good models for their risks.

However, when building a model for mortality or any other kind of risk, you have a number of known issues in the modelling process:

  1. Model risk. You do not actually know what model structure is most appropriate for your portfolio or risk.  This is particularly keenly felt for mortality projections.
  2. Basis risk. Even if you have the correct model, you should be calibrating it using the same population you want to model. However, if you fit a model to the experience from one portfolio, yet use…

Read more

Tags: ICA, Solvency II, model risk, basis risk, concentration risk, model points

Partial buy-outs

(Jul 14, 2009)

It is quite common for a pension scheme to want to reduce its risk, but to be unable to afford a full buy-out.  The question is how best to reduce risk with the funds available, i.e. which liabilities to buy out first.  One argument we have come across is to buy out the older pensioners first, since their life expectancy can be more volatile against your funding assumption.

The answer to this depends on what way you want to measure the risk.  If you are looking at the possible percentage change in life expectancy or reserve, then older pensioners do indeed have a higher volatility: an extra year of life is proportionately larger compared to the baseline life expectancy (similarly for reserves).  Reserve calculations…

Read more

Tags: buy-out, concentration risk, trend risk, tail risk

Measuring obesity

(Jun 23, 2009)

Obesity is a public-health concern throughout the developed world, since it is linked to a variety of chronic conditions such as diabetes.  Obesity is also of interest to insurers, since it is linked to excess mortality from a wide range of causes, including heart disease.  The most commonly used measure of obesity is the body-mass index (BMI), which is calculated from a person's height and weight. The British Heart Foundation has an online BMI calculator which is free to use.

Now, the United Kingdom doesn't often take a leading role in the EU, but sadly obesity is one area where it rather stands out, as shown in Table 1.

Table 1. Prevalence of obesity among adults in selected large EU countries (Source: Health Interview…

Read more

Tags: obesity, body-mass index, BMI, concentration risk, basis risk


(Jan 29, 2009)

One of the challenges in modelling financial portfolios is the concentration of risk arising from the fact wealthier people will usually have significantly higher benefits than the less well-off.

In a small annuity or pension scheme, the stochastic risk (the risk surrounding who dies when) can be highly significant, often the most significant risk the scheme runs. Here is an analysis of one small portfolio, showing a not untypical concentration of risk.

Typical concentration in a pension scheme

It is unsurprising that there is demand to analyse such an important characteristic in a multiplicity of ways. One technique we have introduced recently is geographic heatmap analysis. 

This is a visualisation technique that allows us to map the spread of…

Read more

Tags: concentration risk, visualisation, mapping

Concentration of risk

(Aug 21, 2008)

Liabilities within any given portfolio are rarely equal, and they usually differ widely in size. Typically, a large proportion of liabilities is concentrated in a relatively small number of lives, so this should always be checked.

One measure of inequality in income distribution is the Gini Index, which is widely used in the social sciences. It ranges from 0% (perfect equality) to 100% (one person has all the income). The CIA World Fact Book gave the UK as a whole a value of 36.8% in 2005, and the UK is one of the more unequal countries among developed nations. Equivalent figures for portfolios of insurance-company liabilities and pension schemes routinely exceed this value, i.e. such portfolios are even more…

Read more

Tags: concentration risk, Gini, socio-economic group, lifestyle

Find by key-word

Find by date

Find by tag (show all )