Asset liability (or cashflow) matching and portfolio immunisation are two methods insurance and pension fund managers use to ensure they can pay their liabilities.

To actuaries, the people who must calculate these things, it is the stuff of heroes. In 2003 their professional body, the Institute and Faculty of Actuaries, voted the inventor of immunisation theory, Frank Redington, the greatest British actuary ever.

Redington, who died in 1984 after a career at insurance company the Prudential, secured more votes than all three of the other candidates put together.

So, who better to turn to for an explanation of immunisation and asset liability (cashflow) matching, than the Institute and Faculty of Actuaries?

### Cashflow matching

Cashflow matching, as it is colloquially known, relates to matching the asset and liability cashflows. The institute refers to it as asset liability matching (ALM).

ALM involves assessing the type of cashflows expected to arise from the entity’s liabilities – the amount it must pay out in pensions for example. Step two is to structure assets with cashflows that match or correspond to the liabilities.

The aim is then to reduce risks arising from asset cashflows being ‘inconsistent’ with liability cashflows.

There are a number of cashflow factors to consider with ALM:

- Amount
- Term
- Uncertainty
- Nature
- Currency

The cashflow amount and term (timing) could be considered together. If a liability of £10,000 is due to be paid in one year’s time, then having assets that generate a cashflow of £10,000 also in one year’s time could be appropriate.

If, instead, asset cashflows generated just £8,000 in a year’s time, then there would be a cashflow shortfall to meet the liability. A further £2,000 would have to be found from other assets to meet the liability.

Similarly, if the assets generated a cashflow of £10,000 but in 18 months’ time, again there would be a liability shortfall. If the entity held all its assets in property, some property might have to be dis-invested at short notice to generate the required cashflow at the right time.

So matching cashflows by amount and term helps avoid cashflow shortfalls and reduce liquidity risk.

Both the timing and amount of future cashflows could be subject to uncertainty – and here ALM techniques are modified by using expected values, or projecting different scenarios of the amounts and timing.

### Nature of cashflows

The nature is also important, but more subtle. Nature refers to whether cashflows are fixed, or real – are they likely to increase with some form of inflation?

For example, insurance policies with pre-defined sums assured could have fixed /nominal liabilities such as a fixed amount of £10,000 to be paid in five years’ time.

Alternatively, a pension liability could currently be £1,000 per annum, but increasing in line with the RPI index. In this case, the cashflow is not fixed but ‘real’ and dependent on future inflation.

The cashflow in five years’ time will be £1,000 plus whatever growth in inflation applies between now and then.

ALM means matching fixed liability cashflows with fixed asset cashflows, and similarly matching real (index/ inflation-linked) liability cashflows with real asset cashflows. A real asset would be one where the future asset cashflows were also affected by future inflation.

### Currency of cashflows

If an entity has liabilities denominated in US$, then using ALM would mean you hold equivalent assets also in US$. Otherwise, the entity would run the risk of being exposed to exchange rate fluctuations.

For example, if a liability of $10,000 is due in one year’s time, then with a £/$ exchange rate of 1.3, assets yielding £7,692 in a year’s time would be sufficient.

But if the £/$ exchange rate fell to 1.1 in a year’s time, then the assets would yield $8,461, giving rise to a shortfall of $1,539.

The exchange rate could work the other way, but being subject to the vagaries of exchange rate movements introduces the entity to currency risk.

### Immunisation

Using ALM to match asset and liability cashflows exactly is one way of avoiding cashflow mismatches. However, it is not always practical or possible to find sufficient assets with cashflows that exactly match the liabilities.

One alternative approach is to use immunisation techniques. Here, rather than having to match cashflows by timing/amount exactly, an alternative portfolio of assets could be structured to immunise the entity from movements in interest rates.

This means that the value of liabilities would be immune to small changes in interest rates. This is best illustrated in an example, but first one of the technical conditions needs to be explained – volatility.

### Volatility

The volatility of assets/liabilities is a measure of how sensitive their value is to a change in interest rates. If assets have low volatility at a particular interest rate, this means they are not particularly sensitive to a change in interest rates.

Imagine an entity has to pay out:

- £100,000 in 6 years’ time
- £100,000 in 8 years’ time.

Imagine also that interest rates are constant at 7% a year.

Assets with the following cashflows would ‘immunise’ the entity from small changes to interest rates around 7%:

- £107,420 in 5 years’ time
- £94,908 in 10 years’ time.

These asset cashflows differ by both amount and term compared to the liability cashflows. However, they have the same value in current terms, and also the same volatility to interest rates as the liability cashflows.

They meet two of the conditions required for Redington immunisation.

The table shows the asset and liability values at a range of interest rates, to show how sensitive they are:

A small change in interest rates leads to assets and liabilities moving in similar ways, so the entity would be ‘immune’ to this change whether the interest rate rose to 7.5% or fell to 6.5%. So, immunisation is effective here for small changes in interest rates.

However, with a large fall in interest rates, from 7% to 1%, the assets and liabilities diverge to a greater extent, and immunisation does not work so well. In cash terms, the amounts at stake could be significant.

### Match or immunise

If a fund cannot match cashflows exactly, then it could immunise.

However, were interest rates to move dramatically, then a different portfolio would need to be constructed – and there would be no guarantee that one could be found that would still provide an immunisation effect.

### Simplified definition

Make no mistake, the Institute and Faculty of Actuaries has gone to great lengths to simplify the descriptions of asset liability matching and immunisation and how they work.

Having a fund with a mix of zero-coupon bonds and reinvesting coupon income from bonds at different rates makes the calculations complex, for example.

The sums involved in ensuring a portfolio of predominantly bonds and similar assets match future liabilities can be mind-bending for non-actuaries. The kinds of calculations in the image below are not uncommon.

The fact that Redington developed his theories using these kinds of calculations in the days before computers – he retired from the Pru due to ill health in 1968 – is testament to his skills. There have been later revisions of his theory as computer processing power increased.

### Redington and the Pru

The institute’s newspaper, The Actuary, quoted many supporters of Redington. Here are just a few examples:

“I very much hope that actuaries with a proper sense of historical perspective will vote for Redington and in large numbers. To cavil that Redington’s ideas on immunisation were flawed is like saying that Newton wasn’t the greatest mathematical physicist of all time because his laws didn’t apply universally.”

“As a student actuary I found his work inspiring and, with the greater experience that came with age and responsibility, found it ever more remarkable that he developed his immunisation theory and Flock and Sheep essays without recourse to any of the technology that we take so much for granted today.”

“The mark of a technologist that distinguishes him from a scientist is that he must act; everything he does has some sort of deadline. He has to manage, therefore, with as much truth as is available to him, with the scientific theories current in his time.”

“I think that, for all his theoretical work on immunisation, mortality, statistics and national pensions, Redington’s biggest contribution has been in the way he made Prudential’s long-term fund a peerless role model of shrewd husbandry of a proprietary life company’s long-term fund.”

He may not have been a comic book hero but Redington was a hero nonetheless.