**A version of this article subsequently appeared in the July 2013 of Outlines on page 6**

**UK Pension funds and inflation**

UK defined-benefit pension funds tend to have liabilities linked to inflation, due to the contractual revaluation of benefit payments for active and deferred members each year, and the annual increases granted on pensions in payment.

Historically this risk exposure to (rising) inflation, and inflation expectations, was one of the largest risks facing pension funds, which has over time led pension funds more and more to consider investing in assets linked to inflation in order to best hedge this risk.

**Enter the inflation floors**

When a pension fund starts to build a hedge for its liabilities it quickly discovers a subtle but important feature of its liabilities, while inflation itself can (and has) been negative from one year to the next, in a lot of cases the pension benefits that are paid out **cannot decrease from one year to the next. **

In the language of the capital markets, the benefits contain ** inflation floors at 0%.** Most also contain caps on the annual increase of pensions payments at 3% or 5%.

**Why floors complicate the hedging process**

The presence of the floors changes the behaviour of the true market valuation of the liabilities, compared to a situation where the floor was not present. The theories relating to option pricing help us understand how, but the key outcome is that the change in value of the liability will not be quite “one-for-one” with changes in inflation, but somewhat less than one.

To be even more precise, this relationship is not constant, and in mathematical terms is non-linear with respect to inflation.

**Figure 1 : The relationship between inflation-linked assets, and liabilities which have inflation subject to floors, is not one-for-one – but a clear pattern emerges. Source : Bloomberg**

As a pension fund begins to build an inflation hedge from scratch, this level of detail is not paramount – the most important thing is acquiring more inflation hedging assets.

As the hedge becomes larger, and begins to approach (in percentage terms) the scheme’s funding ratio, it becomes important to take this effect into account. Typically pension schemes have three alternatives:

(1) Invest in instruments which exactly match the behaviour of the inflation floors (“LPI” swaps)

(2) Only invest in “pure” inflation linked instruments and accept that there is a mismatch between this and the true liabilities

(3) Only invest in “pure” inflation linked instruments, ** and** attempt to match the behaviour of the caps and floors –

*this requires careful modelling of the behaviour of caps and floors, and hence of inflation volatility*Although some pension schemes have historically chosen (1), the majority of schemes have opted for option (2) or (3)

In order to match the behaviour of the liabilities with pure inflation instruments, a ** dynamic rebalancing** approach needs to be adopted, which varies the exposure to inflation (RPI) instruments at any given times – in accordance with a particular model, and in response to changes in the level of inflation expectations.

**Figure 2 : The model sensitivity of an inflation linked liability (with a floor at 0% and cap at 5%, on an annual basis) to moves in inflation, compared to an approach that assumes one-for-one sensitivity**

By doing this, schemes effectively monetize the difference between the ** implied** level of inflation volatility (inherent in the floor pricing), and the

**inflation volatility (**

*realized***).**

*see figure 4 below***What’s changed recently?**

There have been several recent developments of relevance.

- The large moves in the market for inflation swaps and index-linked gilts seen in January 2013 due to the CPAC announcement highlighted the need for the
policy*dynamic rebalancing* - The price of the LPI swaps that match schemes’ liabilities decreased quite substantially in early 2013 (see figure 3), raising the question of whether there is value for some schemes of taking this approach as opposed to the dynamic rebalancing approach, however as illustrated by figure 4, the implied volatility of the floors in particular is still substantially above the realised volatility of the 20 year inflation rate

**Figure 3 : The cost of providing an annual floor on the inflation rate for the next 20 years has fallen from around 0.7%p.a. in the middle of 2012 to around 0.3% p.a. as of May 2013. Some of this fall is due to an increase in the underlying inflation expectations, but the majority is due to the implied volatility of the inflation floor. Source: Bloomberg, Calculations: Redington**

**Conclusion **

When a scheme builds its inflation hedge, the effect of the inflation floors and caps in the benefits should be taken into account, and this becomes even more important as the inflation hedge ratio increases.

The scheme continues to have two broad options regarding how to treat the floor:

- Invest in instruments that closely match the behaviour of the floors (“LPI” swaps), the price of these can change through time and has recently cheapened
- Invest in pure inflation linked instruments (RPI swaps) and dynamically manage the exposure to best match the behaviour of the inflation floors. Care should be taken in the model used to calculate this rebalancing, but done successfully a scheme can effectively monetize the difference between the
of the floors and the*implied volatility*of inflation expectations.*realised volatility* - While the cost of inflation floors has cheapened recently, there still remains a substantial premium of implied inflation volatility over realised, which scheme’s can continue to benefit from by using a dynamic hedging approach to their liabilities

* Figure 4 : The implied volatility of 0% inflation floors tends to exceed the realised volatility of the 20 year swap rate *Source: Bloomberg, Calculations: Redington

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