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The Actuary The magazine of the Institute & Faculty of Actuaries

Pensions: Forward thinking on swaps

The majority of pension schemes have seen their liability values increase over the last few years 
and one of the main factors underlying this has been falling interest rates. Not only have short-term interest rates fallen, but long-term rates have also reduced, and as pension schemes typically use a yield curve to discount the liabilities, lower rates along the curve have meant that their liabilities have increased.

In Figure 1, the yield curve is shown as at 30 July 2008 and 29 July 2011. This illustrates that yields at the very short end have fallen by nearly 5%, whereas at the very long end, yields have fallen by about 0.45%. In essence, the yield curve has changed shape from downward sloping (higher short-term yields compared to long-term yields) to steeply upward sloping (lower short-term yields compared to 
long-term yields).

Figure 1

Given that rates have fallen much more at the short than the long end of the curve, pension schemes have been considering 
hedging using forward-starting 
long-dated swaps. For example, a 
forward-starting swap agreed today that exchanges the relevant cash flows starting in five years’ time and ending in 20 years from today is known as 15-year, five-year forward swap (in short 15yr 5yr fwd). Hence, a forward-starting swap enables 
you to lock into the higher long-dated yields without having to lock into the 
low yields in the short end (Figure 2). The perception has been that this sort of strategy provides a pick up in yield or forms a smarter hedge for long-dated liabilities. This article goes through a case study discussing this view in detail and looking at other factors that could play a major part in implementing such a 
forward rate strategy.

Figure 2

Case study
In the case study below, we compare the relative performance of a hedging strategy using spot-starting swaps with one using forward-starting swaps. The case study 
uses a starting date of March 2010, 
when forward rates were particularly high (Figure 3).

For simplicity we have modelled the liability cash flows as four bullet payments at time periods of 20, 25, 30 and 35 years, and each payment is for £10m.

Hedge using spot rates

i) The liability cash flows are valued as at 1 March 2010. For example, the £10m liability cash flow in 20 years’ time, discounted at the 20-year zero rate of 4.5%, would have a present value of £4.1m.

ii) These liabilities are then re-valued after six months and one year on the then zero discount curve.

iii) The difference between i) and ii) gives you the change in the liability and hence the approximate value of the swap if a spot-starting swap of 20, 25, 30 and 35 was used to hedge the liabilities in i) above.

Hedge using forward rates

iv) Hedge the same liabilities described above but using five-year forward-starting swaps, ie. hedge 20-year liability using 
15yr 5yr fwd swap, 25-year liability using 20yr 5yr fwd swap, 30-year liability using 25yr 5yr fwd swap and 35-year liability using a 30yr 5yr fwd swap.

v) The forward rate swap is then valued after six months and one year, ie. 1 September 2010 and 1 March 2011 respectively.

Hence, if the hedge using forward rates was more valuable, then the value of the forward-starting swap in v) above would be higher than the value of the spot-starting swap in iii) above.

The above analysis has been repeated starting at monthly intervals up to 
August 2010. The results of this analysis, the value of v) minus iii) above, are shown in Table 1.

Table 1

The table shows that, apart from the 
six-month period starting from 1 August 2010, none of the time periods showed a relative profit from using forward-starting swaps as opposed to spot-starting swaps. In March 2010, forward rates were at their highest, as shown in Figure 3, and yet forward-starting swaps still underperformed 
relative to spot-starting swaps. Let’s see 
why this happened.

Figure 3

In the six months to September 2010, 20-year spot rates had fallen by about 80bps. The forward rates had also fallen 
by a similar amount. However, the 
4.5-year rate (we now look at the 4.5-year rate as six months have gone by and the forward swap is now actually a 30yr, 
4.5yr fwd swap) had fallen by over 1.2%. The forward-starting swap performed worse than a spot-starting swap because of the effect of a 1.2% fall in interest rates at the short end of the curve where there was no hedge. A similar effect was observed at the 25, 30 and 35-year points in Figure 4.

Figure 4

Let’s now look at the reason for the small outperformance of the forward strategy in the six months starting from 
1 August 2010. In the six months to February 2011, the 20-year spot rates had increased by about 30bps. The forward rates had increased slightly less than the spot rate — about 20bps. However, the 4.5-year rate had increased by about 15bps. The forward-starting swap performed better than a spot-starting swap 
because of the combined effect of a relatively large increase in interest rates at the short end of the curve whereby there was no hedge and a smaller increase in forward rates compared to an overall 30bps increase in the spot rate.

Therefore, we believe there is a misunderstanding about hedging liabilities using relatively high forward rates. Hedging using forward-starting swaps versus spot-starting swaps is about having a view on how the shape of the yield curve is likely to change and how this change in shape is likely to affect the overall liability.

Given the recent European crisis and the likelihood of further quantitative easing 
in the UK, interest rates have fallen 
across the curve in the last three months. 
Schemes that had used forward rates to lock into relatively high long-term rates were probably waiting for 
short-term rates to increase in order to fully hedge their liability at the short end. However, rates have instead fallen and left schemes further away from the levels at which they used to hedge. The fact that schemes have a partial hedge in place by using forward rates is better than having no hedge at all. However, the risks faced by such forward-starting strategies are related to economic news regarding the ongoing crisis, such as further recession fears, potential cuts in interest rates by the European Central Bank and so on.

The point we are making here is that, 
if a scheme had the view three months ago that the entire curve was ‘high’, a 
spot-hedging strategy would have been beneficial regardless of the level of forward rates. However, at that time the market believed that short-term rates were likely to increase and hence a forward-starting strategy may have appeared more attractive.

Unfortunately, the former view has been borne out in reality and schemes using a forward-starting swap strategies would have underperformed relative to a spot starting strategy. Hence, forward- versus 
spot-starting strategies are not just about the level at which you want to hedge your liabilities, but also about having a view on the level and shape of the yield curve and whether what is being forecast in the forward curve will actually happen over the relevant time frame.


Nisha KhiroyaNisha Khiroya FIA is a liability-driven investment specialist at F&C Investments