Swaption case study for pension funds
Partly as a result of the introduction of the new Financial Assessment Framework (Financieel Toetsingskader – nFTK), pension funds are monitoring interest-rate risk. An average Dutch pension fund has a duration mismatch between its liabilities and its fixed-income investments. Several solutions have been suggested which includes buying long-dated bonds, LDI-funds and interest rate swaps. Some pension funds consider the current level of interest rates as too low to hedge their exposure for the longer term. We at Rabobank believe that swaptions provide a viable alternative. Swaptions protect pension funds against an interest-rate decline, and also reduces the equity buffers required under the Solvency Test of the DNB Standard Model. The product also allows pension funds to profit from a rise in interest rates. In this article we will describe how swaptions are used within Dutch pension funds.
A swaption is an option to enter into an interest-rate swap in the future at a previously set rate for a previously agreed period. The nominal amount is also established in advance. The buyer of the option pays a premium. With a receiver swaption, the buyer has the option to receive in the future the previously set fixed interest rate in exchange for the payment of 3- or 6-month Euribor. With a payer swaption, the buyer has the option to pay in the future the previously set fixed interest rate in exchange for the receipt of 3- or 6-month Euribor. The buyer has the right to enter into the interest-rate swap, but has no obligation.
The valuation of swaptions is different from that of, for instance standard interest-rate swaps. Products such as swaptions are known as non-linear products. In an interest-rate swap, there is a linear connection between the underlying value (the level of the interest rates) and the value of the interest-rate swap. There are several factors that affect the valuation of a swaption. A change in one of these elements does not always have the same effect on the valuation of the swaption.
The amount of premium depends on the contract interest rate, the market (forward) interest rate, interest-rate volatility and the tenor of the option. If exercising the swaption would deliver a positive value, the option is in the money. Then, the option has a positive intrinsic value. If the future interest rate is the same as the contract interest rate, the effect of exercise of the swaption is neutral for the buyer. The option is then at the money. There is no intrinsic value. If exercising the option would deliver a loss and therefore not be advisable, the option is out of the money. As the intrinsic value of an option rises, so does its premium.
Use of swaptions by a stylized Dutch pension fund XYZ
To demonstrate how swaptions are applied, we are using a stylized pension fund XYZ. The liabilities (future cash flows) form the basis for using swaptions. Based on the fund’s liabilities, a so-called delta profile can be created. The delta profile indicates the change in value of the liabilities given a 1 basis point move in interest rates. This measure is more accurate than the traditional duration approach, since this demonstrates not only the effect of a parallel change of interest rates but it also captures the effects of changes in particular parts of the yield curve.
The market value of this particular fund XYZ equals e1bn. The total interest-rate risk of the liabilities of XYZ equals e1,341,098. This means that if the entire yield curve declines by 1 basis point, the pension fund’s liabilities will increase by e1,341,098 in value. Further analysis of the fund’s interest-rate risk reveals that the main exposure is to movements in interest rates for 15 years and longer. Table 1 shows that if the 25-year rate declines by 1 basis point (and the rest of the yield curve remains unchanged) the fund’s liabilities will increase by e285,990.
The value of the liabilities is shown in figure 1, which shows the effects of parallel changes in the yield curve on the market value of the liabilities. The interest-rate change is shown in basis points horizontally and the market value of the liabilities (MV) vertically.
As would be expected, figure 1 shows that a fall in interest rates leads to an increase in the value of the liabilities and a rise in interest rates leads to a decline in value.
In figure 2, the value of the liabilities over three years is added. We have assumed for simplicity reasons that pension fund XYZ is a closed fund where no new liabilities are added over the next three years. In reality, new liabilities will be added and normally we extend our analysis to reflect these changes. Figure 2 shows that, with an unchanged yield curve, the value of the liabilities are roughly the same in the course of three years. The cash outflows in the next three years are compensated by the fact that the remaining cash flows increase in value as we move through time.
The period of three years is not chosen by chance. XYZ actually has to decide over which period it wishes to hedge against a fall in interest rates. Pension funds can hedge against a fall in the 30-year interest rate in two years time (a so-called 2 yr x 30 yr swaption), but also in five years time (5 yr x 30 yr swaption). Pension fund XYZ has initially chosen a period of three years on considerations relating to practicality, to avoid frequent execution of transactions. A five-year period is also a common choice.
The swaptions that pension fund XYZ will enter into are primarily determined by the delta profile of Table 1. Table 1 also shows interest-rate risk in the segment up to fifteen years. This is relatively small and will not be hedged. Table 2 gives an overview of the transactions.
By purchasing these receiver swaptions, XYZ will protect itself against a fall in interest rates in three years time. As swaptions are executed in several time-buckets, XYZ is also protected against a non-parallel decline in interest rates. The strike is set at 0.33% below the current market interest rate levels (April 2006).
The horizontal shape of the orange line (future cash value with swaptions) shows that the pension fund is protected against lower interest rates in three years time. However it should be noted that in case of a fall in interest rates at the present time the increase in the value of the liabilities would not be entirely offset by the increase in value of the swaptions. The increase in the value of the swaptions will be smaller than the increase in the value of the liabilities. However, the increase in value of the fixed-income portfolio that would accompany lower interest rates would be an additional compensation.
The purchase of receiver swaptions involves the payment of a premium. The premium required for the above swaptions currently equals e18.5 million. XYZ can decide to finance a hedge at this level by giving up some of the upside potential if interest rates rise. This is known as a zero premium structure. In practice, this is achieved by selling payers swaptions at a level 0.67% above the current market rate.
By selling the payer swaptions shown in table 3, Rabobank acquires the right to enter into an interest-rate swap with XYZ at the levels shown. Obviously, Rabobank will only exercise this option if the market interest rate is higher than this level on the exercise date. If interest rates rise to the strike level, this will favourably affect the pension fund’s cover ratio. In figure 4, the orange line is horizontal if a large rise in interest rates occurs. XYZ will gain no further benefit if interest rates rise above the strike level.
In the introduction we stated that swaptions are an alternative for pension funds that consider interest rate levels too low to hedge their liabilities. But even if interest rate levels are considered appropriate, swaptions still provide potential upside in a zero-premium structure.
The impact of a swaptions-strategy illustrated
Besides interest-rate risk, other factors also pose a risk for the cover ratio of pension fund XYZ. In reality, pension fund XYZ is exposed to various other investment risks and is concerned about the probability of a cover ratio below 105% or less. Executing a swaptions strategy will reduce this probability. For purposes of illustration we have classified the other investment categories as a homogeneous group with an expected geometric return of 8% and a standard deviation of 15%. Also, the current level of interest rates is taken as a starting point. Interest-rate volatility is derived from the swaptions market. A correlation of +0.65 is assumed between the two categories, which corresponds with the assumption of DNB. Figure 5 illustrates the impact of the swaptions-strategy.
The probability of a cover ratio below 105% is relatively high for XYZ without a swaption structure. With a swaption-structure, the probability of a cover ratio below critical levels is significantly lower. This analysis is sensitive to the correlation factor used whereby a lower correlation factor leads to lower probabilities. Although XYZ is concerned about a cover ratio below 105%, other pension funds might seek protection of their cover ratio at 120% or 130%. Implementing a swaption strategy is also for these funds worthwhile investigating.
Risks and mitigating factors
The following risks can be distinguished for pension fund XYZ:
1. Interest rates rise above the strike level of the written options
The pension fund will no longer benefit above the strike levels of the payer swaption. This can lead to opportunity losses. A strong rise could mean that the option will be exercised. On the other hand, the cover ratio will be higher if the option is exercised (apart from the developments of the other asset categories).
2. Large non-parallel move in interest rates
Based on the interest rate risk profile, 5 swaptions will be concluded to reduce interest-rate risk. This could potentially lead to a skewed result, particularly in case of a large non-parallel move in interest rates. More precision could be achieved by setting more interest-rate risk points (known as grid points) and concluding additional swaptions. We have chosen to limit the number of swaptions for reasons of practicality.
3. Exclusion of the fixed-income investments
The fixed-income investments have not been included in this proposal. This could easily be done if required. The fixed-income investments reduce interest-rate risk and lead to lower nominal swaption amounts.
4. Effects of lower interest rates at the present time
The swaptions described are intended to protect pension fund XYZ against a decline in interest rates in three years. One effect of this could be that during these three years, the liabilities could rise in value without this being fully compensated by the increase in value of the swaptions.
Pension fund XYZ has various options at its disposal to manage its interest-rate risk. These range from buying long-term bonds to concluding interest-rate swaps. What these methods have in common is that the pension fund fixes interest rates at the current level for a longer period. The current level of interest rates is not necessarily to be seen as attractive. By using swaptions, the pension fund avoids fixing rates at the current level while it is protected if rates fall.
Based on the delta profile of the liabilities, 5 swaptions could be concluded that would hedge pension fund XYZ against the effects of a fall in interest rates over three years. If swaptions are purchased, there is still the potential to profit from rising interest rates. After all, if rates rise the liabilities will decrease faster in value than the fixed-income investments, meaning that the pension fund’s cover ratio will rise. Executing a swaptions strategy significantly reduces the chance of lower cover ratio.
Swaptions are expensive. It could therefore be attractive to set up a zero premium structure by selling payer swaptions. In this scenario XYZ would no longer benefit if interest rates rise above the various strike levels. If these payer swaptions are exercised, XYZ in fact will have hedged its liabilities at these levels. The level is substantially higher than the current level of interest rates, and thus offers an attractive alternative.
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