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Forwards, futures, swaps and options on a large variety of underlying indices have been around for more than 30 years. Despite their popularity with many investors and corporate users, most pension funds have always carefully managed to avoid the use of derivatives because they can be somewhat complicated. However, derivatives can be used to decrease and increase risk. If you can’t book them your accounting system is probably in need of an upgrade and illiquidity is unlikely to be a real problem.
Interest rate risk is by far the most important risk in a pension fund because of its impact on the value of a fund’s liabilities. When interest rates drop, the value of the liabilities rises and a potential gap between the value of a fund’s assets and liabilities arises. Risk can be managed in a number of ways.
The simplest solution is for a fund to enter into a swaps agreement where (on some notional amount) the fund pays a floating interest rate and receives a fixed rate in return. Since the fixed rate will be set such that the initial value of the swap is zero, no upfront payment is required to enter into such a contract. When interest rates rise, the fund will pay more to receive the same, and will therefore lose money on the swap. This, however, should be contrasted with the money that it makes from the drop in the value of its liabilities. When interest rates drop, the opposite happens. Under the swaps, the fund pays less, but still receives the same. It therefore makes money on the swap, which compensates the rise in the value of the liabilities.
Starting off with a properly funded pension fund, figure 1 shows how this works out in terms of the expected future funding level and the probability of underfunding over a 10-year period. The top line shows the risk-return trade-off in the original case without derivatives, while the bottom line shows how this changes when swaps are introduced. The points on the lines represent different stock-bond allocations, with 20% stocks/80% bonds in the lower left corner and 60% stocks/40% bonds in the upper right corner.
Figure 1 shows, at the cost of a relatively small decline in the expected future funding level, that the introduction of the swaps leads to a very substantial reduction in the probability of underfunding. A pension fund with 60% invested in equity will see the probability of underfunding drop from almost 16% to 11%.
Having hedged interest rate risk, the next step is to tackle the fund’s second source of risk: equity risk. Again, we can do so in several ways. For clarity, however, we will concentrate on the simplest solution: the purchase of long-dated stock index put options. Since the payoff of an option cannot be negative, an upfront payment will be required in this case, which by itself will hurt the expected return. With puts, however, equity is now ‘protected’. We could therefore purchase more of it and by doing so pick up some more of the equity risk premium (assumed to be at 2% annually). In other words, we can use the equity risk premium to finance part of the costs of the options position. Obviously, this will have a significant impact on the shape of the probability distribution of future funding levels. Although the expected value will remain more or less unchanged, we can expect to see more average but less extreme risk. Figure 2 shows how this works out in terms of the expected funding level and the probability of underfunding over a 10-year horizon.
Figure 2 shows that the addition of equity puts leads to a further substantial reduction in the probability of underfunding without any significant loss of expected return. In a pension fund with 60% invested initially in equity, the addition of a simple interest rate swaps and index puts reduce the probability of underfunding from almost 16% to little over 5%.
Although the above degree of risk reduction is impressive enough by itself, it is important to note that more sophisticated swap and option strategies can sometimes do even better. Instead of swaps, we could use swaptions and instead of ordinary puts we could use so-called Asian puts for example. How big the difference will be depends very much on the specifics of the pension fund at hand though. There typically is no one-size-fits-all solution; derivatives strategies must be tailor-made.

BT pension scheme announced the investment of £540m (e784m) in hedge funds. Railpen has recently appointed three US investment managers to manage a £600m hedge fund portfolio. It is therefore interesting to compare the above results with the benefits of investing in hedge funds. Figure 3 shows the impact on the expected funding level and the probability of underfunding of our pension fund if we invested 5% of total assets in the well known HFRI Composite index, for simplicity assuming that future hedge fund returns will resemble past returns. Even with assumed favourable returns, the benefits of diversification into hedge funds are much smaller than those from adding swaps or equity puts. In a pension fund with initially 60% invested in equity, the addition of 5% hedge funds reduces the probability of underfunding from almost 16% to little over 14%. A combination of swaps and puts would have taken that probability down to 5%.
Simple interest rate and equity derivatives strategies can greatly improve the risk characteristics of defined benefit pension funds. Derivatives can allow for a very substantial reduction of the probability of underfunding without damaging the expected future funding level.
Harry Kat is professor of Risk Management and director Alternative Investment Research Centre, Cass Business School, City University, London

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