# Under the hedge

If your base case is that interest rates will rise faster than is already priced in, how much should you under-hedge? The answer could be less than you think.

Deciding on a liability hedge for a defined benefit (DB) scheme depends upon your view of where the market is going. In a recent blog, we highlighted the importance of appreciating that rises in the Bank of England base rate are already priced into the market prices of gilts. It is only if you believe rates will rise faster than this that you should consider under-hedging. A couple of years ago, our liability framework paper touched on trustees’ conviction around the future path of bond yields. To explore this question more thoroughly, we took a fairly typical scheme* and investigated how much faster yields would need to rise than market implied to justify different degrees of under-hedging.

Assuming interest rates are expected to rise as fast as is currently priced into the market, the ideal level of hedging to seek to minimise deficit risk is 100% of liabilities. To allow for any negative views on hedging, we applied a mathematical tilting approach that involved optimising the hedge ratio. This took into account the implicit risk appetite of the scheme and so the essential trade-off involved in under-hedging: increased expected return (due to the negative view) but also increased overall risk**.

The graph below shows how the ideal hedge level changes depending on how strong your view is for this example scheme. In general, the size of the tilt depends on the scheme's circumstances: for example; a scheme with more equity risk would be likely to accept a larger tilt as the marginal impact of under-hedging on overall risk would be less.

Note that there is no view on the volatility of interest rates in these calculations. So, whilst you might take a view that rates will rise faster than implied by the market, you are never *certain* they will rise faster (apart from this representing an incredible level of conviction, the problem would become rather trivial!)

As can be seen, to do no hedging at all would require an expectation that the 20-year spot gilt rate rises faster than market expectations by 120 basis points per annum. Such a surprise increase in interest rates over a one-year period is very uncommon assuming markets are fairly priced; indeed we would expect it to occur in less than one out of 20 years. The model implies it would require a very strong view.

Our 'house' view is for structurally low rates, so we don’t take rates rising faster than market implied as our central case. We appreciate that many trustees will not share that view. But it is worth bearing in mind that, like other forms of risk protection (e.g. car insurance) it can be worth having some, even if it is perceived as incurring a 'cost' in terms of reduction in the expected return of the scheme.

** 75% funded on a gilts basis. Half of the scheme's assets are return-seeking and expected to generate returns of 4.5% over gilts with 10% volatility, assumed to be uncorrelated with rates. For simplicity, and just for illustrative purposes, we further assumed that liabilities were 100% fixed with volatility of 14% and that the scheme is concerned by deficit risk (rather than funding level risk). We also ignored any hedging costs.*

*** Not dissimilar to the Black-Litterman model *