Duration is often thought of as important concept for pension schemes. It is generally known that pension scheme liabilities can have very long durations, and that if the durations of their assets and liabilities differs then it is exposed to duration risk. But what exactly is duration? And how important is it?
One form of duration – Macaulay duration – gives the average time to payment for a series of cash flows. This gives a useful comparator for different cash flows, but little more. The problem is that this metric can be calculated based on any series of cash flows, but it takes no account of how certain those cash flows are. So if an equity is treated as a series of dividends, then whilst its duration can be calculated on this basis the result is heavily dependent on the assumed value of those future payments.
Another issue with calculating the Macaulay duration is that the calculation approach requires the payments to be discounted. If the payments are known with near certainty, then the discount rate is simply the risk-free rate (although what constitutes a risk-free rate is a subject for a different post); however, for a series of uncertain cash flows what interest rate should be used? Probably one that allows for the uncertain nature of future payments, but the assessment of an appropriate rate is not straightforward.
A more practical version of duration is the modified duration. This gives the proportional change in the value of a series of payments for the same proportional change in interest rate. The modified duration is useful when it comes to looking at liability driven investing (LDI) as it allows the sensitivity of assets and liabilities to changes in interest rates to be compared. However, it is only a crude measure of interest rate sensitivity. For example, it says nothing about the shape of cash flows. The principal payment of a 20 year gilt strip and a the payments from a final salary pension scheme may both have durations of 20 years, but they will only respond the same way in response to a small change in interest rates if the change is the same at all terms. Rates rarely change in this way which is why it is also important to consider aspects such as convexity – the rate of change in value in response to a change in interest rates – or to look instead at the effect of interest rate changes at individual terms.
This measure of duration is also useful only when considering values whose sensitivities to interest rates are known with a high degree of certainty. In particular, whilst it might be possible to calculate the modified duration of equities based on the correlation of their returns with changes in interest rates, the instability of such correlations means that such a measure has limited value.
So does duration matter? Well, if you have a duration mismatch then you’re running a risk – but it is important to look at more than just duration.