Market and views
Quarterly Focus - Q1 2010 - Fixed Interest
How it works: Duration
Fixed Income Fund Manager with Aviva Investors in the UK, Trevor Welsh, discusses ‘duration’ – what it is, how it works and why it’s an important concept for investors to understand.
Frequently thrown into discussions by portfolio managers and often misunderstood by those who don’t earn their living working with bond markets, duration is a concept that is important to grasp if you want to understand the performance of your bond portfolio.
In its simplest terms, duration is a measure of how much the price of a bond is affected by the change in its yield, or underlying interest rate. It is a measure of the interest rate risk of a bond or a portfolio of bonds. As bond prices move inversely to yields, when yields fall prices go up and vice-versa. Therefore a bond with a high duration will experience a larger increase in price than a bond with a low duration would for the same fall in yield.
Interest rates and the determinants of duration
An important point to note is that the interest rates or yields we are talking about here are not the same as the interest rate set on a monthly basis by the Bank of England – the Bank sets a short-term interest rate that can influence longer term rates but there are many other factors involved. For example, 10-year maturity rates will include expectations regarding inflation and growth, so even if Bank of England rates rise, 10-year rates may stay unchanged or even fall. A 10-year maturity bond is affected by the movements of 10-year yields, and a 30-year bond is affected by the movements of 30-year yields.
There’s a fair bit of mathematics behind the calculation of the duration of a bond, but the essence is to work out the ‘weighted average maturity’ of all the cash flows the holder will receive over the life of the bond. Cash flows from conventional bonds are coupons and the repayment at final maturity, and the size and timing of these cash flows is what determines a bond’s duration.
A high coupon rate will reduce a bond’s weighted average maturity, and hence duration, because coupons are paid at regular intervals throughout the life of the bond meaning higher cash flows are received sooner than if the bond had a low coupon rate.
However, because the final repayment is much larger than the coupons received, the timing of this repayment is the biggest factor influencing duration – the longer the maturity of the bond, the higher the duration. From this then, we know that the highest duration bonds will have a long maturity date and a low (even zero) coupon rate, and the lowest duration bonds will have short maturity dates and high coupon rates.
Applying the concept to the real world
Once we know the duration of a bond, how can we use that to understand the risk in a bond portfolio? Simplistically speaking, the duration of a bond measured in years will tell us how much the bond’s price will move in percentage terms if the underlying yield changes by 1 percentage point. So the price of a bond with a duration of 7 years, will fall by 7 per cent if the relevant yield rises by 1 percentage point. Therefore if we assume that the volatility of the underlying yields are the same, a bond with a duration of 20 years will be four times as volatile in price terms as a bond with a duration of 5 years.
Portfolio managers use the term duration frequently because it is a simple way of expressing their view on the direction of bond markets. The duration of a portfolio or a benchmark can be calculated by working out a weighted average of the duration of all the bonds in the portfolio or benchmark. If a portfolio has a higher weighted average duration than the benchmark, the manager is said to be ‘long duration’. This would generally be because the manager feels that bond yields are going to fall, and hence prices rise, so wants more exposure to help outperform the benchmark. Conversely, if the portfolio has a lower weighted average duration than the benchmark, the manager is said to be ‘short duration’ and will have a negative view on bond prices – if bond prices fall (yields rise), the portfolio returns will be less negative than the benchmark returns.
The portfolio management process makes further use of the duration concept, particularly when it comes to deciding on the size of trades. In an equity portfolio, active trades are generally measured in percentage terms – for example the portfolio may have a 5 per cent higher holding in a particular stock or sector than the benchmark. In a government bond portfolio, percentage holdings are meaningless because of differing durations of bonds. Holding 5 per cent more than the benchmark of a bond with 1 year of duration will add very little incremental risk to the portfolio, because of the bond’s low duration and hence lower price volatility. But having a 5 per cent overweight in a bond with a very long duration will add a lot of incremental risk because of the increased volatility of the bond.
Therefore bond managers size their trades in duration years – having half a year overweight in 5-year bonds adds the same amount of price volatility as a half year overweight position in 30-year bonds, although the exposure is to different maturity underlying yields. To illustrate the point without going into the mathematics, to get this position in 5-year maturity bonds you would need an overweight versus the benchmark of around 12 per cent. If you were using 30-year bonds, you would need an overweight of just 2.5 per cent. It should be noted that in corporate bond portfolios, where credit risk is a much more important driver of prices than interest rate risk (duration), measuring holdings in percentage terms is much more relevant.
Duration at a glance…
- Changes in interest rate affect a bond’s yield
- Duration measures the sensitivity of a bond’s price to changes in yield (thus interest rates)
- The price of a long duration bond is more sensitive to changes in its yield than short duration bonds
Duration is frequently used to:
- Understand the risk of a portfolio of bonds
- Make decisions on the size of active trades