Duration

What does duration tell you about bond risk? Not as much as you thought!

Duration. It’s a short word, with a simple meaning, but those eight letters cause more confusion in the minds of many investors than almost anything else. In fact, there are many variants of duration: spread duration, Macaulay duration, modified duration, but the most frequently used is the latter, shortened to simply “duration”.

So what does duration mean?

The first point to realise is that duration is not the same as maturity. Furthermore, duration does not increase linearly with maturity, so the duration of a 30-year bond IS NOT three times that of a 10-year bond. The only exception to this is for zero coupon bonds where duration and maturity are the same. Currently the duration of the US 10-year is 8.81 years and the duration of the 30-year is 19.51 years.

Although linked, the different types of duration all have subtly different meanings. For example, Macaulay duration is the weighted average number of years an investor must hold a bond until the present value of the bond's cash flows equals the amount paid for the bond. This is useful for bond managers managing long term liabilities, but it has limited practical use for most investors.

On the other hand, modified duration is useful for both bond managers and investors as this version of duration measures a bond’s sensitivity to changes in interest rates. So, for instance, a bond with a duration of three years will gain or lose 3% if interest rates fall or rise by 1%. That’s just an approximation though, and strictly speaking the duration concept only works for small changes in interest rates. This note is not intended to be overly technical though, so for our purposes we will assume that a bond with a three-year duration will gain or lose 3% for a 1% change in interest rates.

Where confusion tends to creep in, is the assumption that the change in interest rates refers to a change in short term interest rates. When the press refers to interest rates having risen by 0.25 or 0.5 percent, they are almost certainly referring to the Fed Funds rate in the US or the equivalent base rate in other countries. Very rarely do the words interest rates refer to longer dated bonds in the media. In reality, there are a wide range of interest rates which apply to bonds of maturities up to 30 years or more, but to avoid confusion, in this note we will use interest rates or short rates to refer to short term rates and bond yields for longer dated bonds.

So the first thing to realise is that duration DOES NOT measure the sensitivity of a bond to changes in interest rates, i.e. short term rates. Instead duration refers to the sensitivity of a bond to changes in bonds yields, which is an entirely different concept. Very rarely does the yield of a long dated bond move one-for-one with changes in short term interest rates. To try and illustrate this point, chart 1 (over), shows the change in yields across the maturity spectrum from 3 months to 30 years between Jan 1994 and Jan 1995.

Full PDF