Duration
To gain a measure of interest rate risk and volatility for a bond relative to others, bond market participants often use duration. The duration[29] metric is a summary measure of how far into the future is the average date of the cash flows to be received, when the cash flows are weighted by their size after they have been discounted.
In other words,
the duration of a bond is the weighted average maturity time of all payments (coupons and principal) to be received from owning a bond, where the weights are the discounted present values of the payments.
So, for zero coupon bonds the effective duration is the same as its actual term to maturity - the ‘average' maturity time is the same as the final payout, the only cash flow received. A three-year zero coupon bond has a duration of three years.
For coupon-paying bonds the duration is shorter than the stated term to maturity because as the years go by the investor receives income from the bond which pushes the weighted average timing of income flows more towards the start date than is the case on a zero coupon bond.
A three-year coupon-paying bond offering £7 per year (with the first in one year from now) and £100 on maturity can be seen as having cash flows equal to the following three zero coupon bonds:
A one-year zero coupon bond paying £7 in one year's time
A two-year zero coupon bond paying £7 in two years' time
A three-year zero coupon bond paying £107 in three years' time
If the present yields to maturity for bonds of this risk class are also 7% then the duration can be calculated - see Table 13.2 - where the present value
Table 13.2 Calculating duration on a three-year 7% coupon bond
| Period | Coupon and principal | PV (7% discount rate, the current market YTM) | Weights (PV ÷ total PV as a percentage) | Weighted maturity value (period ? weights ÷ 100) in years | ||
| 1 | £7 | £6.542 | (£6.542 ÷ £100) ? 100 = | 6.542% | 1 ? 6.542 ÷ 100 = | 0.0654 |
| 2 | £7 | £6.114 | (£6.114 ÷ £100) ? 100 = | 6.114% | 2 ? 6.114 ÷ 100 = | 0.1223 |
| 3 | £107 | £87.344 | (£87.344 ÷ £100) ? 100 = | 87.344% | 3 ? 87.344 ÷ 100 = | 2.6203 |
| Total PV | £100.00 | 100.00% | Duration = | 2.808 years | ||
As we might expect, the duration of 2.808 years is almost as much as the time to maturity but it is lowered from the full three years because some of the income is received before the end of three years. This three-year 7% coupon bond has the same duration as a 2.808-year zero coupon bond also yielding 7%.