Duration if the term to maturity is lengthened
If we now look at a four-year bond offering £7 per year when the yield to maturity is 7% we expect to find its duration greater than that on the three-year bond - see Table 13.3.
This illustrates a general rule:
Holding other factors constant, the longer the term to maturity of a bond, the longer its duration.
Table 13.3 Calculating duration on a four-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 ? 6.54 ÷ 100 = | 0.0654 |
| 2 | £7 | £6.114 | (£6.114 ÷ £100) ? 100 = | 6.114% | 2 ? 6.11 ÷ 100 = | 0.1223 |
| 3 | £7 | £5.714 | (£5.714 ÷ £100) ? 100 = | 5.714% | 3 ? 5.714 ÷ 100 = | 0.1714 |
| 4 | £107 | £81.630 | (£81.63 ÷ £100) ? 100 = | 81.630% | 4 ? 81.63 ÷ 100 = | 3.2652 |
| Total PV | £100.00 | 100.00% | Duration = | 3.6243 years | ||
Article 13.1 illustrates the importance of length to maturity in creating increased interest rate risk related to duration - sometimes investors are very concerned about it, other times they are more sanguine.
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