Examine the following table showing Bond clean price and duration measures for
selected maturities.
We have seen in previous chapters how Duration is a summation of weighted cash flows, with weights being the TimeSpan (t) applicable to the timing of each such cash flows (as shown in the
formula). We also discussed, various flavors of Duration measures (Effective, Partial / Key-rate, Macaulay, Modified etc.). We also hinted on how these measures (other than KRD) assume a parallel shift across board and what pitfalls might occur with such an assumption.
Today, we will review why the transience of Duration measure is a very significant aspect. This metric is generally to be used for calculating transitory changes in portfolio (and should not be extended to long-term or too much farther into future).
Below is an extreme example of a cautionary note on applying this measure too much distant into future. And how the mechanics simply does not Work.
The purpose of this table is to highlight the importance of proximity of cash flows. Cashflows that occur beyond the 30year horizon have insignificant valuation impact.
(Compare the change in Duration for a 30yr bond with a 100yr maturity - Very
little change, inspite of the three-fold increase in maturity..)
Coupon Rate:
%. Coupon Frequency:
(Input Zero for Cpn and Yld - to see the impact on Zero Cpn bonds)
Yield level:
%.
(straight yield levels assumed for this illustration)
CHANGE the Coupon or Yield above, and click on Refresh button)
| | Bond_Name | Bond_Maturity | Bond_Price | Bond_Duration |
| 2yr Bond | 5/14/2027 | 0.981 | 1.96 |
| 5yr Bond | 5/14/2030 | 0.9551 | 4.67 |
| 10yr Bond | 5/14/2035 | 0.9182 | 8.64 |
| 30yr Bond | 5/14/2055 | 0.8262 | 18.86 |
| 50yr Bond | 5/14/2075 | 0.7845 | 23.21 |
| 100yr Bond | 5/14/2125 | 0.7548 | 25.49 |
As you can see above, the 50 year addition from a 50yr bond to a 100yr bond,
only adds an incremental <10% increase in duration risk measure. Infact, for the
really curious amongst you, change the yield level to 5% (0.05), then you can
notice that the 50year bond and the 100year bond pretty much have the same
metrics, confirming the logic that distant cashflows really mean nothing.