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Subject 3. Properties of Bond Duration PDF Download

Bond duration is affected by many variables.

The fraction of the period that has gone by (t/T). A plot of Macaulay duration (or modified duration) against time for a single bond with constant yield will show a saw-tooth pattern, with Macaulay duration declining steadily until a coupon payment results in an upwards jump.

The Macaulay duration of a zero-coupon bond is its time-to-maturity.

The Macaulay duration of a perpetual bond (perpetuity) is (1 + r) / r.

Coupon rate is inversely related to Macaulay duration and modified duration.

Yield-to-maturity is also inversely related to Macaulay duration and modified duration.

Time-to-maturity and Macaulay and modified duration are usually positively related.

  • They are always positively related on bonds priced at par or at a premium above par value.

  • They are usually positively related on bonds priced at par or at a discount below par value. The exception is long-term, low coupon bonds, on which it is possible to have a lower duration than on an otherwise comparable shorter-term bond.

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