Duration of a bond |

**Around the formula...**

For any fixed-income debt portfolio or security, there is a period over which:

- the loss on the reinvestment of coupons will be offset by the capital gain on the sale of the bond if interest rates decline; and

- the gain on the reinvestment of coupons will be offset by the capital loss on the sale of the bond if interest rates rise.

From a mathematical standpoint, duration is calculated as follow :

Duration is similar to the discounted average life of all the cash flows of a bond (i.e. interest and capital). The numerator comprises the discounted cash flows weighted by the number of years to maturity, while the denominator reflects the present value of the debt.