The interest or yield on a bond is inversely related to its market value, i.e. if the bond's interest rate goes down, the price goes up.
The duration of a non-coupon or zero coupon bond will be exactly the time left until the bond's expiry date. Applied on a daily basis; if a zero coupon bond expires in 10 years, the duration of that bond is 10 years.
For coupon bonds: the duration is longer the more years left before the expiry date, but the higher the coupons, the shorter the duration, because we are actually receiving part of the interest in advance of the expiry date.
The duration of a bond can also be understood as a percentage that will vary the price of a bond in response to a 1% change in the yield on that bond.
How do we calculate bond duration?
The first thing we need to do is to determine the current value of each payment stream (coupons and principal).
- The price of the bond is made of the values of these streams together.
- We multiply the payment flows by the period of time left until each one of them (for example, if the first coupon is paid within one year it will be multiplied by one, if the second coupon is paid within two years it will be multiplied by two and so on for all the payment streams).
- We add them all together.
- Lastly, we divide that total by the price of the bond to get the bond's duration.