Question

Compute the duration of a bond with a face value of $1,000, a coupon rate of 7% (coupon is paid annually) and a yield to maturity of 7% for maturities of 2 to 18 years in 1-year increments (so here we are going to vary the time to maturity and see how duration changes if N=2, 3 … etc.). What happens to duration as maturity increases?

Answer 1

Say, the settlement date is 1/1/2019 and so for first case the maturity date= 12/31/2019 (considering there is 365 days in a year)

Calculation of duration is given below:

If we plot number of year vs duration graphs looks like below:

We can see as maturity increases the slope is of the curve is diminishing i.e. when maturity year is high the duration becomes more and more away from the tenure of the bond.