For a discount bond, duration first increases with longer maturity and then decreases over a range of relatively long maturities until it approacehs the duration of a perpetuity, which is (1+YTM) / YTM.
Can somebody please explain to me what that means exaclty?
Try this in Excel: they have a Macaulay duration function (DURATION):
Set the settlement date as 1/1/2014
Enter a range of maturity dates, from 1/1/2015 to 1/1/2314.
For each maturity date, use the function to calculate the Macaulay duration of a bond that settles on 1/1/2014 and matures on the given date; the particulars of the bond are:
Plot the results, using a range on the y-axis of 17.166 to 17.17, and a range on the x-axis of 1/1/2109 (76338) to 1/1/2300 (146099).
You’ll see that the graph starts below 17-1/6 (= 1.06 / 0.06), rises above 17-1/6 (to a maximum of 17.1695 for a maturity of 1/1/2134), then falls and approaches 17-1/6 asymptotically from above.
That’s what it means.
thanks for that it really helped!
My pleasure.