a- ZCB, b- DISCOUNT BOND, c- PERPETUAL BOND, d- PER BOND, e – PREMIUM BOND.
All b, c, d, e are coupon bearing bonds. For this bonds as maturity increases D increaes at a decreasing rate & approaches a limiting value. i.e duration of a perpetual bond i.e 1+r/r.
Please explain the bold part. How the Perpetual bond is realted to other bonds.
Hi see i can explain it but there would be some friction so i request you to spare me for that. See dont think duration here in terms of % but in terms of years. Lets take conventional coupon bearing bonds. OK and say for years and duration comes out to say (approximately it will come around that only) and then say we made the same bond for 20 years. its duration will be around 10-11. so see there in case of 5 year bond the duration is almost 90%. 5*0.9-4.5. and in case of 20 years its around 50-55%. Now coming to the perpetual bond you will only receive interest lets say for 100 years and you go further 10 years i.e. 110 years your duration will increase but the weights of cashflow will be distributed in 110 parts instead of 100 parts so denominator increased and hence duration will increase but at a decreasing rate.