 # Computing Effective/Modified Duration

Suppose that there is a 15-year option free (noncallable) bond with an annual coupon of 7 percent trading at par. If interest rates rise by 50 basis points (0.50%), the estimated price of the bond will be 95.586 percent. (N = 15; PMT = 7.00; FV = 100; I/Y = 7.50%; CPT → PV → –95.586). What’s the bond’s effective duration? The correct answer is 9.115, however when I use the bond worksheet on TI-BA 2, the duration it shows is 9.9. Can someone else confirm the same?

Hi anupamjain008. The effective duration is 9.1148943. Assuming yields go up by 50 basis points, the price of the bond is 95.58644013. If yields go down 50 basis points, the price of the bond is 104.7013344. Assuming no change in yields, the bond is trading at par or priced at 100. Effective Duration can be computed using the following formula: = (Price when yields go up - Price when yields go down) / (2 x Price when yields are unchanged x Absolute change in yield) = (104.7013344 - 95.58644013) / (2 x 100 x 0.005) = 9.1148943 I use an HP12C calculator; hence, I have no choice but to compute Effective Duration manually. Maybe the duration that your calculator computed is Modified Duration? Am not too familiar with the functionalities of the TI BA2 calculator.

Hey thanks a lot AnimoLaSalle, You are absolutely correct and the Duration calculated by the financial calculator is indeed Modified Duration. I knew this all the time and somehow just dint realise that. Thanks once again… much appreciated!

No worries. =)

Any calculator with bond functions (Excel, etc.) will calculate duration or modified duration but not effective duration when you hit the duration key. For one thing, the first two are characteristics of the bond, the third is a function of the bond and the interest rate move.