What is modified duration?

Modified duration is a concept that interest rates and bond prices move in opposite directions. It tells you how sensitive a bond is to interest rate changes. It is expressed in a formula that expresses the measurable change in the value of a security in response to a change in interest rates.

Key points about modified duration:

A “Bond” with a lower “modified duration” implies that the “returns” are more from accrual income than from capital gains.

A “Bond” with a higher “modified duration” implies that the “returns” are more from capital gains than from accrual income.

For example an investor has a bond of 2 years maturity with 5% annual interest and with a yield to maturity of 5%. If the current price of the above bond is Rs.1000/-, then

PV of first payment will be (1000×0.05) ÷ (1+0.05)=47.62

PV of the second payment, including the maturity amount, would be

[1000 + (1000 ×0.05)] ÷ (1 + 0.05%)^2) = 1050/1.1025 = 952.38

Therefore, Macauley duration would be [(47.62 x 1) + (952.38 x 2)]÷ (47.62 + 952.38), =1952/1000= 1.952.

The modified duration is 1.952÷1.05=1.859,

Modified Duration = Macaulay Duration/ (1+y/m), where ‘y’ is the yield (5%), ‘m’ is  the number of times compounding occurs in a year.i.e. 1 (annual interest)

Related article: What is Macaulay Duration?