Question

How can duration be used to determine a rough measure of the percentage change in the price of a bond as a result of interest rate changes?

Answer 1

The sensitivity of changes in bond's price with change in interest rate or yield to maturity of bond is referred to as duration. . Duration gives us the linear change in price of bond due change in interest rate.

There are various measures of duration.Duration of a bond is most commonly measured by Macaulay duration. Macaulay duration is the weighted average time to receive the cash flows associated with the bond. Another measure of duration is modified duration. Modified duration can give the approximate change in price of bond for 1% change in Yield to maturity or interest rates.

Relationship between Macaulay duration and Modified duration: Modified duration = Macaulay duration / (1+ YTM)

We can use modified duration to measure approximate change in price of bond

Approximate percentage change in price of bond = -Modified duration x change in yield

For example if Macaulay duration of bond is 5.2 years and YTM is 4%, then Modified duration = 5.2 / (1+4%) = 5.2 / 1.04 = 5 years

If the yield or interest rate decrease by 0.5% then change in yield = - 0.5% = -0.005

Approximate percentage change is price = -5 x -0.005 = 0.025 = 2.5%

Then price of bond will increase approximately by 2.5%.

In this way we can use duration to measure approximate percentage change in price of bond due to interest rate changes.