Bond Duration Calculator

How to calculate Bond Duration?

Duration is a measure of a bond's price sensitivity to interest rate changes. It is calculated as a weighted average of the time until all cash flows from the bond are received, where the weights are the present values of those cash flows as a percentage of the bond's total price.

Modified Duration = Macaulay Duration / (1 + YTM/n)

Using the Bond Duration Calculator: an example

Consider a $1,000 bond with a 5% coupon, 10 years to maturity, and a 4% YTM.

Step-by-step calculation:

1. Calculate the present value of every future coupon and principal payment.
2. Determine the weighted average time (Macaulay Duration).
3. Adjust for the current yield to find the Modified Duration.
4. Multiply the result by the interest rate change to estimate the price shift.

Frequently Asked Questions

What is the difference between Macaulay and Modified duration?
Macaulay duration represents the weighted average time to receive cash flows in years, while Modified duration measures the percentage change in a bond's price for a 100 basis point change in yield.

Why do zero-coupon bonds have higher duration?
Zero-coupon bonds have the highest duration relative to their maturity because all cash flow occurs at the final maturity date, meaning no coupon payments exist to pull the average time forward.

How does maturity affect duration?
Generally, the longer a bond's time to maturity, the higher its duration and interest rate risk. This happens because cash flows arriving further in the future are more significantly impacted by discounting changes.