Bond Duration

Bond duration is an actual matter in the field of financial instruments. Duration is a measure of interest-rate risk and it is more accurate as the change in the interest rate becomes smaller.

Frank Macaulay Duration Formula :

= 1 × Payments₁ ÷ (1+yield)¹ + 2 × Payments₂ ÷ (1+yield)²+....+(n-1) × Payments_n-1 ÷ (1+yield)^n-1 + n × Payments_n+Par Value ÷ (1+yield)ⁿ Current Price

Frank Macaulay Modified Duration Formula :

= Macaulay Duration 1 + YTMAnnual Payments

Modified Bond Duration (Δ%/1%) :

Measured in percentage change(in price) per percentage change(in interest rate/yield to maturity).In terms of percent, we can say

Modified Bond Duration (Δ%/1%) :

Measured in percentage price change per unit interest rate change.

Note: If we want to improve our estimate of the % change in the bonds price, we can add a convexity adjustment.