## What is the Duration?

The sensitivity of a bond to interest rate fluctuations is measured by its duration.

Duration describes what happens when there is a small parallel shift in the term structure.

## Example of Duration:

In 1938, Canadian economist Frederick Robertson Macaulay dubbed the effective-maturity concept the “duration” of the bond. He suggested that this duration be computed as the weighted average of the times to maturity of each coupon, or principal payment, made by the bond. Macaulay’s duration formula is as follows:

$ D= \frac{\sum_{i=1}^{T}\frac{t*C}{(1+r)^{t}}+\frac{T*f}{(1+r)^{t}}}{\sum_{i=1}^{T}\frac{C}{(1+r)^{t}}+\frac{F}{(1+r)^{t}}} $

Where,

*D *= The bond’s MacAulay duration

*T *= the number of periods until maturity

*i *= the *ith* time period

*C *= the periodic coupon payment

*r *= the periodic yield to maturity

*F *= the face value at maturity