# Please explain Duration and Convexity

Could someone please further explain duration and convexity? I’m confused by the relationship of these concepts and have a hard time applying them to questions. Thank you for the help!

Duration is the change in Price with change in interest rates. But duration only explains these changes linearly. When convexity is added to duration, changes in price (due to changes in interest rates) are explained more realistically. I guess you will have to go back to text to understand it better, unless you have a more specific question.

5carrots, duration gives the first order approximation of how much bond price will change (percentage wise) if interest rates change by 1%. For example, if duration = 5 and interest rates move by 1%, the bond price will change by 5%. Convexity allows for second order adjustment. if you are familiar with options: duration = delta, convexity = gamma. if you are comfortable with math. assume P = P®, where r is interest rate. Duration = dlnP/dr=(1/P)*dP/dr, convexity = (1/P)*(d^2P/dr^2) (first and second derivatives normalized by P).