# The AI (ChatGPT) Bond Investing Handbook: Macaulay Duration

Here is the response from ChatGPT for the prompt bond Macaulay duration entered on February 14, 2023.

Macaulay Duration is a measure of a bond's price sensitivity to changes in interest rates. It is calculated as the weighted average of the time to receipt of each payment of a bond, where the weights are the present values of those payments.

The formula for Macaulay Duration is:

Macaulay Duration = (C1*(1+y)^(-t1)t1 + C2(1+y)^(-t2)t2 + ... + Cn(1+y)^(-tn)*tn) / Bond Price

where: C = coupon payment t = time until receipt of payment (in years) y = yield to maturity

The Macaulay Duration tells us the approximate percentage change in a bond's price for a 1% change in yield. For example, if a bond has a Macaulay Duration of 5 years and interest rates increase by 1%, the bond's price will decrease by approximately 5%.

Macaulay Duration is named after Frederick Macaulay, who first introduced the concept in 1938. It is widely used by bond investors to manage interest rate risk and to compare the price sensitivity of different bonds.

Modified Macaulay Duration

Bond Duration Calculator - Macaulay Duration and Modified Macaulay Duration (from buyupside.com)