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

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

Modified Duration is another measure of a bond's price sensitivity to changes in interest rates, similar to Macaulay Duration, but it takes into account the bond's yield to maturity.

The formula for Modified Duration is:

Modified Duration = Macaulay Duration / (1 + y)

where: Macaulay Duration is calculated as explained in my previous answer. y = yield to maturity

The Modified Duration expresses the percentage change in a bond's price for a 1% change in interest rates, taking into account the bond's yield to maturity. Therefore, it provides a more accurate measure of price sensitivity than Macaulay Duration.

For example, if a bond has a Modified Duration of 5 years and interest rates increase by 1%, the bond's price will decrease by approximately 5%, taking into account the bond's yield to maturity.

Modified Duration is an important measure for bond investors because it allows them to compare the price sensitivity of bonds with different coupon rates, maturities, and yields to maturity. It is also used in bond portfolio management to measure interest rate risk and to immunize bond portfolios against interest rate movements.

Macaulay Duration

Bond Duration Calculator - Macaulay Duration and Modified Macaulay Duration (from

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