Enter the Macauley duration, the yield to maturity, and the number of coupon periods period year to calculate the modified duration.

Modified Duration Formula

The following formula is used to calculate a modified duration.

MD = MCD / (1+ YTM/n)
  • Where MD is the modified duration
  • MCD is the Macauley duration
  • YTM is the yield to maturity
  • n is the number of periods per year

Modified Duration Definition

Modified duration is defined as the ratio of the change in the value of a security with the change in the value of the interest rate.

Modified Duration Example

How to calculate a modified duration?

  1. First determine the Macauley Duration.

    Calculate the weighted average term to maturity of the cash flows from a bond.

  2. Next, determine the yield to maturity.

    Calculate the yield to maturity of the given security.

  3. Next, determine the number of coupon period per year.

    As stated, calculate the number of periods per year.

  4. Finally, calculate the modified duration.

    Use the formula and information from steps 1-3 to calculate the modified duration.


How does yield to maturity affect modified duration?
Yield to maturity (YTM) directly impacts the modified duration of a bond. A higher YTM typically results in a lower modified duration, indicating that the bond’s price is less sensitive to changes in interest rates.

Why is modified duration important for investors?
Modified duration is crucial for investors as it helps them understand the sensitivity of a bond’s price to changes in interest rates. This knowledge allows investors to manage interest rate risk and make more informed investment decisions.

Can modified duration predict the exact change in bond prices?
While modified duration provides an estimate of the percentage change in a bond’s price for a 1% change in interest rates, it does not predict the exact change in bond prices. This is because it assumes a linear relationship between yield changes and price changes, which may not always hold true for larger interest rate movements.

modified duration calculator
modified duration formula