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

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## 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?

**First determine the Macauley Duration.**Calculate the weighted average term to maturity of the cash flows from a bond.

**Next, determine the yield to maturity.**Calculate the yield to maturity of the given security.

**Next, determine the number of coupon period per year.**As stated, calculate the number of periods per year.

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

## FAQ

**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.