calculation-reference

How to Calculate Modified Duration

Formula, worked example, BA II Plus workflow, and common mistakes for modified duration.

TL;DR

Modified duration converts Macaulay duration into an approximate percentage price sensitivity to a yield change. It is the duration measure used in the standard bond price-change estimate.

Formula Reference

Modified duration

Modified duration = Macaulay duration / (1 + periodic yield)

Periodic yield equals annual YTM divided by payments per year.

Price sensitivity

% price change approx = -Modified duration x change in yield

Use yield change as a decimal, such as 0.005 for 50 bps.

BA II Plus Keystrokes

  1. If Macaulay duration is given, divide it by 1 plus periodic yield.
  2. For a 6 percent annual yield with semiannual coupons, periodic yield is 0.03.
  3. Enter Macaulay duration / 1.03 = modified duration.
  4. Multiply by the yield change and change the sign for price impact.

Worked Example

  • Problem: Macaulay duration is 4.20, YTM is 6 percent, coupons are semiannual.
  • Periodic yield = 0.06 / 2 = 0.03.
  • Modified duration = 4.20 / 1.03 = 4.0777.
  • For a 50 bp increase, price change approx = -4.0777 x 0.005 = -2.04 percent.

Common Mistakes

  • Dividing by 1 plus annual yield when coupons are semiannual.
  • Using basis points as whole numbers instead of decimals.
  • Forgetting that price moves opposite yield.

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