Modified duration

What is it?

Modified duration measures how sensitive a bond's price is to a change in its yield. It is Macaulay duration adjusted for the discounting rate, and it is read directly as a percentage: a modified duration of 2.76 means the price falls by roughly 2.76% when the yield rises by one percentage point, and rises by about the same amount when the yield falls.

The following formula is used:

Modified Duration = Macaulay Duration ÷ (1 + Yield)

• Macaulay Duration – weighted average time to the bond's cash flows, in years.
• Yield – annual rate used for discounting, taken as the bond's yield to worst.

The resulting price change is estimated as:

Price Change ≈ – Modified Duration × Yield Change × BondPrice

• Yield Change – change in yield, expressed as a decimal (0.01 for one percentage point).
• BondPrice – current market price of the bond, including accrued interest.

Modified duration is the standard measure of interest rate risk and the most direct way to compare two issues. It is the basis for hedging: matching duration between a position and its hedge neutralizes the first-order effect of rate movements.