comparison

Macaulay vs Modified Duration

Compare Macaulay duration and modified duration with formulas and exam interpretation.

TL;DR

Macaulay duration is a weighted-average time to receive cash flows. Modified duration converts Macaulay duration into approximate price sensitivity to yield changes.

Formula Reference

Macaulay duration

MacDur = sum[t x PV(CF_t)] / full price

Measured in years.

Modified duration

ModDur = MacDur / (1 + y / m)

Used for price sensitivity.

BA II Plus Keystrokes

If Macaulay duration is given, divide by 1 plus periodic yield.
Use modified duration times yield change for price impact.
Use STO/RCL to keep duration and yield-change terms separate.

Worked Example

MacDur = 7.0, YTM = 6 percent, annual coupon.
ModDur = 7.0 / 1.06 = 6.6038.
A 25 bp yield rise implies price change about -1.65 percent.

Common Mistakes

Using Macaulay duration for price sensitivity.
Not adjusting yield for coupon frequency.
Forgetting that duration is a linear approximation.

Related Guides

How to Calculate Modified Duration - Formula, worked example, BA II Plus workflow, and common mistakes for modified duration.
CFA Level I Fixed Income Calculations - Bond pricing, yield, duration, convexity, spot rates, and forward rates for CFA Level I.
CFA Level I Fixed Income Formula Sheet - Public formula sheet for bond pricing, yield, duration, convexity, spot rates, and forward rates.