Modified duration is one of the most useful — and most testable — bond concepts in the CII R02 exam. In a single number, it tells you how much a bond's price will move for a 1% change in yield.
What modified duration actually measures
Modified duration is a price-sensitivity measure. It is derived from Macaulay duration (the weighted-average time until you receive your cash flows) and adjusted for yield.
Modified duration = Macaulay duration ÷ (1 + y)
Where y is the yield to maturity (per period — usually annual for R02).
The headline rule
A bond with modified duration of D will change in price by approximately −D% for every 1% rise in yield.
So a bond with modified duration of 6 loses roughly 6% if yields rise 1%, and gains roughly 6% if yields fall 1%.
Worked example
A bond has Macaulay duration of 5.25 years and yields 5%.
Modified duration = 5.25 ÷ (1 + 0.05) = 5.25 ÷ 1.05 = 5.0
Now estimate the price change if yields rise from 5% to 6% (a 1% change).
ΔPrice ≈ −Modified duration × Δyield = −5.0 × 1% = −5%
If the bond was priced at £102, the estimated new price is:
£102 × (1 − 0.05) = £96.90
The actual move would be slightly less severe (because of convexity) — but for R02-level questions the linear approximation is exactly what's expected.
What drives a bond's modified duration up or down
| Factor | Effect on duration |
|---|---|
| Longer maturity | ↑ duration |
| Lower coupon | ↑ duration |
| Lower yield | ↑ duration |
| Zero-coupon bond | duration = maturity (the maximum) |
This is why long-dated, low-coupon gilts move so violently when interest rates change — and why short-dated corporate bonds barely flinch.
What R02 actually tests
You'll typically see one of these question shapes:
- Apply the rule — given modified duration and a yield change, compute the expected price change.
- Rank bonds by interest-rate risk — pick the bond with the highest modified duration as the most price-sensitive.
- Conceptual — explain why modified duration falls when coupon rises (because more cash is returned earlier).
Common traps
- Confusing direction. Yields up → prices down. The minus sign matters.
- Mixing Macaulay and modified. Macaulay is in years; modified is a percentage sensitivity. Examiners love to give you Macaulay when they want modified — divide by (1 + y).
- Forgetting it's an approximation. It works well for small yield moves (≤1%); for large moves you need convexity adjustment, which R02 mentions but doesn't compute.
- Treating it as 'how long until I get my money back'. That's Macaulay duration. Modified duration is a price-elasticity measure.
How to remember it
Think of modified duration as the bond's interest-rate elasticity — bigger number, bigger swings. A 7-year duration bond is roughly 7× as price-sensitive as a 1-year duration bond.
Memorise the formula, practise three worked examples (one short bond, one long bond, one zero-coupon), and you'll have one of the R02 fixed-interest topic's reliable mark-grabbers in the bag.