What duration means

The YTM post showed that bond prices fall when yields rise. Modified duration says by how much: it is the approximate percentage change in a bond’s price for a one-percentage-point change in its yield.

A duration of 4 means a 1 percentage point rise in yields knocks roughly 4% off the price; a 1 percentage point fall adds roughly 4%. Longer-dated bonds have higher durations, which is why a gilt fund holding ten-year government bonds swings far more than a liquid fund holding paper that matures in weeks — even though the government bonds carry no credit risk at all.

Duration is the number that turns “interest rate risk” from a phrase into a quantity.

The formula

Two versions. Macaulay duration is the weighted-average time until you receive the bond’s cash flows, with each flow weighted by its present value:

Macaulay duration  =  Σ [ t × PV(CF_t) ] / Price

Modified duration  =  Macaulay duration / (1 + y)

Price change (%)   ≈  − Modified duration × Δy (in percentage points)

Macaulay is in years and has a nice intuition — it’s the bond’s “centre of gravity” in time. Modified is the one you use for price sensitivity. For a zero-coupon bond, Macaulay duration equals the maturity exactly, because all the money arrives at the end. Modified duration is a bit lower, since it’s divided by (1 + y) — 9.35 versus 10 for the ten-year zero in the table further down.

Worked example: the same ₹1,000 bond

Same fictional bond as last time: 7% coupon, 5 years, priced at ₹960 for a YTM (yield to maturity) of 8% (₹960.07 at exactly 8%, the base the percentage changes below are measured from).

Reusing the present-value table from the YTM post and weighting each year by its PV:

   
Macaulay duration 4.37 years
÷ (1 + 8.0%) → Modified duration 4.05

So the rule of thumb says a one-point move in yields should move the price by about 4.05%. Check it against the actual repricing:

Yield moves to Price Actual change Duration estimate
9.0% (+1 pt) ₹922.21 −3.94% −4.05%
7.0% (−1 pt) ₹1,000.00 +4.16% +4.05%

Close, and not identical: the actual fall is a little smaller than the estimate and the actual rise a little larger. That asymmetry is convexity — the price-yield curve bends — and for ordinary bonds without embedded options (such as a call the issuer can exercise), it works in the bondholder’s favour. Duration is a straight-line approximation of a curve; it’s excellent for small moves and drifts for large ones.

Why maturity matters so much

Same 7% coupon, all starting at a 7% yield (so each is priced at par), different maturities. The last column is the actual price change when the yield rises one point, to 8%. (That’s why the five-year row differs slightly from the worked example above, which starts at 8%.)

Bond Macaulay Modified duration Price change for +1 pt
1-year, 7% coupon 1.0 0.93 −0.9%
5-year, 7% coupon 4.39 4.1 −4.0%
10-year, 7% coupon 7.52 7.02 −6.7%
10-year, zero coupon 10.0 9.35 −8.9%

A one-year bond barely notices a rate move. A ten-year bond loses about 7% — seven times as much — on the identical change in yields. And the ten-year zero coupon, which pays nothing until the end, loses nearly 9%.

This table is the whole reason debt funds are not “safe” in the way a fixed deposit is. A fund holding ten-year gilts carries essentially zero risk of not being repaid and very real risk of losing 7% in a year when yields rise a point. A liquid fund, holding paper with a duration measured in weeks, carries almost none of that. Both are “debt funds”. The debt funds tax post treats them alike; the market does not.

Every debt fund factsheet quotes its portfolio’s modified duration for exactly this reason. It is the single most useful number on the page.

🧒 Explain it like I'm 10 (optional — skip if this is already clear)

Think of a see-saw with the bond’s payments sitting along it — small coupons spread out, and one big lump (the repayment) at the far end. Duration is where you’d have to put the pivot to balance it. Payments that arrive far away push the balance point out.

Now: the further out the balance point, the longer the lever — and the more a small push (a change in interest rates) swings the whole thing.

Common mistakes

  • Reading “government bond fund” as “no risk”. No credit risk. A gilt fund with a duration of 7 has as much interest rate risk as the table says.
  • Confusing duration with maturity. A 5-year coupon bond has a duration of about 4, not 5, because the coupons arrive early. Only a zero-coupon bond’s Macaulay duration equals its maturity (its modified duration is still a little lower).
  • Applying duration to big yield moves. It’s a linear approximation. For a 3-point move the convexity correction is no longer a rounding error.
  • Forgetting it cuts both ways. Duration is also how much you gain when yields fall. Investors who bought long-duration funds before a rate-cutting cycle earned exactly this.

Takeaway: modified duration is roughly the percentage a bond’s price moves for a one-point move in yields — 4.05 for our five-year bond, about 7 for a ten-year one. It’s why two funds that are both “debt” can behave nothing alike, and it’s the first number to read on a debt fund’s factsheet.