Bond Duration Explained

You already know that rising yields push bond prices down. The question this article answers is more precise: how much will a particular bond's price move for a given change in yield? That's exactly what duration measures — it turns a vague statement like "this bond is rate-sensitive" into an actual number.

Two bonds, same maturity, different duration

Consider two 10-year bonds, both with ₹1,000 face value:

Both bonds mature on the same day. But they do not have the same duration — and that distinction is the first thing to get straight.

Maturity and duration are not the same question

For the zero-coupon bond, every rupee arrives in Year 10 — so its Macaulay duration is exactly 10 years, identical to its maturity. For the coupon bond, ₹80 arrives every year along the way, so some of your money comes back well before maturity. Its duration must therefore be shorter than 10 years — computed precisely, it works out to 7.25 years for this bond, priced at par. That's a real, sizeable gap between two bonds that mature on exactly the same date.

Duration as a weighted-average time

Suppose a simplified bond pays ₹100 in Year 1, ₹100 in Year 2, and ₹1,100 in Year 3. You wouldn't average (1+2+3)/3, because the cash flows aren't equal — the ₹1,100 in Year 3 matters far more than the ₹100 in Year 1. Duration weights each year by the present value of the cash flow received then:

Working through this bond at a 10% discount rate:

So although this bond matures in exactly 3 years, its Macaulay duration is about 2.74 years — shorter than maturity, because some of the value arrives before the final payment. Using present-value weights rather than raw rupee amounts matters here: ₹100 arriving next year is worth more today than ₹100 arriving in three years, so duration correctly gives the earlier payment less pull on the average than its face amount alone would suggest.

A useful picture: cash-flow center of gravity

Imagine every future cash flow sitting on a timeline, with larger payments pulling harder. Big cash flows pull the balance point toward them; early cash flows pull it toward today; late cash flows pull it toward maturity. Where the timeline actually balances is roughly what Macaulay duration represents — not the formal definition, but a genuinely useful way to hold the concept in your head.

From timing to price sensitivity: modified duration

Macaulay duration answers a timing question. Modified duration converts that into something directly usable: an estimate of how much price actually moves for a given change in yield.

In plain terms: percentage price change is approximately negative modified duration times the change in yield. This is a first-order approximation — good for small yield moves, less accurate for large ones, which is exactly the gap that convexity fills in the next article.

A worked example, using Bond B

Bond B — the same 10-year, 8% coupon bond from earlier, priced at par — has a modified duration of 6.7101. If yield rises by 1 percentage point, from 8% to 9%, duration alone estimates:

That's the duration-only estimate. The bond's actual price at 9% yield, computed properly from its full cash-flow schedule, is ₹935.82 — about ₹2.92 higher than duration alone predicted. That small gap isn't an error in the formula; it's the real, curved shape of the price-yield relationship showing up. Duration draws a straight line tangent to that curve at today's yield, which is a good approximation nearby but understates how well the bond actually holds up as yield moves further away. That gap is precisely what the next article, on convexity, explains and quantifies.

The calculator may show ₹935.77 rather than ₹935.82 — a rounding difference from exact-date day counting over 10 years, the same effect explained in the pricing article.

DV01: duration in rupees, not percentages

Once modified duration is in hand, DV01 (sometimes called PVBP) is a short step away. Where modified duration speaks in percentages, DV01 speaks in currency — the rupee change in value for a 1 basis-point (0.01%) move in yield.

Suppose a portfolio holds ₹10 crore of bonds with a modified duration of 6:

A 1 basis-point rise in yield costs approximately ₹60,000; a 1 basis-point fall gains approximately the same. This is the practical unit traders and risk desks actually use, because rupee amounts are directly comparable across positions of different sizes in a way that percentage duration alone isn't.

What determines a bond's duration

• Maturity — longer maturity generally means longer duration, since more of the bond's value sits further in the future.
• Coupon size — a higher coupon returns more cash earlier, generally shortening duration relative to an otherwise similar lower-coupon bond.
• Yield level — duration itself shifts somewhat as the discount rate changes, since it's a present-value-weighted calculation.
• Cash-flow structure — amortising bonds, sinking funds, and callable or putable bonds all have duration behaviour that a simple "years to maturity" figure can't capture, which is exactly why effective duration exists as a separate concept for option-embedded bonds.

Duration is an estimate, not a guarantee

Duration of a portfolio, briefly

If you hold three bonds with durations 3, 8, and 12, your portfolio's overall interest-rate sensitivity depends not just on those three numbers but on how much you have invested in each — it's a value-weighted exposure across your holdings, not a simple average of the three durations. This becomes especially relevant once you start thinking in DV01 terms across a portfolio, since DV01 amounts add directly in a way that duration percentages alone don't.

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