Bond Duration Explained: Why Long G-Secs Swing More When Yields Move

Every time the RBI hints at a rate move, some bond funds barely flinch and others swing hard. The reason fits in one word. With bond duration explained properly, you can look at any government security, corporate bond or debt fund and roughly estimate how much its price will move when yields change, before the market does it for you.

This guide sticks to the mechanics. We’ll use the RBI’s own definitions, rebuild its worked example, and then run three hypothetical G-Sec style bonds through the same maths so you can see why the long ones feel so much more nervous.

First, the seesaw: prices and yields move in opposite directions

A bond pays fixed coupons. If market yields rise after you buy, new bonds pay more than yours, so the only way your bond finds a buyer is at a lower price. If yields fall, your older, higher coupon looks attractive and the price goes up. Investopedia’s duration explainer puts it simply: bond prices generally have an inverse relationship with interest rates.

That much most investors know. The useful question is how much the price moves. Duration answers that.

What duration actually measures

The RBI’s FAQ on government securities defines duration, also called Macaulay duration, as a measure of the time taken to recover the initial investment in present value terms. Think of it as the payback period of a bond, expressed in years, where each coupon is weighted by when it arrives and what it’s worth today.

Two things follow from that definition, and the RBI spells both out:

• Duration is always less than or equal to the bond’s remaining life. Only a zero coupon bond has a duration equal to its maturity, because it pays everything at the end.
• Keeping maturity the same, a higher coupon means a shorter duration. You get more of your money back earlier, so the weighted payback point moves closer.

It’s easy to confuse duration with maturity. They’re different. Maturity is just the date the principal comes back and it doesn’t care about interest rates. Duration shifts as yields change and shrinks as the bond ages.

How the RBI calculates it, step by step

The RBI’s method, for a bond paying coupons every six months, goes like this:

1. Discount each future cash flow to its present value. With half-yearly coupons, one period is six months, so a two-year bond has four periods.
2. Multiply each present value by its period number: the first coupon by 1, the second by 2, and so on.
3. Add up those weighted values and divide by the bond’s current price (the sum of the present values from step 1). That gives duration in periods. Divide by two to get years.

The RBI’s own illustration uses a two-year bond with a 10% coupon when the two-year yield is 9%. The cash flows are ₹5, ₹5, ₹5 and ₹105. Their present values add up to a price of ₹101.79, the weighted values add up to 379.28, and 379.28 divided by 101.79 gives 3.73 periods, or 1.86 years. We reran the numbers and got the same result.

Modified duration: turning years into a price change

Macaulay duration is a time measure. Traders want a price measure, so they use modified duration. The RBI describes it as the change in value of the security for a one per cent change in yield, and shows the calculation for its example: 1.86 divided by (1 + 0.09/2) gives 1.78.

In plain terms, a modified duration of 1.78 means the bond’s price should fall roughly 1.78% if yields rise by one percentage point, and rise roughly 1.78% if they fall by the same amount. The RBI gives another example in the same FAQ: a 15-year bond with a duration of 7 years would fall roughly 7% in value if interest rates rose by 1% per annum.

The shortcut formula is worth remembering:

Approximate % price change = − Modified duration × change in yield (in percentage points)

Maturity tells you when your money comes back. Duration tells you how much your price will hurt before it does.

PV01: the same idea in rupees

There’s a rupee version of the same idea, called PV01: the change in a bond’s price for a one basis point move in yield. The RBI notes it’s often used as a price alternative to duration. One basis point is one hundredth of a percentage point, so 100 basis points make 1%.

The RBI works it through for its example. A modified duration of 1.78 on a price of ₹101.79 means about ₹1.81 of price change for a 100 basis point move, so PV01 is ₹0.018, roughly 1.8 paise. If the yield moves from 9% to 9.05%, five basis points, the price drops from ₹101.79 to about ₹101.70, a fall of 9 paise.

PV01 is handy because it scales. A treasury holding ₹100 crore face value of a bond with PV01 of 1.8 paise per ₹100 knows almost immediately what a 10 basis point surprise costs it.

Worked example: three bonds, one rate shock

Now the part that explains the headline. Take three hypothetical bonds, each with a 7% coupon paid half-yearly and each priced at par (₹100) because the market yield is also 7%. The only difference is maturity: 2 years, 10 years and 30 years. We calculated each one using the RBI’s method above.

Notice the 30-year bond’s duration is nowhere near 30. Coupons arrive every six months for decades, and each one pulls the weighted payback point earlier. Still, its duration is almost seven times that of the 2-year bond.

Now push yields from 7% to 8%, a full 100 basis point jump, and reprice each bond exactly:

Same shock, very different pain. An investor in the 2-year paper loses less than two rupees per ₹100. The 30-year holder loses more than eleven. That’s why long-dated G-Secs, and the gilt funds that hold them, swing so much more around policy meetings.

Run it the other way, yields falling from 7% to 6%, and the 2-year bond rises 1.86% while the 30-year bond gains 13.84%. Long duration is a double-edged tool. It’s exactly what you want when you expect rates to fall, which is why Investopedia notes that a long-duration strategy tends to work when rates are falling.

Why the estimate drifts: convexity

Look again at the second table. The duration estimate overstates the loss every time, and the gap grows with maturity. For the 30-year bond it’s more than a full percentage point off.

That gap is convexity. The RBI’s FAQ explains that duration-based price changes work only for small yield moves, because the price-yield relationship isn’t a straight line. For a plain bond without options, the actual fall when yields rise is smaller than duration predicts, and the actual gain when yields fall is bigger.

For small moves, duration is close enough. Try a 25 basis point rise, a quarter of a percentage point. Our 10-year bond actually falls 1.76% against a duration estimate of 1.78%. The 30-year bond falls 3.04% against an estimate of 3.12%. Close, but you can already see the long bond drifting.

Coupon matters too, just less than maturity

Keep the 10-year maturity and the 7% market yield, but change the coupon:

• A 5% coupon bond would trade around ₹85.79, with a modified duration of about 7.53.
• A 9% coupon bond would trade around ₹114.21, with a modified duration of about 6.79.

The higher coupon returns more cash earlier, so its duration is shorter, just as the RBI says. And a 10-year zero coupon bond at a 7% yield has a Macaulay duration of exactly 10 years and a modified duration of about 9.66, the most sensitive of the lot for that maturity.

If two bonds have the same maturity, the one that pays you less along the way will move more when rates change.

Using duration as an Indian investor

You don’t need to compute any of this by hand every time, but knowing what the number means changes how you read a bond or a debt fund. A few ways we’d use it:

• Size your rate risk. Investopedia’s rule of thumb is that a bond or bond fund with a five-year average duration would likely lose about 5% of its value if rates rose 1%. If that would keep you up at night, it’s too long for you.
• Match duration to your holding period. Money you need in a year has no business sitting in long-duration paper. Short-dated instruments like treasury bills carry far less price risk.
• Read the curve before you go long. Duration bets are bets on where yields go next. Understanding the shape of the curve, including what an inverted yield curve signals, helps you judge whether a long bond is being priced for cuts that may not come.
• Remember a portfolio’s duration is roughly a weighted average. Put 40% in our 2-year bond and 60% in our 10-year bond, and the mix has a modified duration of about 5.0.

A quick checklist

1. Longer maturity means higher duration and more price swing.
2. Higher coupon means lower duration, for the same maturity.
3. Modified duration times the yield change gives an approximate percentage price change, with the opposite sign.
4. PV01 turns that into rupees per basis point.
5. For big moves, convexity means the real loss is a bit smaller and the real gain a bit bigger than duration suggests.

The bottom line is simple. When someone says a bond is “long”, ask for its duration, not its maturity. That one number tells you how hard the next rate surprise will hit.

Disclaimer: This article is for educational purposes only and is not investment advice. The 2-year, 10-year and 30-year bonds and all their prices and durations are hypothetical illustrations. Please consult a SEBI-registered investment adviser before making investment decisions.