Duration

Chapter 3 said bond prices fall when rates rise. The obvious next question is how far, and duration is the answer.

The rule of thumb

Modified duration is a number of years, and it is used like this:

price change ≈ − duration × change in yield

A bond with a duration of 6 facing a 1 percentage point rise in yields falls about 6%. A duration of 2 falls about 2%. If yields fall 1% instead, the same bonds rise by roughly the same amounts.

That is the whole working rule, and it is enough for almost every decision an individual makes.

Why it is not just maturity

A 10-year bond does not have a duration of 10, and the reason is worth understanding.

Duration is roughly the average time until you get your money, weighted by how much arrives when. A 10-year bond paying coupons hands you cash twice a year all the way through. Those early payments arrive long before year ten and pull the average in.

So a 10-year bond with a healthy coupon might have a duration around 7. Three things follow.

A higher coupon means lower duration. More of your money comes back early, so the bond is less sensitive. Of two 10-year bonds, the one paying 9% moves less than the one paying 5%.

A zero coupon bond's duration equals its maturity. Nothing arrives until the end, so there is nothing to pull the average in. T-bills, from chapter 2, are zero coupon — but they are so short that their duration is tiny anyway.

Longer maturity means higher duration, strongly. This is the big one, and it is why a 30-year government bond with no credit risk at all can fall further in a year than many equities. "No credit risk" and "no risk" are different statements, and duration is the gap between them.

Reading it on a debt fund

Every debt fund publishes its portfolio's modified duration, usually on the monthly factsheet of chapter 7 of the mutual funds subject. It is the single most useful number there, and it converts directly into the question you care about:

If rates rise 1%, this fund falls about [duration]%.

That gives you a sense of the downside before you buy, which almost no other number in fixed income does so cleanly.

It also explains the categories. A liquid or overnight fund holds very short paper, so its duration is near zero and its NAV barely moves whatever rates do. A gilt fund or a long duration fund can carry a duration of 7 or more, and its NAV moves accordingly — in both directions.

So when SEBI's material notes that debt NAVs rise in the short run when interest rates fall "and vice versa", duration is how much.

Matching duration to your horizon

The practical use, and it is more useful than forecasting rates.

If you need the money in a year, a fund with a duration of 7 can be down 7% exactly when you need it. That is not a bad fund; it is the wrong fund for that money.

If you need the money in seven years, a duration of 7 is close to a hedge. Rates rise, the price falls, and the coupons now reinvest at better rates — and over roughly the duration those two effects offset. This is not a coincidence: it is the reason duration is defined the way it is.

The discipline is therefore the same as chapter 8 of the mutual funds subject: decide the horizon first, then pick duration to match it. Choosing duration by which fund returned most last year gets it backwards, because last year's winner is usually whatever had the most duration while rates happened to fall.

Where the rule of thumb breaks

Two limits, both worth knowing and neither fatal.

Large moves. The relationship is slightly curved, so for a big rate move duration overstates the fall and understates the rise. The curvature is called convexity and it works mildly in your favour. For moves of a percentage point or so, ignore it.

Credit. Duration measures sensitivity to interest rates only. A bond can fall because its issuer deteriorated, and duration has nothing to say about that. Chapter 7.

The point

Duration converts a change in rates into a change in price: roughly minus duration times the change in yield. Coupons pull it below maturity, and long bonds carry a lot of it — which is how a government bond with no credit risk falls hard. Match it to when you need the money.