# Duration and Convexity [Concepts Series]

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Duration is a fundamental financial concept, but it’s more part of the fixed income investor toolkit than the equity investors’. For reasons I’ll get into, duration is usually a misleading concept for equity investors, but there are a few cases where that’s changing.

Duration in bond investing refers to two different measures, which are, conveniently, measured roughly the same way:

- The weighted average time in the future at which a bond pays its returns — i.e. the number of years from now when you’ll realize half of the net present value of the bond, and
- A bond price’s sensitivity to changes in interest rates, all else being equal.

It’s intuitive that these concepts would be related: the longer in the future a given stream of cash flows is, the more sensitive its value is to interest rates.

Here’s a quick table, looking at a bond with a 4% coupon paid every six months:

The important things to pay attention to are the discount rates (at the top) and the PV/Duration numbers at the bottom. The PV number is the present value of the cash flows at a given discount rate; the duration is the weighted average time at which those cash flows are received.

There are some obvious wrinkles to this, however. A somewhat uninteresting one is that bonds with different terms can have different duration profiles: if a borrower has the right to buy back a bond at a fixed price, the bond is insensitive to interest rate changes once it reaches that price (because the company could refinance it at a lower rate).

More interesting, and germane to equity investors: that “all else being equal” line hides some complications. All else is *not* equal: interest rates respond to external variables. Specifically, they tend to be low when the economy is slow, and high when it’s doing well. For a risk-free bond, the economy doesn’t matter, but for risk*y* bonds, default risk is important.

To factor this in, investors look at *effective* duration: how much a bond’s price actually…