Buying bonds? Beware the convexity risk

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The bond buyer's friend is poised to become an enemy in a bear market.

For the past few years, as bonds have rallied on all fronts, buyers have had an extra push helping their returns. But when bonds turn around, the push will go the other way and weigh on bond values heavily in the first stretch of a bear market.

The force at play is known as convexity, and it has aided investors for years. But it could easily bite buyers of the current crop of bonds with their low coupons, so it pays to be wary.

In as much of a nutshell as is possible with bond math, convexity is a term for the shape of the curve representing the relationship between a bond's price and its yield. Yields rise when prices fall, and vice versa. But the relationship is not linear; on a graph it will look like a curve. Think of the cross section of a satellite dish that's pointed up above the horizon.

A video explainer can be viewed here

For most bonds, the shape of the curve means that as yields approach zero, price gains accelerate. That's been helping investors who are buying bonds of late, as declining yields that are getting close to zero on many issues have resulted in nice gain in the value of bonds, adding a little extra juice to returns in the form of capital gains.

The reverse is true when yields that are close to zero begin to rise. Price declines in bonds that exhibit convexity will be steeper when the bond yield is moving from, say, 1 per cent to 2 per cent than when the yield is going from 8 per cent to 9 per cent.

To be sure, convexity is not a fast-moving process, but it will explain why the prices of bonds in a portfolio are now moving more than it appears they should to the naked eye. Since it's working in investors' favour though, odds are many folks are not spending much time thinking about it.

Why is convexity a particular worry now? It's not only that yields are lower on most bonds than they have ever been, leaving them in the steepest part of the curve.

The issue is exacerbated by the kinds of bonds that are now on sale.

Generally speaking, the closer the coupon rate on a bond is to zero, the more convexity a bond will exhibit. And which way have coupons been going? Closer and closer to zero. Late last year, the Government of Canada auctioned a five year bond with a 1.25 per cent coupon and a 10-year bond with a 1.5 per cent coupon. Corporate bonds are similarly issued with ever smaller coupons.

In other words, pretty much all the new issue product out there in the bond market is coming out with more and more inherent convexity. The potential for steeper than expected capital losses in the early stages of a move higher in yields is built into the bonds that people are now buying.

Bond pros are well aware of convexity, but as bonds and bond-based products like exchange traded funds have become more and more popular with investors in general, the bear-market effects of convexity could well sneak up on some people who are less steeped in the math behind bonds.

And that could lead to some unpleasant surprises.

(Boyd Erman is a Globe and Mail Capital Markets Reporter & Streetwise Columnist.)

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