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If you follow the financial news, you probably know that the Treasury yield curve has gotten extremely flat, with signs pointing to a possibly inverted yield curve in the next few months. And if you pay close attention, you probably know that an inverted yield curve tends to happen before a recession, which is why this is an important issue that’s getting quite a lot of attention. But what exactly is a yield curve, why does an inversion happen, and why is this so important?

First, let’s define our terms. The U.S. Treasury is the Federally issued bonds that the U.S. government offers to creditors, who buy the bonds and get a coupon (or interest payment) on the bonds at fixed intervals. There are also municipal bonds, issued by smaller non-national governments and government-connected agencies, and corporate bonds, issued by companies. All of these types of bonds pay a coupon at different rates, and when we compare the rates between two types of bonds, we’re talking about the spread between bonds.

For instance, if a 2-year corporate bond pays a 4% coupon and the 2-year Treasury pays a 2.4% coupon, the spread is 1.6%. Simple stuff.

But when we compare bonds from the same issuer that have a different duration, we are talking about the yield curve, although the calculation is done the same way. So if the 2-year Treasury pays a 2.4% coupon and the 10-year pays a 2.8% coupon, we say that there is a 40 basis point yield curve. Again, simple math.

Longer bonds almost always pay a bigger coupon than shorter bonds, and this is where the problem hits. When the short-term Treasury pays a bigger coupon than the long-term Treasury, that’s usually the signal of something going wrong in the financial markets. And since many interest rate benchmarks and bonds are connected to Treasury rates, when this happens a lot of companies, who tend to pay off existing bonds by issuing new ones, suddenly see their borrowing costs increase by a large amount. This makes servicing debt difficult if not impossible, causing defaults or cost cutting, ultimately resulting in a recession.

One of the ways to understand this dynamic is to think about something called convexity. This is rarely discussed in the mainstream financial press, which is a shame because it sheds a lot of light on how important the inverted yield curve really is.

Convexity refers to just how much of a relationship there is between bond prices and bond yields. Generally, as interest rates go up, bond yields go up, and that causes bond prices to go down (bond prices are always inverted to yields, just like dividend stocks’ yields go up when their prices go down and vice versa). However, the relationship varies from bond to bond. Some bonds are more sensitive to interest rate increases—i.e., their bond prices will fall further as interest rates rise, and vice versa.

Why do we need to know this? If we are bond traders, knowing convexity is essential for pricing in interest-rate risk into a bond. And if the market fails to do this—which happens a lot, since the bond market is much less efficient and more thinly traded than the stock market—that becomes an opportunity to buy bonds that are undervalued relative to their interest rate risk, and vice versa.

While convexity won’t necessarily measure the likelihood of an inverted yield curve, it does tell us a lot about the likelihood of a decline in bond prices and higher borrowing costs for companies and municipalities if interest rates keep rising. And that is extremely useful information in determining just how much risk there is in a recession coming.