Never Mind Yield Curves, What’s Negative Convexity?

As bond yields rise and fall past certain levels, there are episodes of highly technical yet increasingly familiar flows that can accelerate moves in either direction. Analysts and traders use terms like negative convexity and convexity hedging to explain a phenomenon that’s been compared to a “beast” in the market. The result can lead to market distortion that makes it tricky to interpret what bond markets are really saying. What does it all mean, and why does it matter?

1. What’s convexity?

To take on convexity, we need to first grasp what’s known as duration. As interest rates drop, bond prices will rise and vice versa. The extent of the move is typically larger for bonds with a longer time to maturity. That relationship is known as duration. The change in the price and interest rate, or yield, of a bond isn’t linear. If you chart it with prices on one axis and interest rates on the other, you end up with a line showing the curvature in the relationship -- convexity. The higher the convexity, the quicker prices will rise as interest rates fall, and the opposite is true.

Never Mind Yield Curves, What’s Negative Convexity?

2. What’s negative convexity?

Most fixed-income bonds or securities have a positive convexity, which roughly means the price moves in the opposite direction to interest rates. But mortgage-backed securities have negative convexity. Their price tends not to rise as quickly, and can even drop, when Treasury and other market rates go down. That’s because the people holding the underlying mortgages are more likely to prepay and refinance into a lower rate. When that happens, the duration of the securities is shortened.

3. What’s convexity hedging?

Mortgage bonds are often held by large investors such as money managers and banks. They tend to prefer stable returns and constant duration as a means to reduce risk in their portfolios. So when interest rates drop, and mortgage bond duration starts to shorten, the investors will scramble to compensate by adding duration to their holdings, in a phenomenon known as convexity hedging. A hedge is basically investing in something that tends to go up when the first thing goes down (or vice versa). To add duration, so as to extend payments into a longer period, investors could buy U.S. Treasuries, which would further push down yields in the market. Or they could use interest-rate swaps, which are a contract between two parties to exchange one stream of interest payments for another.

4. Anyone else involved?

Asset-liability managers, typically insurance companies and pension funds that have to manage cash flows over time to meet future liabilities. Their ability to do that is affected as interest rates fall, so they have to plug the gap. One popular strategy for these funds is to also enter the swap market, where they would collect fixed rates and pay floating ones. That enables them to boost income without spending a lot of cash, as they would need to do if they just buy Treasuries.

5. What’s the impact?

Convexity hedging can become so large at certain trigger points that it can actually drive the whole Treasury market, meaning moves in yields can become exacerbated as players rush to adjust their portfolios. That was said to be the case in March 2019, when the yield on 10-year Treasuries fell below that offered on the three-month for the first time in over a decade. (This is known as an inverted yield curve, the appearance of which often precedes a recession.) The inversion was fueled by this hedging activity, which pushed swap rates down further and faster than 10-year Treasury yields.

6. Can convexity hedging go in reverse?

Absolutely. A sharp rise in interest rates means fewer homeowners will refinance their mortgages, increasing the average repayment period and in turn extending the duration of the bond. In that scenario, big investors will try to reduce the duration in their portfolios -- perhaps by selling U.S. Treasury bonds or by entering into swap contracts where they pay fixed rates and receive floating ones. Again, this hedging can exacerbate the upward moves in Treasury yields. Major “convexity events” in this direction occurred in 2003 and the so-called bond market massacre of 1994.

7. How has it changed?

While the potential for convexity hedging remains, the anticipated size of the flows has arguably been shrinking in recent years, and that comes down to who owns the mortgage bonds. The U.S. Federal Reserve bought a lot of mortgage-backed securities during its various “quantitative easing” programs and doesn’t do much hedging. JPMorgan Chase & Co. strategists estimate that, if yields were to jump 50 basis points, around 60% of the potential hedging would now fall on those who don’t hedge, including the Fed, foreign holders and money managers. This suggests the chance of another severe convexity event might be lower than previously.

8. So why does convexity matter?

If you care about the U.S. economy then you should care about convexity (really!). The size of convexity flows can drive the acceleration of moves in bonds, and sometimes be responsible for the re-pricing of market expectations. For example, many investors pointed to the inverted yield curve in 2019 as a sign that recession could be looming (the coronavirus pandemic the following year, however, blew up all such forecasts). During periods of volatility, such as the taper tantrum in 2013, market moves become exacerbated by the flows. If yields are being distorted by hedging activity, then the signals that market prices are sending may not be as meaningful as they would be otherwise.

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