Convexity relates to the interaction between a bond's price and its yield as it experiences changes in interest rates. In general, the higher the coupon, the lower the convexity, because a 1% bond is more sensitive to interest rate changes than a 10% bond.
- When the level of interest rates is 1% and rates increases by 1%, a bond with a 1% coupon would be 50% below the current rate of 2%.
- When the level of interest rates is 10% and rates increase by 1%, a 10% coupon would only trail the 11% interest rate level by 10%.
Therefore, a high convexity bond's principal value is more sensitive to changes in interest rates and should consequently witness larger fluctuations in principal price when interest rates move to compensate for the difference between their current coupon and the higher level of interest rates.
If we think about the current level of interest rates, we are in a period of historic lows brought on in many ways by the Federal Reserve Bank purchases of massive amounts of notes and bonds (or now ETFs) to provide market liquidity and to keep interest rates low.
Think about the last 10 years. In early 2010, just after the 'Great Recession' where the Fed used 'quantitative easing' to drive rates down, the 10yr note was @ 3.5% so new 10 yr notes were issued with a 3.5% coupon today the 10yr note is around .7% so if new notes are issued with a .7% coupon they are far more convex than 2010. Furthermore, if US Treasury 10yr note interest over the long term is supposed to represent a return over inflation and inflation is 1.5% then the real return you are receiving currently is negative. Assuming markets are going to be ‘normal’ at some point and the 'historic premium' for the 10year note over the rate of inflation 1.5% the 10yr note would have to have a total return of 3% TODAY (coupon interest plus price discount) just at the current levels – which it doesn’t.
Now, consider that demand for goods has continued even while production globally has dropped and that there are kinks in the supply and transportation chain for raw materials and finished goods – that means a very likely increase in inflation. If inflation rises to 3% and we expect a premium of 1.5% over inflation, 10yr notes would have to return 4.5% annually – and with a .7% coupon (or higher coupon issued at a premium) the bonds would have to be discounted by 3.8% annually, and using a 5yr holding period that could mean a price discount of almost 20%. If the market were left to its own devices, there would be a massive rush to sell rather than realize a 20% capital loss on your notes/bonds.*
The Fed in its effort to fight Covid, 'the economic event', is saying that the Fed will let inflation run higher than normal for a period of time and that the Fed expects to maintain an extremely low level of interest rates for the next 3-5 years. It could be that what they are really telling the market is they are going to be a buyer, or even 'the buyer', for at least that period so you don’t need to dump your bonds if inflation picks up because they won’t let the rates increase.
In the early 1950s there was a similar problem and the Fed guaranteed the capital value of US Treasuries for banks holding them as regulatory capital and it worked. But, that was a very different market and average individuals were not nearly as involved in the purchase of bonds, through 401Ks, mutual funds, and ETFs. The loss of purchasing power due to inflation versus the interest payments at these current levels might not be palatable if inflation rises.
Will the Fed be able to make it work? Maybe, they have so far, but if they lose credibility or the market decides the Fed doesn’t matter and real return does, maybe not. Are bonds a good investment? US Treasuries are probably not if you want a return over the rate of inflation or believe inflation is going to rise and you are working on a ‘real return’ basis. The Fed will likely be able to 'manage' the problem for some time, but if inflation really increases, their purchases could just create an even bigger convexity problem.
*This is a very simplified example used for the purpose of explanation, while it is not mathematically correct, it is close enough to make the point.