It has been a long time since we have had to worry about and think about the phenomenon of mortgage convexity and the effect that it can have on the bond market. But with 10-year interest rates up 50bps in less than 1 month, and some of the sell-off recently being attributed to "convexity-related selling," it is worth reminiscing.
We need to start with the concept of "negative convexity." This is a fancy way of saying that a market position gets shorter (or less long) when the market is going up, and longer (or less short) when the market is going down. That's obviously a bad thing: you would prefer to be longer when the market is going up and less long when the market is going down (and, not surprisingly, we call that positive convexity).
Now, a portfolio of current-coupon residential mortgages in the U.S. exhibits the property of negative convexity because the homeowner has the right to pre-pay the mortgage at any time, and for any reason - for example, because the home is being sold, or because the homeowner wants to refinance at a lower rate. Indeed, holders of mortgage-backed securities expect that in any collection of mortgages, a certain number of them will pre-pay for non-economic reasons (such as the house being sold) and the rest will be pre-paid when economic circumstances permit. Suppose that in a pool of mortgages, the average mortgage is expected to be paid off in (just to make up a number, not intended to be an accurate or current figure) ten years. This means that the security backed by those mortgages (MBS for short) would have a duration of about ten years, so that a 1% decline in interest rates would, in the absence of convexity, cause prices to rise about 10%. (I am abstracting from the niceties of Macaulay versus modified versus option-adjusted duration here for the purposes of exposition.)
