Source: Bloomberg
Source: Bloomberg

In my previous post, I argued that bondholders will probably be able to tolerate any "tapering" of the Federal Reserve's asset purchases so long as they aren't using much leverage and are willing to hold to maturity. After all, the Fed has been bidding up financial asset prices to stimulate the economy, and I doubt financial policymakers would consciously choose to inflict substantial losses on savers.

That said, the prices of bonds could get a lot more volatile over the next few years. One possible scenario: the Fed starts tapering its asset purchase program only to observe large increases in interest rates, thereby leading to an increase in stimulus. This sort of start-stop (or slow-down, speed-up) behavior would fit with the pattern we have seen over the past few years with QE1 and QE2.

While all long-dated, fixed-income securities would be affected, mortgage-backed securities could be in for a particularly rough ride because of something known among traders as a "convexity vortex." What follows is my attempt to explain and assess this phenomenon. And, no, it does not figure in the plot of "Star Trek Into Darkness."

Finance blogger Bruce Krasting raised the issue in a recent post, although the reigning expert seems to be Credit Suisse's Harley Bassman. Bassman published a refresher on the subject back in March (sorry, no link, as it was not posted online). Before I get into his main points, it's worth explaining what convexity means in the context of fixed-income trading.

Bonds are promises to pay fixed amounts of cash at certain times. The value of these promises changes depending on expectations of inflation, creditworthiness and the relative attractiveness of other investments (among other things). Those expectations are expressed as a set of interest rates. A given bond becomes less valuable as interest rates rise and more valuable as interest rates fall.

The maturity of the bond and the distribution of its payments determine the extent to which a bond loses or gains value as interest rates change. In other words, rates affect bond prices depending on how long it takes the bondholder to get paid. Roughly speaking, this is the bond's "duration." Bonds with small coupons and large bullet payments at maturity are relatively more sensitive to changes in interest rates (longer duration) than bonds with large coupons and smaller bullet payments (shorter duration).

These properties also affect the extent to which a bond's duration changes with the level of interest rates -- its "convexity." Most fixed-income securities have a positive convexity. In other words, bond prices increase by more than you might expect (if you were relying solely on the bond's duration) when interest rates fall and decrease by less than you might expect when interest rates rise.

This relationship is visualized in the chart below, which shows the price of a hypothetical 30-year bond with a $100 principal and an annual coupon of $5 at different interest rates. The tangent lines show how you could calculate the impact of small changes in interest rates using duration. The gap between the tangent line and the bond's actual price is caused by the bond's positive convexity.

Source: Bloomberg
Source: Bloomberg

Unlike most other types of fixed-income securities, mortgage bonds have negative convexity: Their prices become more sensitive to changes in interest rates as rates rise and less sensitive as rates fall. This is because mortgage borrowers have the option to prepay and refinance basically whenever they want. Borrowers are willing to pay for this option (with marginally higher interest rates) because it makes it much easier to move.

More important for people who trade mortgage-backed securities, the prepayment option also allows borrowers to refinance existing mortgages whenever interest rates fall below what they are currently paying. (Bassman estimates that borrowers won't want to refinance unless they can lower their rate by at least 1.4 percentage points.) Unsurprisingly, borrowers tend not to refinance when rates are rising. Traders try to hedge this negative convexity by short-selling Treasury bonds with an equivalent duration.

According to Bassman, the "convexity vortex" emerges when mortgage rates have been unusually stable for several years. New buyers have all taken out mortgages at the prevailing rate. Those who had borrowed at higher rates in the past (and who are sufficiently creditworthy) are all renegotiating their deals. This refinancing activity would slow down suddenly if rates increased even a little, which in turn could dramatically increase the duration of most mortgage bonds. That could push hedgers to sell a lot more Treasuries, which in turn could push up mortgage rates further and lead to a large sell-off in bonds.

We have some examples of this in recent history. In the summer of 2003 and again the following spring, mortgage rates quickly soared by more than a percentage point, only to fall back to previous levels. Similarly, the prices of long-duration U.S. Treasury bonds slumped during those periods. Fannie Mae and Freddie Mac, which were among the largest active convexity hedgers, were thought to have been responsible for exacerbating what were initially small moves into large sell-offs.

Are we vulnerable to something like this happening again? Bassman is skeptical, noting that "many of the factors that drove previous MBS shocks have been reduced." Most obviously, rates haven't actually been stable for the past few years. Instead, they have been steadily declining.

Others are less sanguine. I personally wouldn't rule out the possibility of some big swings, although I strongly suspect that the Federal Reserve would eventually respond. Investors in highly-leveraged "agency mortgage-backed REITs," on the other hand, might get blown up before that happens. Indeed, the share prices of many of these vehicles have already plunged by nearly 20 percent since the end of April. And there's probably not much the Fed could do to bail them out.

(Matthew C. Klein is a contributor to the Ticker. Follow him on Twitter.)