MBS Relative Performance and Bond Duration - An Intro
MBS went through an interesting Employment Friday. I know it’s hard to remember back after a long weekend (especially for N.E. fans), but the bond market sold off pretty substantially on Friday after a better-than-expected employment report. The interesting aspect of the selloff was how it was focused on intermediate- and long-maturity Treasuries. While the yield on the 2-year barely budged, the 5-year yield rose 6 basis points on the day, and the yield on the 10-year was more than 10 bps over the previous day’s close.
This type of move impacts MBS investors, since they always want to see how MBS are performing versus some benchmark. One way to measure "relative performance" is to compare the price change for a security versus what it should have done, based on its duration relative to that of the benchmark. An easy way to calculate the projected price change for a security is to multiply the price change of the benchmark by a security’s “hedge ratio,” which is the duration of the subject security as a percentage of the benchmark’s duration. An easy example now is that 30-year Fannie 3.5s had, after Friday’s move, a duration of 4.0; using a duration for the 10-year of 8.9 results in a hedge ratio for Fannie 3.5s of around 45%. Therefore, if the 10-year note declined by a full point, Fannie 3.5s should have dropped by roughly 15/32s. (This is sometimes also referred to as “duration-neutral performance.”
There are a few challenges implicit in this discussion. One is that the relative performance (i.e., the price change of a security adjusted for hedge ratios) is going to vary if you have a significant shift in the yield curve, such as what we had on Friday. That’s why most MBS underperformed the 5-year Treasury while tracking the performance of the 10-year. (By my measure, Fannie 3.5s underperformed the 5-year by 5/32s while performing roughly in line with the 10-year.) Some people will attempt to measure performance using a different benchmark, such as the 7-year Treasury. However, the 7-year is not nearly as liquid as 5s or 10s, making it less useful as a “benchmark.” It’s also possible to measure performance versus a blend of the 5- and 10-year Treasuries, although this just splits the difference between the two Treasury securities.
The other qualifier is that there is no single “duration” for MBS, mainly because of prepayments. The subject of duration can be fairly complex; without getting highly technical, I think it will be helpful to briefly address the issue. Keep in mind that “duration” itself is simply the measure of the expected percentage change in price, given some standard change in the subject security’s yield.
The duration of a fixed-maturity bond is easy to calculate, since the cash flows are fixed. The durations quoted are “modified durations,” which are essentially calculated as the amount of time the present value of a cash flow is outstanding. (The basic calculation is call “Macauley duration, and it’s quite similar in concept to “weighted average life,” or the amount of time a bond’s principal is outstanding.) With a few adjustments or “modifications,” the modified duration gives the price sensitivity of a bond for small moves in interest rates.
However, MBS durations can be calculated in a variety of ways. The duration of 4.0 for Fannie 3.5s quoted above is based on the calculations of an OAS model (YieldBook , in this case, which is owned and marketed by Citigroup). The durations from an OAS model are, fittingly enough, call “OAS durations.” OAS durations (or OADs) are complex to calculate, but relatively simple in concept. The models calculate prices for a move up and down in interest rates, and the prices in the two scenarios are then used to calculate the duration.
There is also a simpler measure in MBS called “cash flow durations,” which are simply the modified durations for securities using some prepayment assumption. (The cash flow is generated using a prepayment assumption; the modified duration is then calculated for the cash flows.) Cash flow durations are often used by investors, particularly for MBS pools and fairly straightforward securities. A separate category of durations are calculated using historical price changes for the subject security relative to yield changes for a benchmark. An analysis could “regress” the daily percentage price change of Fannie 3.5s versus the daily yield change of the 10-year Treasury. The slope of this regression line is the “empirical duration.” I don’t like to use empirical durations (“empiricals”) directly as a hedging tool, since they’re backward-looking. (I think of them like trying to drive down the highway using your rear-view mirror; as long as the road doesn’t curve, you’ll be okay. But it always does, eventually.)
However, empirical durations are useful in describing MBS performance. For example, if the empirical duration for an MBS is longer than its OAD, the security is said to be “trading long.” This is a good thing for bondholders if bond prices are rising, but hurts performance when bond prices are soft and Treasury rates are rising. It’s best to think of all forms of duration as tools that allow you to calculate expected performance and measure portfolio risk.