By the Numbers
Comparing convexity in the BAM and Yield Book models
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MBS entered uncharted prepayment territory over the last year and a half as mortgage rates increased to levels last seen in the early 2000s while many outstanding loans had historically low coupons. This has put prepayment models to the test. Assumptions are often guiding forecasts more than past data, and there is a greater divergence between models than usual. Bloomberg’s Agency Prepayment Model (BAM), for example, shows many MBS trading below par to have positive convexity while Yield Book’s model on those same securities shows negative convexity. Yield Book’s model appears to fit recent speeds more accurately than Bloomberg’s, but, perhaps surprisingly, Bloomberg’s model is too slow on most cohorts.
Bloomberg’s model has similar convexities to Yield Book’s model at higher coupons but adds convexity more quickly at lower coupons (Exhibit 1). The left-hand chart plots the option-adjusted convexities (OAC) for various coupons of the 2023 vintage, for both BAM and Yield Book’s version 23.1 prepayment model. MBS typically have negative convexities, which means that the price falls more when rates increase than the price goes up when rates decrease. A positive convexity indicates the opposite—that the price upside is greater than the price downside. The two models appear similar for coupons above 5.5% but diverge at lower coupons. Both models add convexity as the coupon falls, putting the cohort further out-of-the-money. But Bloomberg’s model adds convexity more quickly and turns slightly positive in the 4% coupon, while Yield Book’s is still negative.
Exhibit 1. Bloomberg’s model adds more convexity than Yield Book at lower coupons.
Source: Bloomberg, Yield Book, Santander US Capital Markets
The right-hand side repeats the exercise for the 2020 vintage. This vintage has a variety of coupons available in respectable size but all at deep discounts to par. Mortgage rates were very low throughout most of 2020. Bloomberg’s model has positive convexity on each of these coupons, but Yield Book’s model does not turn positive until the 2.5% coupon.
Comparing model speeds to actual speeds over the last year shows that Bloomberg’s model has been consistently slow (Exhibit 2). The chart shows speeds for cohorts with coupon 3.5% and below and outstanding balance of at least $10 billion. Yield Book’s model has tracked actual speeds more closely than Bloomberg’s, although also was biased a little slower than actuals. It is somewhat surprising that Bloomberg’s model was too slow—one explanation for Bloomberg’s positive convexity would be that Bloomberg maintains a higher floor on prepayment speeds, but this data suggests that is not the case.
Exhibit 2. Bloomberg’s and Yield Book’s models tended to underpredict discount speeds.
Historical prepayment speeds from October 2022 through September 2023 for conventional 30-year TBA-eligible pools.
Source: Bloomberg, Yield Book, Santander US Capital Markets
Plotting the difference between the models’ speeds and actual speeds helps show the pattern (Exhibit 3). Both models tended to track speeds on seasoned cohorts relatively well. In some seasoned vintages, like 2012 and 2015, Bloomberg’s model was more accurate than Yield Book’s. But Yield Book’s was more accurate in 2019 and newer vintages, while Bloomberg’s was much slower than actuals for most cohorts. However, Bloomberg’s error gets smaller at lower coupons, and is very close to actual speeds in the 2020 and 2021 1.5% cohorts.
Exhibit 3. Model difference vs. actual speeds.
Historical prepayment speeds from October 2022 through September 2023 for conventional 30-year TBA-eligible pools.
Source: Bloomberg, Yield Book, Santander US Capital Markets
This data suggest that Bloomberg’s model probably slows turnover too quickly for pools slightly below par, which leaves lower coupons less rate sensitive than they should be. This boosts the convexity, and OASs, on those coupons. The implication, however, is not that the model is too fast, but that it is too slow. It needs faster speeds for coupons closer to par, which would allow for a stronger lock-in effect that extends to lower coupons, lowering convexity.
On the other hand, Yield Book’s errors tend to be larger in the 1.5% coupon than other coupons of the same vintages. And Yield Book is slowing down more than actuals. This suggests that Yield Book’s lock-in may be a little too strong, and it is slowing down too much. Softening the lock-in effect would lift Yield Book’s convexities. Maybe the truth is somewhere in between the two models.
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