How Prepayment Sensitivity Shapes Mortgage-Backed Security Convexity
Summary
The document explains how mortgage-backed security convexity depends on the sensitivity of prepayments to interest-rate incentives. In a typical pass-through, falling rates tend to accelerate prepayments and shorten duration, limiting price gains; rising rates tend to slow prepayments and extend duration, worsening price declines. This embedded borrower response usually creates negative convexity.
The key framework is the prepayment S-curve. Securities near its steep elbow have the greatest rate sensitivity and thus the strongest negative convexity. Deep-discount and ultra-premium securities near the curve’s flatter ends may have less negative or even positive convexity because rate changes have less effect on prepayments. The exact result depends on the curve and on the security’s cash-flow profile. The answer also notes that separating principal into a principal-only bond can create positively convex cash flows, while the interest-only component is typically strongly negatively convex. These are qualitative explanations, not measured examples or a universal prediction for every MBS.
Key ideas
- Mortgage borrower prepayments usually give pass-through securities negative convexity.
- Falling rates can speed prepayments and shorten duration, while rising rates can slow them and extend duration.
- Prepayment sensitivity is greatest near the steep elbow of the S-curve.
- Deep discounts and ultra premiums can have less negative or positive convexity where the curve is flatter.
- Separating principal and interest cash flows can create a positively convex PO and a negatively convex IO.
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# What are the causes of positive convexity in the mortgage market? # What are the causes of positive convexity in the mortgage market? In general, mortgage assets are negatively convex. However, I've seen cases of positive convexity and have never seen an adequate explanation for why this might be the case. I suspect it has something to do with where the portfolio sits on the S-Curve (maybe a highly burned out portfolio). My other hypothesis is a problematic forward primary rate/current coupon model. ## Answer by Sharad (score 1) https://quant.stackexchange.com/a/66695 Your intuition about positive convexity being related to where an MBS bond sits on the S-curve (i.e., the relationship between its prepayment rates and rate incentive) is correct. Negative convexity in an MBS results from adverse exposure to prepayments. A typical pass-through cashflow extends in duration when rates sell off (prepayments slow) magnifying price decreases, and shortens when rates rally (prepayments increase) dampening price increases. [We can define the convexity of a bond as the percentage increase in price when rates decline less the percentage decrease when rates increase (by the same amount).] The most negatively convex pass-throughs are parked at the "elbow" of the S-curve where prepayment rates are most sensitive to a change in rates. By extension then, the least negatively convex/most positively convex pass-throughs correspond to deep discounts and ultra premiums (the left and right asymptotes of the S-curve respectively) where changes in rate incentive have little to no impact on prepayments. Exactly where this happens will of course depend on the precise shape of the S-curve. The above analysis is sensitive to the cashflow profile of the MBS in question. For example, we can synthetically create positively convex MBS cash flows by stripping out the principal portion of a pass-through cash flow into a principal-only (PO) bond. [The interest cash flows in this context are typically funneled into a very negatively convex bond known as an IO (interest-only)].
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