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.
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$\begingroup$ Your suggestion about burnout is certainly correct. A completely burnt out mortgage is like a regular bond , thus has positive convexity. $\endgroup$– dm63Commented Aug 30, 2021 at 1:48
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1$\begingroup$ The classic Salomon Smith Barney Guide to Mortgage-Backed and Asset-Backed Securities, edited by Lakhbir Hayre, Wiley (2001) chapter 4 "Anatomy of Prepayments" - has a discussion of burnout and related phenomena that I found very enlightening $\endgroup$– Dimitri VulisCommented Aug 30, 2021 at 2:01
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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)].
