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MBS Negative Convexity (Extension and Contraction Risk)

One-line definition

An MBS's effective duration lengthens when rates rise (extension) and shortens when rates fall (contraction) — the opposite of a normal bond's convexity, which helps in both directions.

Mechanism

When rates fall, refinancing_incentive_cpr rises (more prepayments) — principal comes back faster, capping price appreciation and shortening duration (contraction). When rates rise, prepayments floor at base_cpr — principal comes back on the original schedule plus the pool now runs longer than a bullet bond of the same duration would (extension). Either way, the borrower's option to prepay works against the investor.

What's demonstrable here, and what isn't

Compute weighted_average_life at a rate with an active refinancing incentive versus one without, using refinancing_incentive_cpr to set the prepayment speed at each rate first — WAL genuinely shortens as rates fall and floors (stops shortening further) once rates rise past the pool's coupon. That WAL shift is extension/contraction, and it's a correct, verifiable result of this repo's simple prepayment model.

Full negative convexity in price terms is not demonstrated here. Naively discounting the prepayment-adjusted cash flows at a flat market rate does not reproduce it — that approach doesn't capture the actual mechanism (principal is returned at par, capping upside versus what an equivalent option-free bond would be worth at that rate), which requires comparing against an option-free benchmark under a proper term-structure model. That's exactly the OAS machinery this repo doesn't build — see OAS.

Why PMs care

A portfolio that looks duration-neutral against cash bonds can still be short convexity if it holds MBS — it will underperform in both a big rally (price capped) and a big selloff (duration extends right when you don't want it to) relative to a position with normal convexity.

Limitations

The refinancing_incentive_cpr model correctly signs the WAL/extension effect but is not sophisticated enough to correctly price the option cost — don't use it to argue about MBS price behavior, only cash-flow timing behavior.