Negative Convexity and MBS Hedging

Hand a homeowner a 30-year mortgage and you have also handed them a free option: the right to refinance whenever rates drop, paying off the old loan and taking out a cheaper new one. The bank — and whoever ends up owning that mortgage bundled into a security — is short that option. Every mortgage-backed security (MBS) investor is, without asking for it, short a pile of embedded call options on interest rates.

A regular bond behaves like a rubber band: stretch it (rates fall) and its price rises more and more for each further rate drop — that curving-up shape is ordinary, "positive," convexity. An MBS behaves more like a rubber band tied to a rock: it stretches normally at first, but once rates fall far enough, homeowners refinance en masse, the mortgage pool gets paid off early, and the bond's price gets pulled back down toward par just as it should be rallying hardest. That inverted curve — price gains that shrink, then reverse, as rates keep falling — is negative convexity.

Why it happens: the prepayment option

A pass-through MBS's price can be decomposed conceptually as:

$$P_{\text{MBS}} = P_{\text{option-free bond}} - V_{\text{prepayment option}}$$

Here $P_{\text{option-free bond}}$ is what the cash flows would be worth if homeowners never prepaid early, and $V_{\text{prepayment option}}$ is the value of the refinancing option homeowners hold, which the investor has implicitly sold them. In words: the MBS is worth less than a plain bond with the same coupon, because the investor has given away an option, and that option's value grows precisely when rates fall — eating into the price gain the investor would otherwise get.

Worked example: price compression near the coupon

A 6 percent-coupon MBS pool is priced near par, $100, with mortgage rates in the market at 6.2 percent. Rates fall 100 basis points to 5.2 percent.

An option-free bond with similar cash flows might rally to $107 on that move, using standard duration of about 5.5 years. But at 5.2 percent, refinancing into a cheaper loan is attractive for most of the pool, so expected prepayment speeds jump — the effective average life of the security shortens sharply, cash comes back at par sooner than priced in, and the MBS instead rallies only to about $102. The 500-basis-point difference from the option-free comparison is the cost of the prepayment option the investor is short.

Worked example: hedging goes wrong

A portfolio manager hedges $100 million of this MBS pool by shorting Treasury futures sized to the pool's current effective duration of 4.5 years. Rates then fall 150 basis points. The Treasury short loses money as expected — but the MBS's own duration has also fallen as prepayments accelerated, so the hedge, sized for the old duration, is now too large relative to the MBS's reduced rate sensitivity. The manager is over-hedged and the position that was meant to be rate-neutral now loses money on rallies. This is why MBS desks re-hedge dynamically and rely on effective duration, recomputed as rates move, rather than the static duration used for option-free bonds.

What this means in practice

Because both duration and convexity of an MBS change with the rate level, hedgers cannot set a static hedge ratio and walk away — they must rebalance as rates move, and buy convexity elsewhere (via swaptions or Treasury options) to offset what the mortgage pool is short. This dynamic hedging demand from MBS investors is itself a major driver of implied volatility in the interest-rate options market.

Key terms

• Prepayment option — the homeowner's right to refinance early, effectively a call option the MBS investor is short.
• Negative convexity — a price-yield curve that bends against the investor: capped gains on rallies, amplified losses on sell-offs.
• Effective duration — duration recomputed to account for how prepayment speeds themselves change with rates.
• Average life — the expected time to receive principal back, which shortens as rates fall and prepayments speed up.