How to Profit from the Hidden Optionality in Mortgage-Backed Securities
and some scribbling about convexity, MBS, swaption rates, banking system
Banks that hold mortgage-backed securities (MBS) as assets on their balance sheets are inherently short convexity due to the prepayment options embedded in these assets. In the US residential mortgage market, borrowers have significant flexibility to refinance their loans when interest rates fall in order to secure a lower monthly payment. This ability to prepay existing loans results in accelerated prepayments on the underlying pools of mortgages backing MBS.
MBS provide additional yield compared to similar duration Treasuries precisely because of the prepayment uncertainty inherent in the embedded borrower options. When purchasing an MBS, investors do not know the exact cash flow schedule as borrowers have the discretion to refinance at any time based on market rates.
One way to conceptualize this extra risk is by modeling an MBS as a buy-write strategy on U.S. Treasuries. The investor buys a 10-year Treasury for $100 to gain exposure to the underlying coupon payments. Then they sell a 3-year expiry call option on that Treasury with a strike of $105.
This call models the prepayment risk, as borrowers may refinance before the Treasury's maturity if rates fall sufficiently to make exercising the option profitable. The option sale premium provides extra yield to the buyer in exchange for taking on uncertainty regarding the bond's average life.
It is here where the interplay between interest rates and implied volatility become paramount. The value and risk profile of this synthetic MBS is dictated by these two factors, unlike simple Treasury bonds. Changes in rates and volatility will shift both the option's price and its Greeks like delta (sensitivity to rates) in turbulent, harder to predict ways.
Higher rates decrease the likelihood of refinancing and option exercise, lowering prepayment risk. But higher volatility increases the option's time value as the uncertainty around rates makes exercise more valuable. These dynamic interactions determine the ongoing risk exposures assumed by MBS investors.
Let me explain further.
When rates decline substantially or suddenly, prepayment activity surges as borrowers rush to refinance their loans. The expectation of higher prepayments leads the duration of the MBS assets to shorten more than what typical prepayment models may initially project. This results in the bank becoming short duration, leaving it exposed to further declines in interest rates.
When interest rates rise, it decreases the likelihood that borrowers will refinance their mortgages. Refinancing becomes less economically appealing the higher rates go. From the perspective of the embedded call option modeling prepayment risk, higher rates move the option further out of the money. The current mortgage rate is now higher than the strike price the option holder can refinance at. As rates rise, the intrinsic value of the option declines towards zero. There is less chance the option will be exercised through prepayment of the underlying mortgage. This lowers the overall prepayment risk faced by the MBS investor. However, high interest rate volatility has the opposite effect. Even if rates are high on average, sharp downward spikes make refinancing more valuable as an option. The uncertainty around future rate movements increases the option's time premium. Higher implied volatility raises the option's extrinsic or time value component, independent of its intrinsic value. This makes the prepayment option inherently more valuable from the perspective of the mortgage borrower considering refinancing.
In contrast, Treasuries have fixed cash flows and thus reliable valuation irrespective of rates or volatility. Only price differences due to yield make their duration profiles marginally different. MBS demand this extra complexity premium precisely because borrower behavior injects non-trivial uncertainty absent in riskless government debt. Modeling with options provides valuable insights into how MBS derive their risk-adjusted returns.
Precisely modeling this "prepayment option" is difficult due to its path-dependent, stochastic nature. Prepayment rates are highly non-linear functions of numerous input variables, including loan-to-value ratios, borrower profiles, and macroeconomic factors affecting borrower behavior. Even small changes to these inputs can significantly alter projected prepayment trajectories.
Meanwhile, interest rate movements themselves are inherently unpredictable. Sharp downward spikes in rates fuel outsized "prepayment shocks" as refinancing incentives surge non-linearly. These shocks truncate asset durations far more than standard prepayment models anticipate based on gradual parallel rate shifts.
Hedging this structural short OAS optionality typically involves entering fixed-paying interest rate swaps. However, correctly sizing swaps to offset MBS duration changes proves challenging given option model uncertainty. Misjudging prepayment sensitivity, especially in turbulent markets, can leave sizable hedging gaps on banks' balance sheets.
For this reason, typically banks and investors holding MBS in their portfolios will purchase receiver swaptions. A receiver swaption gives the holder the right but not the obligation to enter into a receive-fixed, pay-floating interest rate swap.
The key is that the swap rates are set on the option expiration date. This mimics the behavior of the embedded mortgage prepayment options.
If rates fall, mortgage borrowers will likely prepay, shortening the cash flows of the MBS. At the same time, the value of the receiver swaption increases, allowing the holder to lock in lower swap rates on exercise.
This offsets the duration loss from prepayments on the MBS side. The swap receiving fixed mitigates reinvestment risk at lower rates from prepaid principal.
By contrast, if rates rise, prepayment activity slows, extending the MBS duration. The swaption decays in value but doesn't need be exercised, avoiding the cost of hedging an unlikely scenario.
Still, the complex interactions between numerous market factors exacerbate hedging difficulties during episodes of acute volatility. For example, the 2013 "taper tantrum" spurred a self-reinforcing prepayment/hedging spiral as rate plunges intensified prepayment activity, shortening MBS durations further and forcing larger swap purchases to hedge residual short positions.
As rates decrease further, prepayment activity ramps up disproportionately more than with a parallel shift up in rates. This negative convexity forces banks to take on additional receiving swaps to hedge the even shorter duration of their assets caused by the spike in prepayments. The heightened demand from banks for receiving swaps in turn puts downward pressure on swap rates as they compete to enter these hedges. The lower swap rates fall, the greater the incentive for prepayments and need for further hedging, creating a self-reinforcing cycle.
As such, even sophisticated option adjustment techniques struggle to capture MBS optionality in highly nonlinear, regime-shifted environments. The challenges of modeling complex embedded options and hedging effectively against their risks are amplified for banks during periods of outsized interest rate turbulence.
Implied volatility and the yield curve shape have an outsized impact on option pricing. Currently, interest rate sits well above historic norms and credit risk levels. An inverted curve also artificially inflates expected prepayment speeds. Mortgage spreads, has a tendency to widen significantly during periods of economic turmoil. While these widening spreads are often seen as a sign of financial distress, I believe they can mostly be accounted for by changes in the expected duration of mortgages due to shifts in the yield curve. Specifically, economic stress typically results in an inverted yield curve where short-term rates are higher than long-term rates. This inversion increases the likelihood of refinancing activity shortening the durations of outstanding mortgages. With shorter durations, mortgage pricing is more impacted by movements in shorter-term Treasury rates rather than longer rates. However, an inverted yield curve means short rates are higher than long rates, so mortgage rates will be unusually elevated relative to the benchmark 10-year Treasury yield.
If implied volatility normalizes and the curve regains a positive slope long-term, prepayment risk premiums embedded in options should compress. This would appreciate newly issued MBS more than collections concentrated in lower coupons built for rapid prepayment.