Interpreting MBS OAS and Building a Model-Based Hedge

# Extracting the OAS out of an MBS?


# Extracting the OAS out of an MBS?












I was reading about OAS and I'm wonder how one could "extract" (or "capture") the OAS out of a product by hedging out all the other risks.

One of the explanations I got from OAS from a book was this: "Essentially a positive OAS implies that once hedged against the forward LIBOR rates, a security will have positive returns".

This seems to jive with an explanation given by a member here: Interpretation of OAS on MBS

My question is, how does one actually go about hedging? Assume we live in a perfect model world, and I own an MBS product with 100 OAS. Which instruments would I use to hedge my product in order to try and extract that 100 basis points of OAS on average?

When calculating OAS, all the equations I've seen use the 1 period forward rate to discount paths forward, so would you hedge with the 1 period discount rate? In other words, at the start of each month would you sell short a 1 month libor contract?

## Answer by Sharad (score 1)

https://quant.stackexchange.com/a/63150

"Essentially a positive OAS implies that once hedged against the forward LIBOR rates, a security will have positive returns": I don't believe this statement is correct. Essentially, the OAS is a statement about expected excess returns (after hedging out duration and volatility risk as described in the comments above) and says little to nothing about what return can be realized on any one realized path of interest rates.

Reviewing the construction of OAS: we generate a number of interest rate paths using a term structure model, project cash flows for the relevant bond along each of these paths, present value these cash flows using discount factors extracted from the underlying yield curve plus a spread to get a price for each path, and then average all these prices to see if we match the market price. If not, we iterate again until we find the spread that achieves a match.

Now, if we pick a path for which the price (after discounting with the OAS) is below the market price and it somehow happens that rates (and volatility) evolve exactly along this path then in fact we're guaranteed an excess return less than predicted by the OAS.

Added (April 10th, 2021)

While I think my critique above of being able to extract the OAS is spiritually correct, it wasn't completely satisfying and here's an attempt to make it more rigorous. We'll follow Tuckman's Fixed Income Securities (3rd edition, pp. 222-224). Denote the market price of the security at time $t$ by $P_t(x, OAS)$, where $x$ is a risk-factor (say, interest rates). Then, under the assumption of risk neutrality we have ($r$ is a short-term rate):

\begin{align} E[\frac{dP}{P}] &= (r + OAS)dt \\ dP &= (r + OAS)Pdt + \frac{\partial P}{\partial x} (dx - E(dx)) + \frac{\partial P}{\partial OAS} d(OAS) \end{align}

The first equation says that the expected return under risk-neutral probabilities is the short-term rate plus the OAS. The second equation says that the return of the security along a realized interest-rate path is equal to a carry-roll-down component, a component due to changes in interest rates, and a component due to OAS changes.

Now, if we hedge out $x$ and finance the position at $r$ then the return is equal to the OAS plus a contribution equal to change in OAS times the spread duration.

To summarize, while the expected return of the hedged position under the risk-neutral process is equal to the OAS (because the expected OAS change is 0), the specific return along different realizations of $x$ depends on changes in the market pricing of the OAS risk premium. This makes sense because even though a hedge may synthetically replicate the interest rate and volatility exposures of an MBS, it will not account for changes in OAS. In short, hedging does not allow you to extract the OAS every single time, just "on average."

## Answer by wgajate (score 1)

https://quant.stackexchange.com/a/63153

> how does one actually go about hedging?

Your OAS model determines your hedging instruments, hedge ratios, and hedging (model) risk. If your OAS model calibrates to the LIBOR swap curve and swaption vols (which is common), then you can generate hedge ratios by computing key rate durations of the underlying swap and swaption instruments.

For example:

| Hedging Instruments/Calibrated model | Instrument Duration | MBS Duration | Hedge Ratio |
| Zero Coupon LIBOR Swap | 5.0 | 2.5 (key rate) | 1/2 x 5yr Swap |
| Zero Coupon LIBOR Swap | 10.0 | 1.0 (key rate) | 1/10 x 10 yr Swap |
| LIBOR Swaption (5yr expiry into 10yr Swap) | -1.0 | -3.0 (vega) | 3x Swaption |

The table above provides a stylized example of a duration neutral hedging program. It employs simplifying assumptions like ignoring key rate exposure from swaptions.

The hedge ratios inherit model risk from the OAS model which embeds both interest rate model and prepayment model risk. Such a simplified approach would expose the hedger to historical biases in the prepayment model and distributional assumptions of the interest rate model.

Hedge ratios become stale after several days due to (possibly large) movements in the market prices of the underlying calibrated instruments and the specific MBS instrument we are hedging, which forces us to recalibrate the OAS model to current market prices, recompute hedge ratios and rebalance the (synthetic mortgage) hedging portfolio accordingly.