Valuation Commentary

prOAS Delivered, Explained and Discussed
by Alex Levin

The May issue of The Pipeline wrapped up the introduction of valuation with prepay risk-and-option-adjusted spread (prOAS). Since then two major things happened. First, AD&Co hosted it's 12th Client Conference. The first half of the day was dedicated to these new modeling approaches. Second, a new AD&Co's Quantitative Perspectives, "Divide and Conquer: Exploring New OAS Horizons", has been published and was made available to conference attendees. Those who missed the conference can download the paper from the Research Report section of our website. This report is a 52-page trilogy covering topics ranging from the Active-Passive decomposition (APD) mortgage model to practical valuation and calibration exercises using prOAS. In short, it is about what AD&Co believes is an approach that provides a more consistent and realistic assessment of the relative value of MBS. These analytics can be demonstrated through our web-based platform, ValueNet.

The main themes of the trilogy were presented in several conference talks and were met with genuine interest by the audience. During and after the sessions, questions raised by the audience led to discussions about the practical applications of the new analytical paradigm. I thought that the essence of those conversations might be interesting for all our readers so I decided to compile them and share.

Q. How many clients have already been using ValueNet and the prOAS valuation method?

A. A number of firms requested free trial for ValueNet, which, being a WEB demo, requires no installation hassles.

We started consulting several large clients on using customized risk-neutral tunings for AD&Co prepayment model v.4.3.3, which is widely employed. Since March 19, we have been publishing these recommendations on our WEB site assuming clients use the Hull-White term structure model through our OAS system or through a third-party vendor.

We also can and do derive values for clients' portfolios of fairly illiquid instruments using the prOAS method.

Q. Have we considered various CMO tranches for prepay risk assessment and calibration?

A. One important point to recognize about prepay risk-adjusted valuation is that the risk is located in a prepayment model, not in the CMO structure. The cash distribution rules are set in stone for every deal. Therefore, a particular CMO tranche should bear no additional wisdom of how the market regards prepayment risk or risks. I do not mean that all tranches should be priced at the same OAS as their collateral. We know that the collateral risk is amplified in an IO and dampened in a PAC affecting their OAS levels accordingly.

It is possible that some CMO tranches are practically priced in disparity with the collateral, which means an arbitrage opportunity.

Q. Have we accounted for liquidity differences? How does the prOAS method work for illiquid MBS or non-agency MBS?

A. The prOAS measure differs from the traditional OAS in that it accounts for prepayment risk. An appropriate liquidity spread should be added to the "perfectly liquid" prOAS level, which is the agency debenture level. Any credit adjustments should be made too. In accounting for imperfect liquidity or credit, the prOAS method and the OAS method share the same recipes. In particular, our Trust IO analysis has been performed using a 25 bps prOAS in recognition of the impact of liquidity.

Q. Is the discovered IO - TBA disparity a typical anomaly of the MBS market? Or, is it a once-in-a-life arbitrage opportunity?

A. In the paper and during the talk I pointed out that the TBA market clearly shows the risk of faster refinancing and slower housing turnover whereas the Trust IO market looks at prepayment risk as a single-dimensional source of risk. The prOAS valuation with prices of risk calibrated to TBAs do a decent (at times, stunningly accurate) job in predicting prices of the IOs, without consideration of the turnover risk. This fact leads to an arbitrage opportunity: combining a discount MBS with a discount, similar-pool, IO we hedge out the prepay risk while earning positive OAS off both positions. On August 29, 2003, Trust IOs were several points cheaper (200-300 bps wider) than the prOAS theory thought they should have been.

Now, after having looked at more trading days, I have found that this TBA-IO dislocation might actually be an exception rather than the rule. Upon request, I could forward charts similar to those shown in the Quantitatve Perspective and in the powerpoint presentation, for these additional market dates and conditions. We are now inclined to state that two market anomalies we found and documented, exaggerated prices of risk in times of panic and the TBA-IO disparity, may, in fact, represent the same phenomenon. Moreover, prices of risk as well as relative prOAS pricing of IOs versus collateral are not as much functions of the rate level, as the rate dynamics. Sharp change in rates destabilizes both TBA and IO markets; when rates get "stuck" to the new level, panic dissipates. Price of risk steadies and is recognized by the market; the TBA-IO arbitrage disappears.

Q. Does the arbitrage argument require lognormality of prices and factors?

A. No, it does not. The risky ("derivative") asset can follow any stochastic behavior, but its return should be linear in logarithmic derivative of price with respect to factor of risk (i.e. factor duration). As for the risk factor, it does not have to be normal or lognormal - it can even be a non-traded random variable. For example, prepayment error is not a price of any "underlying" asset.

Q. Prices of risk appear to be time-dependent. Is it a blow to the prOAS theory? Should the market participant recalibrate prices of risk regularly?

A. Let us re-read John Hull's 4th edition of "Options, futures, and other derivatives". He denotes factor of risk as q , time as t, and the value of derivative as f. The market price of risk, Hull asserts on page 500, "may be dependant on both q and t, but it is not dependent on the nature of the derivative f".

All words in this concise statement are worth considering. First, a risk-adjusted valuation model with constant prices of risk is an over-simplification not required by the arbitrage pricing theory. Variability of prices of risk is the rule rather than an exception. However, we believe that exaggerated dynamics, clearly seen in times of panic, present opportunities for successful speculative investment decisions. As for the practical matter, the prOAS model needs a live market feed and must be re-calibrated regularly - in the same way we re-calibrate a term structure model with rates and volatilities changing.

On the other hand, the TBA - IO market disparity, when exists, is a true arbitrage opportunity because prices of risk appear to depend on instruments. And, if the TBA-IO convergence is inevitable, combining IOs and TBAs can be viewed as a hedged speculation.

Q. Does the term structure model selection matter when using the prOAS model? Will it reconcile valuation differences seen under traditional OAS?

A. I mentioned that valuation results provided by two different brokers or analysts would differ less if they employed risk-neutral versions of their respective prepayment models. This is true because a set of undisputed MBS prices become a common denominator in risk-neutral modeling thereby making prepayment models closer.

What I also meant is that all other modeling assumptions are kept identical including the rate model selection. It may sound counter-intuitive and paradoxical at first glance, but the MBS duration differences obtained under the Hull-White model and the Black-Karasinki model will increase rather than decrease with the use of risk-neutral prepay models. We will cover this important topic next time, but the "conscientious" choice of the rate model has apparently become more important than ever.

Q. What is the current instrument coverage by ValueNet?

A. All Fannie and Freddie fixed-rate pass-throughs with other types to follow.