Option-adjusted spread (“OAS”) analysis is not well understood by our industry. OAS should not be used to *generate* an assessment of value but, rather, as a very useful *output* of the valuation process. It is an important financial tool that adds tremendous insight into the risk dynamics of mortgage related assets, but it does not produce a market or economic value.

The process of developing an OAS is very telling:

- Generate a large number of randomly generated future interest rate paths;
- Produce cash flows along each path at a risk-free rate plus a spread;
- Obtain a simple average of the net present value of these cash flows;

This produces a simulated price.

- If this simulated price does not equal the market price, choose another spread and rerun;
- Repeat this process until the simulated price equals the market price

The resultant spread is the OAS. This OAS is calibrated to market value; not the other way around.

The current usage of OAS analysis as a tool to determine price implies that we know the risk spread that the market demands and, thus, can use this spread to determine price. This is intellectual hubris. The spread is predicated on a large number of very complex assumptions and models, few of which are directly observable in the marketplace. These assumptions include, but are not limited to:

- Rate volatility (the speed at which future short rates change from their current implied values
- Rate constraints (high/low)
- Mean reversion properties
- Distribution (normal or log normal)
- Yield curve model (instantaneous forward rate or short rate)
- Interest rate path generation (single or multi-factor)

Additionally the OAS, while ostensibly a stochastic measure, is heavily influenced by a deterministic prepay model. While most analysts would test their OAS with sensitivities based on 90% or 110% of these prepay models, this simply “measures the sensitivity of OAS to consistent misestimation of the prepayments … not to random fluctuations around the model’s predictions.”[1]

And, even if these assumptions were observable and defensible, the option adjusted value is still meaningless from a valuation perspective. It is an average of hundreds of different interest rate paths. Possibly one of them is the *correct* path (i.e. what actually occurs), but there is no assurance that this is true, nor is there even a meaningful probability that this path is the “average” path that the OAS concludes. “It is extremely unlikely that a security will actually earn its calculated OAS.”[2]

If you look at the distribution of values that an OAS analysis produces, you will see my point. A greatly simplified example is shown below.

This simplified example shows only five possible outcomes: a yield on the investments of: 0%, 7.5, 15, 22.5 or 30%. The model generates a frequency distribution of these returns as indicated from a low of 3% to a high of 40% (naturally they sum to 100%). As is typical with mortgage related investments, the distribution is not normal; it is negatively convex (skewed to the left). Because an OAS value is a simple average of values over the entire distribution, the OAS value in this case would result in an average return of 15% (the “mean”). Not only is this value far from a certain outcome, but it is not even the most probable outcome. The most probable outcome (the “mode”) returns only 7.5%.

I would not pay a price that equates to a yield of 15% when the most probable outcome is a yield of 7.5%. Additionally, I would look closely at the dispersion of the expected returns emanating from these hundreds of paths. If the deviation around the mode is small, I may be willing to pay the price related to the modal price (never the mean price). If the dispersion, however, is large, I would discount the price substantially.

OAS provides very useful information about the expected cost arising from the mortgagors’ ability to prepay at will. It does not, however, measure credit risk nor does it provide the answer to the question of “what is the value of this asset”?

OAS has become a fad; one number that ostensibly summarizes the entire range of financial dynamic of the mortgage asset. Yet this is not what the architects of OAS intended. They never “intended the OAS to be viewed as a ‘yield takeout’ over Treasuries. Because it’s the result of an averaging process.”[3] Financial analysts love to talk about OAS while disparaging scenario and other analyses. Yet, from a market value perspective, OAS is a very elegant and expensive way of being wrong.

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N.B. Blogs do not allow for a lengthy discussion of any subject. I will be publishing a more comprehensive discussion of this topic in Mortgage Banking Magazine and will advise those who are interested as to its publication date.

My next blog will address level 1 (under FAS 157) alternatives to valuing mortgage related assets. This will not be available until the first week of September. For the remainder of this month I will be focused on producing an article for Mortgage Banking Magazine (October 2010 edition) on identifying paradigm shifts in our industry *before* they wreak their havoc on us.

[1] Robert W. Kopprasch, Financial Analysis Journal, May-June 1994; page 45

[2] Robert W. Kopprasch, Financial Analysis Journal, May-June 1994; page 43

[3] Robert W. Kopprasch, Financial Analysis Journal, May-June 1994; page 43

Dr. Healy makes some excellent points on the use and “abuse” of OAS models and an analyst must first determine if he or she desires a market value or economic value (i.e. the value to the organization). If the market buyers are ultimately buying assets using static analysis then that is the approach that should be used to determine market value regardless of the flaws (and there are many). That does not imply that OAS has no place in the analyst’s tool kit. On the contrary, stochastic analysis can yield incredible insight in the inherent optionality of mortgage assets that is impossible to gleam from static analytical techniques alone. One important measure of risk is standard deviation of the returns calculated in an OAS analysis. The deviation or “variation of returns” provides a valuable risk metric such as Value at Risk (VAR). I do concur with Dr. Healy in that the prepayment model can heavily influence value outcome. Often this model is a “Black Box “ of prepayment predictions giving what we know about mortgage behavior in various interest rate environments. This is known as calibrating a model based on empirical or historical data. The problem lies in the fact the future behavior is often quite different than the past. Take the current situation we are in now for example!