Risk-Neutrality is another important concept that values an asset in question relative to other assets (benchmarks) that reflect various market expectations and prices of risks. The “risk-neutral economy” is a mathematical medium where evolutions of market factors are purposely adjusted for these expectations and risks. For example, the assumption underlying any good OAS model is that the random dynamics of interest rates is adjusted to generate the observed prices of bonds or swaps and their vanilla options. OAS will be earned by the investor if the underlying asset is perfectly hedged against the interest rate risk (read April 2005 article). The assumption underlying AD&Co’s prOAS model is that the random dynamics of interest rates and prepayment components (turnover-refinancing) are adjusted to yield the observed prices of bonds (swaps), their derivatives, and some MBS instruments. Hence, prOAS is earned for sure if the interest rate risk and prepayment uncertainty (model risk) are both hedged out.

It is now clear that all three notions are closely related. Suppose the asset in question can be synthetically replicated by traded assets that, coincidentally, are the benchmarks for a risk-neutral economy. Then, the model-free price can be computed and should agree with the risk-neutral fair value. In the case when a direct model-free value cannot be computed, a fair value within a properly constructed risk-neutral economy is what most models attempt to compute.

Nevertheless, risk-neutrality and model-free valuation are not identical. Risk-neutrality still relies on some form of a risk model that may misspecify risk factors and their dynamics. For example, OAS models value embedded-option bonds (including MBS) in an economy where the entire notion of risk is associated with interest rates and the option exercise laws are known. A deeper look suggests that the risk of not knowing the exact prepay option exercise law is usually priced by the MBS market, but not reflected in OAS models. This observation has led us to the prOAS concept, which we proved tracks historical prices, hedge ratios and relative values better than OAS.

MBS-Related Examples

IOs and TBAs. Let us assume that we employ the prOAS method and calibrate prices of risks, i.e. prepay model tunings, to a set of liquid TBA benchmarks. We then apply this risk-neutral prepayment model to IOs and, using prOAS levels reflecting the liquidity difference between IOs and TBAs (about 25-30 bps), derive fair values for IOs. We refer to the Divide and Conquer trilogy (part III) for details. For example, on May 30, 2003 when the rates were extremely low, IOs were traded very cheap, at 1000 – 1500 bps of traditional OAS. Values derived using the prOAS method were surprisingly close to actual market prices. This is because the TBAs’ prices reflected the fear of refinancing, too, and the IO market leveraged this risk properly.

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