Note: Price of Risk is equal to the annualized excess return demanded for bearing 1% of price volatility due to risk.

When rates dropped to their 40-yr record lows (May-June 2003), refinancing fears reached the stage of panic. High premiums (FNCL7.5 and FNCL8.0) did not appreciate, indicating that their Libor OAS levels increased to 100 bps and above to absorb much of the rate plunge. Calibrated price of refinancing risk surged over those months. No concern about turnover was observed in the calibration, as the discount sector had evaporated.

When rates sharply rose through summer of 2003, the refinancing wave started to cool off; large volumes of freshly originated FNCL4.5 and FNCL5.0 became discounts. In this period, the turnover concerns became apparent. During the rest of the time, we witnessed a general stabilization of the risk prices.

Comparing the heights of purple and blue bars in Figure 1, one can draw the mistaken impression that the MBS market is systematically dominated by the refinancing, not the turnover, fear. In fact, as seen from our last-month article, the principal components of OAS due to each of these two sources of risk may be of comparable magnitudes. Indeed, if the rates drop, prepayments surge, and the shortened mortgage life limits potential price uncertainty. After all, agency pass-throughs rarely trade beyond the 108 - 110 price range. In contrast, when rates rise, the MBS extends and its value takes a deep plunge that is constrained by and, hence, highly depends on the turnover rate. Investors will bear considerable risk as the resultant price varies widely with turnover rate.

Valuation of IOs and POs with prOAS
Valuation of strip derivatives is one of the most important applications of the new model. With the components of prepayment risk well established and quantified, we can prove or disprove that IOs should indeed be priced "cheap", at hundreds or even up to a thousand basis points of OAS. Since POs stripped off premium pools should be looked at as hedges against prepayment risk found in IOs, they have to be traded "rich" - according to the arbitrage pricing theory (risk directionality).

Let us apply the prOAS valuation model to the Trust IO market using prices of risk calibrated to the TBAs. Figure 2 exhibits valuation results for some 60 agency Trust IOs using prices of risk constants, sizeable for refinancing risk and a near-zero for turnover risk, obtained from the calibration to Fannie Mae TBAs on May 30, 2003 (Figure 1). The application of the prOAS method first leads to values, which are then converted into conventional OAS measures. The prOAS model explains IO "cheapness" (therefore, PO "richness") naturally and correctly predicts OAS level of (and above) a thousand basis points. Our prOAS model successfully places virtually all OAS for Trust POs deep in negative territory (not drawn). Results in Figure 2 also provide some degree of confidence in MSR managers' portfolios, not actively traded or frequently quoted, they can employ the prOAS measure to better assess the risk of their portfolios.

Figure 2. Valuation of Trust IOs on May 30, 2003

As we showed in historical risk chart (Figure 1), on May 30, 2003, the entire risk perception was evolving around a refinancing scare. Figure 2 shows that both the TBA market and the Trust IO market agree with one another when incorporating this risk into pricing.

In the summer months of 2003, rates rose sharply, pushing lower-coupon MBS (4.5s and 5s) into discount territory. Figure 1 confirms that by the end of that summer, the refinancing fear cooled off, making the room for turnover concerns. As we explained last month, slower-than-modeled turnover results in a loss for a discount MBS holder. Not surprising, the price for turnover risk, virtually non-existing in May 2003, became sizable (Figure 1). What if we apply prices of risk calibrated to the August 29, 2003 TBA market to value Trust IOs? Figure 3 below shows two stages in application of the prOAS model, valuation with refinancing-risk only, and with the total risk.

Figure 3. Valuation of Trust IOs on August 29, 2003

Comparing the blue lines (market prices and related OAS) with the purple lines (prOAS model with refinancing risk only), we see that the single-refinancing-risk-factor prOAS model just slightly overstates values relative to the actual market. It shows directionally correct OAS tendency (tighter spread for discount IOs, wider for premiums) and magnitude.

Disaster strikes when we add the true turnover risk calibrated to the TBAs (orange lines). Since IOs can be used as hedges against turnover risk, the APT says that they should be penalized not rewarded. An almost constant 250 basis point OAS reduction is seen as the result. The actual IO market does not seem to appreciate this theory. Price quotes are much lower than the full two-risk-factor prOAS model suggests they should have been. According to the APT, such mispricing should lead to an opportunity of constructing a fully hedged, risk-free, portfolio that earns more than the risk-free rate. It is easy to implement this theory by simply combining pass-throughs and IOs. The prOAS model automatically measures sensitivities to the risk factors as a part of the "risk accounting" process so that the two-factor delta-hedging becomes just a natural application of this job.

Our analysis, if correct, therefore, proves that there exists both theoretical and practical opportunity to create a dynamically hedged mortgage fund that is prepay-neutral and earns an excess return over funding rates.

Readers may find further details on the prOAS method in our new research publications, A.Levin, "Divide and Conquer: Exploring New OAS Horizons," AD&Co. Quantitative Perspectives.

Part II. Prepay-Risk-and-option-adjusted Valuation Concept, Feb 2004
Part III. A prOAS Valuation Model with Refinancing and Turnover Risks, Coming June 2004

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