Valuation Commentary

The Lessons of an Eventful Year
By Alex Levin & Jay DeLong

In 2003, we saw interest rates plunge and surge, an ultra-steep curve, accounting turmoil at Freddie and excessive portfolio risk at Fannie. Mortgage rates dropped to a 40-year record-low of just above 4% in June only to quickly rise by over 150 bps. Multi-billion pools were running off at 70-75 CPR, frightening investors and making MBS look hazardous.

Dynamics of OAS
Par Coupons (Figure 1) · Since OAS for mortgage instruments is earned for bearing prepayment risk, it tends to widen when investors fear the worst. According to our OAS model, in mid-June current-coupon conventional TBAs were priced at a Libor OAS level approaching 50 bps (40 bps for GNMA). After the summer's refinancing wave cooled, OAS numbers started to converge to their long-term equilibrium levels. With the rates seemingly returning to their starting levels, OAS numbers are lower now than they were in January.

Figure 1. Dynamics of par-coupon LOAS

Conventionals vs. Governments (Figure 1) · The turmoil Fannie and Freddie eroded some investor confidence in mid-summer. The conventional-government OAS widened to 20 bps and remained roughly at that level. Interestingly enough, mortgage current coupon rates (MTGEFNCL vs. MTGEGNSF) have been just 4-6 bps apart, but the steep curve is detrimental to the value of Ginnies that prepay more slowly. Freddies and Fannies have traditionally been priced in a complete unison. They are 2-5 bps apart now - assuming identical prepayments.

Premiums (Figure 2) · With the same concept in mind (OAS = compensation for prepay risk), we are able to explain the dynamics of premium MBS. When rates drop, their prices exhibit visible "compression", i.e. prices do not rise as the constant-OAS Duration predicts. For example, FNCL7.5 has been priced in a narrow range between 106 and 107 - regardless of the rates. Correspondingly, OAS "absorbs" all rate moves and is far from being constant.

This is a low blow to the OAS theory, but its extension, prepay-risk-and-option-adjusted valuation (prOAV), explains many phenomena. Since higher coupon MBS are fragile, they should be progressively discounted for bearing the refinancing risk. This puts a limit on practical price appreciation. The same theory explains dynamics of IO/PO/MSR pricing; we expect prOAV and the related risk-adjusted spread measure, prOAS, to become hot topics in 2004.

Figure 2. OAS for premium FNCLs

Race of the models
In our June pipeline, we introduced a new measure of volatility - a single volatility index. The idea is very simple - replace the entire ATM volatility surface with one best-fitting short-rate volatility number. First, it is useful for risk managers because is drastically simplifies quantitative understanding of the role of volatility in a retrospective risk assessment. In particular, it sets up a framework for measuring the Vega. Second, this method may become a fair judge of the performance of term structure models. Indeed, each short-rate model has its own volatility specification, i.e. produces its own volatility index. The best model is the one in which the index is most independent of the rate level. For the ultimate model selection, we usually complement this type of analysis with others, such as historical, day-to-day, rate behavior, and the evidence of volatility skew for traded swaptions.

For quite a long time, the Hull-White (HW) model performed very well across all metrics. With rates continuing their freefall through spring, many started wondering whether HW would remain creditable. A simple reason for this doubt is that a normal model does not preclude a plunge into the negative rate territory -- unseen in U.S. history. The only way to prevent negative rates is to reduce the basis point volatility when rates fall. Both Black-Karasinski (BK) and Squared Gaussian (SG) models accomplish this mission, albeit at a different pace.

As shown in Figure 3, a sharp decline in rates in June of 2003 (below 3%) triggered a new mode. The SG model performed visibly better with HW to follow. As for the BK model, it has remained a minor-leaguer, where it seems to have been relegated some 10 - 15 years ago. As we see, any change in the rate level causes a mirror reflection in the BK (i.e. proportional) volatility. A strong remaining dependency on rates indicates wrong functional volatility form for this model.

Figure 3. AD&Co's volatility indices in 2003

Does this finding mean that all users should switch to the SG model? Perhaps this move would be overreacting. As seen on Figure 2, the HW model has recovered nicely from this blow once rates rose. The race of the major league indices remains close. On a more serious note, the SG model and related Cox-Ingersoll-Ross (CIR) model, both with the square-root volatility specification, have always been decent choices.