Valuation Commentary
Measuring and Managing Prepay Model Risk
by Alex Levin
AD&Co develops, maintains, and licenses OAS models, and strives to make the models as accurate and useful as possible, but the assumptions behind these models should not be taken for granted. The OAS method is highly dependent on modeling assumptions, most notably, the prepay model. Other problems could stem from improper interest rate distribution or volatility assumptions. With most, if not all, attention focused on controlling the interest rate risk that an OAS model can explain, mortgage companies and banks operating on an accrual accounting basis often regard OAS instability as “spread risk.” They view this risk as a ghost, a mathematical residual, something not concerning them or realized by them as long as they don’t intend to sell assets. A closer look at the spread risk reveals a “real” component that, if not quantified, hedged, and supported by capital, may dominate the bank’s exposure and even run a “well-hedged” firm into troubles.
Consider this: Spread Risk = Real Bias + Imaginary Forces
If a prepay model systematically drifts away from market expectations of prepayments, OAS levels will drift too. Hence, “spread risk” may simply reflect prepay model inadequacy which can be termed “real model’s bias.” If the model (or the market expectations) differs from the true realized prepayments, then spread risk can translate into actual losses. If, for example, the refinancing model is too slow, then the net income generated by premium MBS and IOs will be overstated – it can easily be positive on paper and negative in the real world. If the prepay model overstates housing turnover rate, then the same becomes true about discount and current-coupon MBS.
The other components of the OAS instability can indeed be attributed to the market technicalities and risks that mortgage investors are often willing to take. For example, the liquidity component would fall into this “imaginary” category – its volatility is not realized until assets are sold. Interestingly enough, a part of prepay model risk can be considered compensation for market fears that refinancing and turnover speeds cannot be predicted perfectly. The boundary between bias and risk is not easy to draw in practice; however, there exists definitional difference between them. A prepay model bias is a drawback of a particular physical (real-world) prepay model that is employed by an OAS system. In essence, any concrete prepay model can be biased versus the best guess of the market. Unlike a prepay model bias, prepay model risk comes from the conceptual inability to predict prepayments and accounts for the difference between the real-world and a risk-neutral prepay world. The imaginary forces don’t alter expected cash flows and incomes; rather they simply explain the cause of them. For example, investing in an illiquid asset generates income that is due to the lack of liquidity and related initial price break, not the skills of the portfolio manager.
Let us return to prepayment bias, which is a real factor not only affecting market prices, but cash flows and income forecasts, too. For buy-and-hold investors, it may become the dominant risk after the interest rate risk is fully hedged. Below we show how one can quantify this risk and what kind of risk management ideas can come from our analysis.
A basic VAR-type illustration
Let us assume, for simplicity, that we use the AD&Co prepay model, but allow the turnover and refinancing scales (AKA “tunings” or “dials”) to carry a 15% uncertainty (standard deviation). For this conceptual presentation, we ignore complex dynamics of prepay model factors. For example, current turnover rate can be documented and known better than current refinancibility; both errors can exist at time zero and diffuse forward.
Figures 1 (flat curve) and 2 (steep curve) show prepay model risk profiles for TBAs arising from refinancing acceleration (red), turnover deceleration (green); the resultant Pythagorean VARs (violet) assume both errors are mutually independent. Since we can’t be sure about the exact magnitude of prepay errors, we calculated VARs using three extreme assumptions: “15/15” (refinancing and turnover errors are each of 15% magnitude), “30/15” (turnover dominates), and “15/30” (refinancing dominates).
Figure 1
Figure 2
There are several messages coming from this basic analysis. First, there exists a coupon with minimum combined risk. This coupon depends on the current mortgage rate and the shape of the yield curve. It is not a par coupon at all; it is a coupon that “looks par” from the forward market standpoint. When the curve is relatively flat (Figure 1), the minimum risk is achieved at a 101-103 price range; when the curve is steep (Figure 2), it slides to a 103-105 region.
Second, the combined risk (one standard deviation) is greater than ¼ price point. Imagine a firm operating at a 5% capitalization. The entire MBS-specific risk is typically found on the asset side, hence ¼ MBS pricing point is worth 5% of equity. This is just one standard deviation of prepay model risk at the least risky point!
Finally, the par MBS is not at the low risk point on the curve. We discuss this important observation below.
A risky price temperature: 100 (and below)
I have met MBS managers who conscientiously elected to rebalance their positions to stay close to par – they consider this strategy an immunization to prepayment uncertainty. Further, many mortgage banks and agencies can naturally find themselves in this position if (A) they retain the current origination volume and (B) rates have not changed much recently. As seen from Figure 2, in a steep rate environment, the par-priced MBS carries a ½ to ¾ point prepay error VAR, or 10% to 15% of equity for the same 5% capitalization example. The turnover uncertainty is the primary cause of the risk.
The “stay-at-par” strategy traces its roots to the old-time finance when the yield-to-maturity measure dominated the fixed income industry. Indeed, the yield of a par-priced MBS is equal to its coupon, regardless of prepayment speed. Hence, if MBS were priced using constant yields, their par prices would stay immune to prepay assumptions. The flaw of this logic is pretty apparent: even before the OAS methodology considers options and volatility it accounts for the benchmark (funding) rate. In fact, a par-priced MBS should strongly deteriorate in value once housing turnover slows down because the MBS life would extend requiring borrowing at a typically higher funding rate. The steeper the curve, the stronger the turnover-related risk of a par position.
What is to be done?
There exists a variety of hedging techniques that mortgage bankers may consider. One is proper positioning in the prepay risk profile (Figures 1, 2) by either buying or selling certain MBS coupons or injecting IOs or POs into the mix. The feasibility and economic efficiency of this strategy can be verified analyzing different MBS markets. For example, at times the Trust IOs/POs tend to dislocate from TBAs in pricing prepayment risk, thereby presenting an opportunity to combine them and earn significantly more than the risk-free rate (see A. Levin [2004]).
Figures 1 and 2 were plotted for the range of TBA coupons, but comparable profiles can be drawn for a single GWAC by varying the servicing spread. We have done a similar analysis and have proven that to reduce prepay model risk, (1) discount-to-par coupons require buying IOs or selling POs, (2) cuspy premiums look close to optimal and (3) high premiums require selling IOs or adding POs.
Whether prepay model risk is hedged or not, capital requirements should be set-up for each MBS strategy. A fixed-rate MBS strategy typically demands more capital for prepayment risk than an ARM strategy, but less than an IO strategy taken alone. For example, we showed that the stay-at-par strategy puts 10%-15% equity at risk on a single-sigma VAR basis. If this is unacceptably high risk, one can consider allocating more capital for the investment strategy.
Hedging prepay model risk is a demanding but feasible task requiring sophistication and an understanding of different segments of the MBS market.
Reference
A. Levin, Divide and Conquer: Exploring New OAS Horizons, part III, Quantitative Perspectives, AD&Co (June 2004).