Model Risk in Mortgage Servicing Rights

The table below shows the reported valuations for mortgage servicing rights for 8 large U.S. financial services firms between December 31, 2009 and September 30, 2011. The aggregate reported value of mortgage servicing rights has declined from $62.5 billion to $35.6 billion in 21 months.  Even at the lower valuation, the very large absolute value attributed to mortgage servicing rights and the tremendous volatility of the valuation in the current market makes an examination of the conventional wisdom essential from both a risk management and corporate governance point of view.

One of the things that these figures make obvious is that the mortgage servicing business is an enormously concentrated business with highly skewed market shares.   Another obvious point is that the percentage of total market capitalization for these firms that is attributable to mortgage servicing rights is very large.  Mortgage servicing rights are classified as a Level 3 asset for accounting purposes because there are very few observable traded prices and because many of the inputs to a reasonable valuation are also unobservable and the result, in the end, of educated guesses. If there is model risk in reported mortgage servicing rights valuation, equity market participants need to be informed of these model risks, and those hedging mortgage servicing rights need to take great care because of potential errors in both the amount and direction of the hedging needed.

An Introduction to the Valuation of Mortgage Servicing Rights

As is common in the risk management business, the head of a mortgage servicing rights hedging program once said “I don’t care about accuracy, I just want to do the same MSR calculation as everybody else.”  Therein lies the problem.  What if “everybody else” in total is only 7 firms?  How can they be sure that there are no errors in this complex valuation calculation?  One approach is to survey all of the other participants in the market, which is commonly done, to insure consistency.  Unfortunately, the assumptions that home prices don’t go down and that copulas are appropriate for CDO valuation were consistent modeling assumptions in US financial markets in 2006.  The consistency alone is not sufficient to establish accuracy.  The recent controversy about potential manipulation of the U.S. dollar Libor market during the credit crisis, when the U.S. dollar Libor panel consisted of 16 firms, illustrates another risk: the risk that the 8 firms who dominate the mortgage servicing business have an economic incentive to agree on a valuation methodology that maximizes the value of this large asset.  For all of these reasons, an independent approach of maximum accuracy in valuing mortgage servicing rights is essential.

Starting from the ground up, one can approach the valuation of mortgage servicing rights as the valuation of a fixed income (broadly defined) security subject to default risk and prepayment risk.  A recent paper that provides an introduction to this approach is

Che-chun Lin, Ting-heng Chu and Larry J. Prather, “Valuation of Mortgage Servicing Rights with Foreclosure Delay and Forbearance Allowed,” Review of Quantitative Finance and Accounting, 26: 41–54, 2006

A copy of the paper is available here:
http://ideas.repec.org/a/kap/rqfnac/v26y2006i1p41-54.html

In the next section, we follow Lin, Chu and Prather and decompose mortgage servicing rights into their component cash flows and compare the “conventional wisdom” and best practice.

Comparing Best Practice and Common Practice in
Valuing and Hedging Mortgage Servicing Rights

There are so many differences between best practice and common practice in valuing and hedging mortgage servicing rights that we will have to be brief to keep this blog of reasonable length.  We address these differences point by point.

Valuation Yield Curve for Cash Flows

Best practice discounts cash flows using a series of yield curves, depending on the nature of the cash flows, particularly when some cash flows are best valued in nominal dollars and some are best valued in real dollars.  Common practice discounts all cash flows at the same yield curve, typically the U.S. dollar Libor-swap curve.  There are many reasons why this assumption potentially leads to serious errors, as weekly readers of the Kamakura “implied forecast” for US Treasuries and the swap curve already know.  The use of this curve is usually justified with the phrase “all mortgage market participants use the swap curve for hedging.”  Unfortunately, that has nothing to do with whether the curve is appropriate for valuation.  As we shall see, the right valuation curve depends on the characteristics of the mortgage servicing right (“MSR”) cash flow component’s credit risk, prepayment risk, and inflation-sensitivity (real or nominal), and many of the relevant curves are closely tied to home price movements.  The Libor-swap curve has a number of serious problems when employed for valuation. We list many of those problems here:

1. The British Bankers Association quotations for Libor have been consistently different from the cost of Eurodollar deposit costs reported by the Federal Reserve on its H15 statistical release.  For documentation of the differences, see the Kamakura blog
   

   van Deventer, Donald R. “Kamakura Blog: Default Probabilities and Libor,” Kamakura blog, www.kamakuraco.com, June 7, 2010. Redistributed on www.riskcenter.com on June 8, 2010.

   The blog is available here:
   http://www.kamakuraco.com/Blog/tabid/231/EntryId/206/Kamakura-Blog-Default-Probabilities-and-Libor-Updated-June-8-2010.aspx

2. Consistent with the blog above, there is an increasing amount of evidence that Libor quotations have been manipulated by major banks who participate in the Libor setting panel in various currencies. For background, see this summary “London Banks Seen Rigging Rates Losing Credibility With Markets” (Bloomberg.com, November 22, 2011).
3. The potential manipulation is so significant in monetary terms that Charles Schwab formally filed a lawsuit against major banks participating on the Libor panels. For background on the lawsuit, see “BofA, Citigroup Are Accused by Schwab in Suit of Manipulating Libor Rates” (Bloomberg.com, August 25, 2011).
4. Market participants commonly assume that fixed rate mortgage yields are a simple spread over an interpolated swap yield at two key maturities, such as the 2 year and 10 year interpolated swap rate at an effective maturity of 6 years. This assumption is false. Over the period from January 8, 2004 to November 17, 2011 using weekly data, the appeal of using swap rates for valuation is deceptively attractive, as shown by the high correlations of swap yields with the 30 year conventional fixed rate mortgage rate.

   

   The true relationship between swap and Treasury yields and fixed rate mortgage yields is more complex, as we discuss next.

5. Using conventional 30 year fixed rate conventional mortgage reported on the Federal Reserve H15 statistical release, the interpolated 2 and 10 year swap rates explain only 82.8% of the weekly variation in fixed rate mortgage yields with a standard error of 30.47 basis points.

   

   By contrast, a simple linear regression using multiple points (13) on both the swap curve and the U.S. Treasury curve explains 98.17% of the weekly variation in fixed rate mortgage yields with a standard error only one-third as big as the conventional wisdom, 9.9 basis points.

   

   The conventional wisdom, to benchmark valuation off of two points of the Libor-swap curve or off of the entire swap curve alone, has no basis in the facts. The U.S. Treasury curve plays at least as great a role in the movements of the 30 year fixed rate mortgage yield as does the Libor-swap curve and there is much less risk of manipulation by market participants.

6. The spread between the 30 year swap yield and the matched maturity Treasury yield has been consistently negative since October 24, 2008. The reason for this negative spread is the difference in credit exposures in the two yield curves. A default by the U.S. government, which is no longer an unthinkable possibility, puts potentially the entire principal amount at risk. If there is a default by a swap counterparty, the amount at risk is, at a maximum, the change in the present value of the swap position since its value at origination (which would be zero for a swap done “at market” at the time). With the increase in the perceived risk of the U.S. government, the spread between the swap yield at 30 years and the 30 year U.S. Treasury yield has been negative on 749 business days from February 9, 2006 to November 17, 2011.

   

   Over the same period, the 10 year spread between the swap curve and the U.S. Treasury curve has been negative for 67 days, with the first negative spread reported on January 21, 2009.

   

   It is unthinkable for market participants to value mortgage servicing rights by discounting at yields below U.S. Treasury yields given the current relative default risk of mortgages and the U.S. Treasury. There is no legitimate argument that justifies such a valuation choice. This graph from December 2, 2011 plots the zero coupon yields, using advanced yield curve smoothing techniques, for the swap curve versus the U.S. Treasury curve. The negative spread at 30 years “contaminates” the spread at much shorter maturities (on this date, maturities 13 years and over), so the choice of the swap curve as a valuation yield curve is a dramatic error. The short end of the curve shows a hump in discount rates for the Libor-swap curve because the credit risk of 1, 3, and 6 month Libor is incompatible with the credit risk of the swap yields used for 1 year and longer maturities, as discussed above:

   

Simulation of Random Movements in Yields

The conventional wisdom for simulating the random interest rate environment when valuing mortgage servicing rights is embedded in legacy asset and liability management systems.  For the most part, these systems rely only on one factor models of the term structure.  As commonly implemented, these one factor models imply that changes in yields can only (a) all rise together, (b) all fall together, or (c) all remain unchanged.  Unfortunately, this implication of one factor term structure models is false.  This issue was addressed in the November 7, 2011 Kamakura blog “Pitfalls in Asset and Liability Management: One Factor Term Structure Models” available at this link:

http://www.kamakuraco.com/Blog/tabid/231/EntryId/347/Pitfalls-in-Asset-and-Liability-Management-One-Factor-Term-Structure-Models.aspx

U.S. Treasury coupon-bearing yield curve movements from January 2, 1962 to August 17, 2011 were only consistent with one factor term structure models on 37.7% of the 12,386 business days studied.  For monthly zero coupon bond yields and forward rates, the consistency ratios were much lower, 24.8% and 5.7% respectively, as shown in this table:

The U.S. dollar Libor-swap curve movements were studied in a similar matter in the November 23, 2011 Kamakura blog “Pitfalls in Asset and Liability Management: One Factor Term Structure Models and the Libor-Swap Curve” available at this link:

http://www.kamakuraco.com/Blog/tabid/231/EntryId/350/Pitfalls-in-Asset-and-Liability-Management-One-Factor-Term-Structure-Models-and-the-Libor-Swap-Curve.aspx

Over 10,150 business days from November 1, 1988 to August 17, 2011, Libor-swap curve movements were consistent with one factor term structure models on a miniscule 7.2% of the business days, as shown in this table:

With respect to the simulation of random interest rates, the conventional wisdom is dramatically wrong and is in violation of the Basel Committee on Banking Supervision’s December 31, 2010 Revised Basel II Framework for Market Risk, which requires on page 12 that

“For material exposures to interest rate movements in the major currencies and markets, banks must model the yield curve using a minimum of six risk factors.”

Because the conventional wisdom assumes away the yield curve twists that are very heavy influences on mortgage prepayments and defaults, the resulting valuations could potentially be grossly incorrect.

The Role of Home Prices in Defaults and Prepayments

The conventional wisdom in the servicing of a whole loan portfolio is to assume a constant default rate that is not influenced by home prices or interest rates.  This assumption is false, and that is well recognized by many.  They are constrained by legacy asset and liability systems to use a valuation assumption that they know to be false.  Default rates are very sensitive to home prices as shown in this graph of actual and predicted prime fixed rate mortgage defaults as reported by the Mortgage Bankers Association and embedded in the Kamakura Risk Information Services mortgage default service:

The change in home prices is statistically significant in predicting defaults, with a t-score equivalent well above the t-score level of 2 that is normally the benchmark for judging statistical significance.  Modern enterprise risk systems allow mortgage servicing rights valuation with default rates that are determined by the simulated random movements in home prices, interest rates and other key factors.  The erroneous assumption of constant default rates is avoided.

Similarly, it is very common in the valuation of mortgage servicing rights to assume a constant, linear, or tabular prepayment function in which home prices play no role. This assumption is also false.  Recent publications by Calhoun and Deng (Journal of Real Estate Finance and Economics, 2002) and Campbell and Cocco (“A Model of Mortgage Default,” Harvard University research paper, October 2011) are among many research papers which document the very significant role of home prices in prepayment as well.

Other Sources of Cash Flow Related to Mortgage Servicing Rights

The total cash flow from mortgage servicing rights can be broken into components as follows:

• Net servicing fee, equal to the gross servicing fee less guarantee fee, if any
• Net cost to service
• Net cash flow triggered by delinquency and default
• Float on taxes and insurance
• Float on principal and interest
• Float and costs from prepayments

The magnitude and very existence of these cash flows depends on the probabilities of default, partial prepayment and prepayment in full, which have been mis-specified in the conventional approach to valuing mortgage servicing rights as explain above.

There are many other significant errors that can be made in valuing individual components of cash flow.  The cost of service, for example, might be assumed to constant, but that assumption is false.  The cost of service is affected both by inflation and by the economies of scale in servicing relative to other competitors.  The float on taxes and insurance could be calculated on the assumption that taxes and insurance are constant, but that assumption is also false.  Both taxes and the cost of assumption are strongly linked to the value of the house.  One might assume, as a better approximation, that home prices are correlated with inflation.  Unfortunately, looking at correlation between the Case-Shiller home price indices and the consumer price index shows a wild variation in the linkages as documented in the June 1, 2009 Kamakura blog “Risk Management Strategies for Individual Investors, Part 4: Home Prices and Inflation”:

http://www.kamakuraco.com/Blog/tabid/231/EntryId/57/Risk-Management-Strategies-for-Individual-Investors-Part-4-Home-Prices-and-Inflation.aspx

The float on principal and interest and the float and costs from prepayments are complex derivatives that depend not just on interest rates but also on home prices.  The conventional wisdom ignores the home price linkage.  Stated more precisely, analysts recognize the linkages but they are constrained by legacy systems that are unable to take advantage of this economic reality.  A modern state of the art enterprise risk management system avoids this valuation error.

Incorrect Hedging of Mortgage Servicing Rights

The conventional wisdom notes that mortgage servicing rights are to be reported at market value under generally accepted accounting principles.  The corollary to that fact, however, is wrong—the conventional wisdom concludes that, since these market values are random, mortgage servicing rights need to be hedged.  That conclusion is potentially wildly incorrect, for a simple reason.  Market participants have simply ignored the “factory” which services mortgages (other than assuming the constant dollar cost above).  This factory is not marked to market on the balance sheet under GAAP, but in fact the value of the operations center (buildings, software, hardware, staff, and so on) rises and falls with the value of mortgage servicing rights in a highly correlated way.  By ignoring this link and partial or full offset, those who hedge may in fact be INCREASING RISK, not reducing it.  Take the example of a scenario like that of today, where U.S. home prices have fallen sharply.  This both reduces the value of mortgage servicing rights (because default rates have increased) but it also has reduced the cost of being a participant in the operational processing of mortgages.  If all of the mortgages being serviced, for example, defaulted, what would happen? The present value of labor costs of mortgage servicing would essentially go to zero, because all staff would be laid off.  The present value of computer hardware needs would go to zero, because the hardware used would be sold or moved to other businesses.  The present value cost of software used would go to zero (in the case of annual rental pricing, since the contract would be terminated) or be sharply reduced (in the case of perpetual license pricing, since the maintenance fee would be terminated). If the mortgage servicing business were terminated, the value of the related buildings and land would go to their value of the next best use.

In short, there is a natural offset of some or all of the variation in the value of mortgage servicing rights.  The conventional wisdom, however, has completely forgotten this simply because the accountants treat mortgage servicing rights and the physical and intellectual property of the operations center differently.  This is a very common source of risk management disasters, in which risk managers pay attention to the accountants and ignore the true economics of what they are trying to hedge.

Conclusions

The conventional wisdom in the valuation of mortgage servicing is notoriously “sticky” because there are so few market participants in the business and because reported values are so large.  There is no one inside the mortgage servicing industry with a vested interested in pointing out that the Emperor’s wardrobe may be a bit threadbare. Only the accountants and regulators who would have to deal with any mark downs in value have downside risk.  The shareholders and taxpayers who would ultimately have to pay were one of the large servicing banks to fail are not given sufficient information to make their own judgments about the value of mortgage servicing rights.  As pointed out in the previous paragraphs, tens of billions of dollars in “value” relies on a series of assumptions that are known to be false.

Kamakura Corporation has a complete transaction level capability to value both sides of the mortgage servicing business: those cash flows that stem from the mortgage itself and those that stem from the operations of the servicing business.  Kamakura Corporation is pleased to assist those firms whose management believes that a second opinion of these multi-billion dollar assets would be in the best interests of the firm.  Kamakura is equally pleased to serve the accounting industry and bank regulators in this regard.

Mark Slattery and Donald R. van Deventer
Kamakura Corporation
Honolulu, December 5, 2011