Consulting
Corner
The Competing Risks of Mortgage Prepayment and Default
by Kyle G. Lundstedt, Ph.D.
The Increasing Relevance
of Credit Risk to Mortgage Investors
There is an enormous amount of credit risk in the mortgage sector. Government
statistics show that over $3.8 trillion in single-family residential (SFR)
mortgages were originated in 2003. Even a very small percentage credit loss
on such an enormous asset class would have serious repercussions for the U.S.
economy.
For many years, however, credit risk has been of little concern to investors
in mortgage securities. Historically, the housing government-sponsored enterprises
(GSEs) - Fannie Mae, Freddie Mac, and Ginnie Mae -have provided significant
if not total protection from credit risk for well over half of the mortgages
originated in the U.S. each year. The remaining credit risk traditionally
was held in portfolio as whole loans by financial institutions such as banks
and thrifts. Nonetheless, in the last ten years, mortgage investors have seen
the emergence of a significant secondary market for "non-agency"
mortgage-backed securities (MBS), mortgage-related asset-backed securities
(ABS), and the collateralized mortgage obligations (CMOs) derived from there.
As a result, fixed income investors now must concern themselves with measuring
and understanding credit risk, in addition to the traditional market and prepayment
risks for mortgages.
In this article, we describe some commonly used tools for measuring credit
risk. We discuss the pros and cons of these tools and then describe a methodology
called "competing risks" models. We discuss how prepayment and default
constitute competing risks in the context of mortgages and give some examples
of why mortgage investors might consider this methodology for use in evaluating
"non-agency" MBS and ABS.
Types of Consumer Default Models
There is a long history of attempts to quantify the amount of credit risk
in mortgages. One might categorize these attempts (Lundstedt 2004) into four
types of methodology:
- Scoring models
- Roll Rate or Migration models
- Life-of-loan Loss/Actuarial models
- Option-based Structural models
Lewis (1992) provides an excellent history of consumer scoring for retail
lending as a whole. Scoring models tend to use single-period classification
(logit and variations) techniques to assess the probability of default for
a loan. These techniques have been commercially developed as Fair Isaac's
FICO score, Fannie Mae's Desktop Underwriter, etc. Historically, such "origination"
or "behavior" scores predict default likelihoods over 12-18 months.
Dubitsky (2003) is a good example of so-called "roll rate" or "rating
migration"-type models. These tools historically have looked at delinquency
status and default, or alternatively bond ratings, as states in a multi-state
time-constant Markov model. Banks and thrifts have applied roll-rate models
to mortgages, credit cards, personal loans, etc. Ratings migration models
are popular with secondary market participants in the MBS and ABS sectors,
as well.
For a description of the life-of-loan loss or actuarial approach, Mays (2003)
is an authoritative reference. This methodology generates estimates of lifetime
defaults based on origination characteristics. Often, ratings agencies and
large banks use this methodology, along with an assumed timing curve, to project
loss behavior for pools or portfolios of loans over time.
The final method used to measure credit risk is applying option-based structural
models. Kau et. al. (1985) and Capozza (1998) are good examples from the academic
literature on mortgages. Such models look upon default as an American option
on underlying value of the collateral. While this approach has proven successful
in the corporate sector (i.e., Moody's KMV), consumer lending tends to be
characterized by "inefficient exercise" of the default option.
Default Models for Mortgages
For consumer lending, in general, academic and practitioner research confirms
that data-driven approaches outperform pure option-based models such as Kau
(Merton-like option model). Most banks utilize internally developed models,
rather than externally developed vendor models. In particular, "data-driven"
approaches tend to dominate mortgage default modeling (i.e., S&P Levels).
However, the traditional consumer default methods outlined above all tend
to have significant drawbacks. Scoring and life-of-loan loss models ignore
timing of default and the effect of prepayment, as well as fail to account
for covariates changing over time. Roll rate models do not incorporate predictive
variables, and assume that "history repeats itself" with respect
to macroeconomic risk factors. Finally, option-based structural models insist
that default option is ruthlessly exercised.
Mortgages pose a particular challenge for default modelers. As with other
types of consumer assets, it would be beneficial to address the timing of
the default event, as do roll rate models, and to account for static predictive
variables, as do scoring and life-of-loan loss models. However, a mortgage
default model also must allow for prepayment and other options, as do roll
rate and option-based models, as well as incorporate time-varying predictive
variables (i.e., current loan-to-value or asset-to-liability ratios) as do
option-based models.
Hazard Models
The Hazard model is a modeling technique that addresses many of the concerns
raised above. Moreover, hazard models are heavily used in prepayment modeling
(Davidson et. al. (2003), Hayre (2001), etc.). As a result, though the technique
is less commonly applied to default, its usage in the prepayment modeling
area makes it well-understood by investors on Wall Street. In fact, the valuation
and market risk measurement of MBS, ABS, CLO, CDO, etc. most commonly depend
upon hazard models of prepayments.
There is an enormous amount of academic and regulatory literature that applies
hazard models to both prepayments and defaults. For example, Alexander et.
al. (2002) examines subprime mortgage performance; Calem and LaCour-Little
(2002) is the foundation for the current Basel II regulations for mortgages;
and OFEHO (2002) explains the application of hazard models to mortgages in
the context of capital regulation for Fannie Mae and Freddie Mac.
Why are Default and Prepayment "Competing" Risks?
Since the hazard technique is well-understood on Wall Street and in academia,
one might expect that a default model for mortgages could simply be estimated
and then used with an existing prepayment model. As it turns out, however,
prepayments and defaults are "competing risks" that require simultaneous
development and estimation of models.
Consider the fact that two hazards, such as prepayments and defaults, may
not be statistically related, but the outcomes may be related in other ways.
For each hazard, the probability of transition over longer time intervals
will depend on transition probabilities of the other hazard. For example,
the lifetime default probability for a mortgage may be lower if monthly prepayment
probabilities are higher.
Moreover, some observed predictive variables, such as the current loan-to-value
(LTV) ratio or the FICO score, might affect both the hazard of prepayment
and the hazard of default. Clearly, increased current LTVs or decreased FICOs
likely increase defaults for mortgages; however, the same variables may decrease
prepayment likelihood. Separating out the effects of these predictive variables
on both hazards simultaneously is best handled by a modeling technique known
as "competing risk" hazard models.
Understanding How Prepayment Affects Default, and Vice-versa
Understanding the ins and outs of competing risk models is beyond the scope
of this article. However, it is important to understand how using such a technique
can have very significant impacts in real-world situations. Competing risk
hazard models, like traditional prepayment models, have different effects
depending upon the projected economic scenario. In fact, one of their principal
benefits is the ability to separate the effect of portfolio composition (static
characteristics such as documentation type or original FICO score) from the
effect of macro risk factors (dynamic effects driven by interest rates or
housing prices).
Consider the following graphs taken from Hall and Brown (2004). This study,
done by two researchers at Wells Fargo's Home Equity Group, included default
and prepayment estimates from a competing risk model in a variety of "good"
and "bad" future scenarios. In the first graph, a hypothetical portfolio
is subjected to an increase in interest rates. The second graph shows the
exact same portfolio subjected to a decline in interest rates.
The projected prepayment and default rates obviously are significantly different.
In the falling rate scenario, fast prepayment rates leave many fewer opportunities
for loans to default; hence, prepayment rates are high but default rates are
low for the same collateral. In the rising rate scenario, however, the increased
duration of the portfolio leaves more opportunity for default; hence the default
rate is much higher for the same collateral.
As the following pair of
graphs illustrate, changes in prepayments driven by rate effects not only
affect the magnitude (cumulative defaults), but also timing (default incidence).
Recall that the graphs above held collateral quality constant, since the hypothetical portfolios were the same. Imagine, however, two portfolios or underlying collateral pools with different characteristics. The first pool has collateral characteristics (i.e., high LTV, low rate, etc.) that lead to low prepayments, while the second pool has attributes (i.e., lower LTV, higher loan rates, etc.) that lead to higher prepayments. The graph below illustrates the effects of combining rate changes with different collateral types.
It is obvious
to see that different prepayment rates can lead to enormously different default
rates. Consequently, it is critical to use modeling techniques, such as competing
risks, that account for the effect of prepayment on default, and vice-versa.
Andrew Davidson & Co., Inc. (AD&Co) long has been the market leader
in providing prepayment models to fixed income investors. Over the next year,
AD&Co will be adding competing risks to its industry-leading suite of
prepayment models, and we look forward to working on the challenge with current
and prospective clients.