Regulatory Testing For Mortgage Loan Portfolios
Introduction testing of loan portfolios is a concept that has been around for many years, but as an outgrowth of the credit crisis, stress testing has become much more important, both as a regulatory requirement and as an internal risk management tool. While the level of sophistication of internal stress testing varies widely across institutions (for many reasons), regulatory stress testing of loan portfolios has become a systematic yet complex process that integrates multiple functions and disciplines such as credit risk, corporate finance, statistical/econometric modeling, and information technology. The level of rigor required by post-crisis regulatory stress testing protocols such as CCAR (Comprehensive Capital Analysis and Review) and DFAST (Dodd-Frank Act Test) have presented challenges for even the most sophisticated financial institutions. For the most recent round of CCAR testing, several of the largest 8 banks were required to either resubmit their stress testing results or overhaul their capital plans, indicating a strong need to understand quickly how a portfolio will fare before submitting the results to the regulators. As the standardized stress testing mandate is applied to smaller institutions, many will face operational challenges alone in responding promptly, separate from the capital implications that will be revealed. Background Traditional Testing Traditional stress testing historically has addressed both intrinsic value and measures of credit risk (e.g., loan losses). testing has incorporated deterministic stresses on individual and multiple risk factors. An example of a stress test on an individual risk factor is the interest rate sensitivity of a loan portfolio, as measured by the DV, or the change in portfolio value that results from a % change in interest rates. Depending on the type of loan, the changes in interest rates may be as simple as a direct change to interest earnings, or they may be more complicated, such as when changes in interest rates drive prepayment or default behavior for a mortgage loan (incentive to refinance vs. payment shock that might lead to default). Further, traditional stress testing tends to vary one risk factor at a time, possibly in different ways, to isolate its effect on the portfolio. Revisiting the interest rate stress test example, additional scenarios can be created that may steepen or flatten the yield curve, which may produce different results for the portfolio than simple parallel up/down shifts of rates. 4 by Opera Solutions, LLC. All rights reserved.
In some instances, analysts will design stress testing scenarios that vary multiple risk factors simultaneously. These may be completely theoretical or based on specific historic situations, such as a major stock market collapse or interest rate spike. When done properly, this can be a useful way to see how a portfolio reacts under more complex hypothetical scenarios. However, strong expertise is required, as there is appreciable risk that the scenarios may be designed unrealistically. Also, as more factors are varied at once, the odds of producing meaningless scenarios increase. When altering several risk factors concurrently, it is important to consider the degree to which each factor is correlated with all of the others and to design stress testing scenarios that have logically consistent interactions between the variables. Traditional stress testing does not generally involve advanced methodologies, such as Monte Carlo simulation, in which random, probability-weighted realizations of one or more risk factors are sampled to create hypothetical, state of the world scenarios against which a portfolio is analyzed. When done properly, correlations between the risk factors, usually based on past history, will help produce realistic scenarios that are sampled according to probability of occurrence. While Monte Carlo simulations have many important applications, including the determination of key risk measures, such as Value at Risk (VaR) or quantifying the potential range of future credit losses, it is not typically associated with stress testing. The likelihood of the simultaneous realization of multiple risk factors, which is controlled for in a simulation through the statistical sampling process, is not generally relevant to stress testing, as the goal is to determine how a portfolio will react under a particular view of the economy, markets, and so on without regard to probability of occurrence. Both deterministic stress testing and simulation-based methods continue to have important applications to internal risk management. However, we now focus on regulatory stress testing, in particular the CCAR/DFAST scenarios prescribed by the Federal Reserve, FDIC, and the OCC, which involve only deterministic stress testing scenarios that vary several risk factors simultaneously. Regulatory Testing d on Credit Models Statistical models that predict credit risk have been and continue to be a basis for stress testing in addition to their everyday uses, such as estimating loan loss reserves and performing portfolio valuations. Such loan-level models are often of the following form: EL = PD x LGD x EAD, in which EL refers to the Expected Loss, PD is the Probability of Default, LGD is Loss Given Default (the fraction of the loan exposure that would be lost in the event of default, also known as Loss Severity or LS), and EAD is the Exposure At (the time of) Default, also known as the outstanding balance in the time period when a default occurs. For mortgages (both residential and commercial), models that predict PD, LGD, and EAD are often indexed by time: EL t = PD t x LGD t x EAD t, where t represents the time period or loan age (often in months). Thus, PD, LGD, and EAD are themselves functions of time. 4 by Opera Solutions, LLC. All rights reserved.
The primary advantage of using loan-level credit models is to minimize the potential for adverse treatment under the stress testing. A bottom-up approach that uses more detail regarding the loans in the portfolio typically leads to better accuracy in the expected loss estimates; without loan-level analysis, more assumptions need to be used. In the context of stress testing, such assumptions are often conservative or they ignore key risk drivers, either of which can lead to higher expected losses than what would be estimated by a loan-level approach. The main drawback to using a loan-level approach is the availability of relevant data. Inaccurate or missing data for key risk drivers, such as the Debt Service Coverage Ratio (DSCR) for commercial real estate loans or credit scores for residential loans, may necessitate data collection and/or cleaning efforts, making various assumptions, or both. However, most models are designed to accommodate some amount of missing information through proxies or otherwise have defensible default assumptions in place. Also, collecting and organizing the type of loan-level data needed for stress testing has additional benefits, as it often results in better storage of and access to the information, making it readily available to support other portfolio management objectives. An alternative to the loan-level analysis is a top-down approach that relies on historical loan portfolio losses. In this approach, a lender s actual history is used to establish a baseline loss expectation upon which stresses are layered, such that losses under various scenarios are estimated as multiples of historical losses. While generally easy to do, such an approach has serious limitations. Depending on the historical period used for the baseline and the underwriting standards that were in place at the time, the portfolio may have been exposed to severe economic periods, shifting underwriting standards, or both. Therefore, past performance might not provide an appropriate loss performance basis for the current portfolio. As an illustration, a lender whose loan loss experience spans from 8 to likely would have experienced large losses during those years and thus would generate high-stress loss estimates, as the portfolio was exposed to a severe economic period brought about by the credit crisis. A time series of commercial real estate loan charge-off rates from the Federal Reserve is shown in Figure. The Historical line represents the actual industry charge-off rates; the Reverse Average line shows the cumulative average charge-off rate going backward in time. A portfolio of loan originations that began in 8 would have had an average annual charge-off rate of.8% to date (peaking at.9% in late 9). By contrast, a newer portfolio that began originating loans in would have had an average rate of about % to date with a peak at the beginning of of.8%..5 Figure : Historical CRE Charge-Off Rates. Historical Reverse Average Charge-Off Rate (%).5..5..5 Q 99 Q 996 Q Q 6 Q 4 by Opera Solutions, LLC. All rights reserved.
4 Further, a 8 portfolio might look much different today than it did when it was originated. Many of the weakest credits likely would have already defaulted, leaving behind a portfolio of survivors with a healthier portfolio credit profile overall. Yet under a top-down historical loss approach, it would be treated with loss assumptions based on the performance of an older, lower-quality portfolio. In addition, given the dramatic impact of the credit crisis on loan performance, lenders who survived are likely to have tightened, or at least maintained, their underwriting standards, which would result in better average loan credit quality going forward compared with the loan quality in the past. Finally, even if a top-down approach is augmented through the analysis of losses versus key risk drivers, aggregations across loans may skew the results if relationships between defaults or losses and those drivers are nonlinear, which is quite common among many asset classes. For example, Figure shows an empirical relationship between DSCR and PD for commercial real estate loans. Note that the rate of change in PD varies depending on the value of DSCR, rather than being constant across DSCR (which would appear as a straight line). Therefore, even knowing the average DSCR of a portfolio is not sufficient to estimate the portfolio s average PD. However, at the loan level, such a relationship can be used to produce reliable estimates of PD, and ultimately expected losses, using a bottom-up approach. 4% Figure : PD vs. DSCR @LTV=6 Probability of Default.5.6.7.8.9.....4.5 DSCR Returning now to loan-level models, PD and LGD are typically derived from the statistical analysis of historical loan performance data. These components of expected loss are driven by certain risk factors. For example, for residential real estate, borrower creditworthiness, as often measured by credit score, is known to be a critical driver of PD. Similarly, loan-to-value ratio, or LTV, is known to drive both PD and LGD. Further, some risk factors may change over time. LTVt, or the LTV ratio at time=t, represents a dynamic risk factor that changes as a function of both asset price movements and outstanding loan balance. Other risk factors may also be relevant and may be either static or dynamic, such as loan payment amount for adjustable-rate mortgages. Another example is the Debt Service Coverage Ratio, or DSCR, for commercial mortgages. This is the ratio of the income generated by the underlying property and the amount of debt service (loan payment). DSCR can become dynamic if the property income varies over time or if the debt service changes over time (e.g., larger interest payments from floating rate resets). 4 by Opera Solutions, LLC. All rights reserved.
5 By contrast, EAD is a function of the amortization type, or term structure, of the loan. For example, if the loan is a simple amortizing loan, the EAD will decrease over time based on an amortization curve. However, if the loan contains an interest-only (IO) period, followed by an amortization period, then the EAD will reflect a flat period (during the IO) followed by a decline (during amortization). As a special consideration for commercial real estate loans, the debt service component of the DSCR is a function of the term structure of the loan, thus making it a dynamic factor (i.e., DSCR t ) in the PD model. Tables and list typical risk drivers used in PD and LGD models for residential and commercial real estate loans. Table : Residential PD, LGD Drivers Table : Commercial PD, LGD Drivers Credit Score LTV (driven by value, term structure) Property type Location Term structure Lien position Interest rates (macro factor) Unemployment rate (macro factor) Occupancy type Performance history DSCR (driven by income, term structure) LTV (driven by value, term structure) Property type Location Term structure Lien position Interest rates (macro factor) Income (driven by macro factors) Value (driven by macro factors) Performance history Regulatory Testing Macroeconomic Risk Factors Beyond static and particular amortization-based risk factors that help predict PD and LGD over time, certain external, macroeconomic factors also need to be taken into consideration. Some of the components, such as residential home prices (as measured by home price indices), affect loans LTV ratios. Others, such as unemployment rates, can impact PDs on their own (i.e., not as part of another factor, such as LTV). Various macroeconomic factors, such as interest rates, have been mentioned already. However, there are others that can be shown statistically to impact PD and LGD (directly or through other risk factors) and therefore must be incorporated into the credit model. Once there, these dynamic factors provide a basis for constructing stress testing scenarios. This is the essence of the regulatory stress tests. Table shows a list of the macroeconomic factors prescribed by the Federal Reserve to be used in the previous CCAR stress tests. Further, the Fed also provides the assumptions over time for each of these factors. Note that the Fed specifies three deterministic scenarios: baseline, stress, and severe stress. Each of these scenarios is defined by the respective sets of assumptions for each of the macroeconomic factors. Figures a d show graphically the Fed s assumptions over time for four of the macroeconomic factors in the severe stress scenario; a complete list is available from the CCAR website (http://www.federalreserve.gov/bankinforeg/bcreg5a.xlsx). 4 by Opera Solutions, LLC. All rights reserved.
6 Table : CCAR US Macroeconomic Factors Real GDP growth Nominal GDP growth Real disposable income growth Nominal disposable income growth Unemployment rate CPI Inflation -month Treasury yield -year Treasury yield BBB corporate yield Mortgage rate Dow Jones Total Stock Market Index Market Volatility Index (VIX) House Price Index Commercial Real Estate Price Index Note that the set of macroeconomic factors and their assumed values are subject to change. The ones displayed above reflect the assumptions provided for stress testing; it is expected that the Fed will publish its assumptions for 4 before the end of this year. Figure a: Real GDP Growth () 5 History Projection 5-5 - 976 98 988 994 6 4 Figure b: Unemployment Rate () 8 6 4 History Projection 976 98 988 994 6 4 by Opera Solutions, LLC. All rights reserved.
7 8 Figure c: DJ Total Stock Index () 5 History Projection 9 6 976 98 988 994 6 5 Figure d: US Home Price Index () 5 History Projection 5 976 98 988 994 6 From Figures a d, it is clear that in the severe stress scenario, the Fed is assuming very harsh conditions (by historical standards) for several of the macroeconomic factors over the first five quarters of the projection, followed by nearly equally aggressive recoveries over the following eight quarters. This is expected to cause significant near-term stress on many portfolios. However, the evaluation period for CCAR is nine quarters out, or four quarters into the assumed recovery. Depending on the portfolio, this allowance for some economic improvement should mitigate some of the earlier portfolio performance impact while allowing banks some time to strengthen their capital position. While the Fed has provided this list of macroeconomic factors and specified its assumptions to use for stress testing, it does not provide guidance as to which factors are relevant for different asset types. To establish relevance, Opera Solutions statistically estimated the empirical relationships between each of the prescribed macroeconomic factors and PDs, LGDs, or their various dynamic components (such as property income and value for commercial real estate). For this, we matched historical time series data for each macroeconomic factor (kindly provided by the Fed) to the historical loan and property performance data in the respective time periods. In other words, we incorporated the regulatory list of factors directly into our statistical regression models. Noting fundamental differences between residential and commercial real estate loans, incorporation of the macroeconomic data into the commercial real estate model is done slightly differently compared with how data is incorporated into the residential model. For the latter, we used regression to capture the relationships between the macroeconomic factors and PD and LGD directly. However, for commercial real estate, supplemental historical data from Reis, the industry leader in commercial property data and analytics, was used to develop a series of statistical models that relate changes in property income and value directly to the macroeconomic factors. In this way, a set of assumptions for factors such as GDP, unemployment, and others are used to drive future paths of property income and value, which in turn affect DSCR and LTV over time, and thus also affect PD and LGD. 4 by Opera Solutions, LLC. All rights reserved.
8 Examples Figures 4a and 4b show the impact of the CCAR macroeconomic stresses on net operating income (NOI) and property value (Value) for a single commercial real estate loan (shown as changes from the starting values), backed by the income and value from one property. Figures 4c and 4d show how the resulting NOIs and Values translate into DSCR and LTV; Figures 4e and 4f show the final impact on PD and LGD. After the initial shock to PD and LGD resulting from the CCAR assumptions, a rapid recovery takes place until Year (Quarter )... Figure 4a: Impact of CCAR on NOI.. Figure 4b: Impact of CCAR on Value NOI(t) / NOI()..9.8.7 Value(t) / Value()..9.8.7.6.6 Figure 4c: DSCR(t) d on NOI(t) Figure 4d: LTV(t) d on Value(t). 8%.. 6 DSCR(t)..8.7 LTV(t) 4.6 Figure 4e: PD(t) Driven by DSCR(t), LTV(t) Figure 4f: LGD(t) Driven by LTV(t) % 8% 8 6 PD(t)` 6 LGD(t) 4 4 v An additional observation is that the recovery for the severe stress scenario is more aggressive than for the stress scenario, such that in the final period of the Fed s projection horizon, the marginal PD and LGD are actually slightly lower for the severe stress than for both of the other scenarios. Still, with larger losses in the first quarter of the analysis, the intended effect of the stress testing assumptions is clearly seen throughout the critical period (nine quarters) of the projection horizon. 4 by Opera Solutions, LLC. All rights reserved.
9 Figure 5: Mobiuss CCAR Results Expected Loss Rate (%).8%.6.4...8.6 Expected Loss Rate Over Time Scenario Comparison CCAR Severe Year: 4 EL:.% Quarter 9 measurement period for CCAR CCAR line CCAR Adverse CCAR Severe Summary Credit Measures Scenario PD (%) LS (%) EL (%) EL ($M) CCAR line CCAR Adverse CCAR Severe 4.6 8.87.7 4. 4.8.57.48 5.9 5. 4.4.7 6.5.4 4 5 6 7 8 9 Year Figure 5 shows the results of CCAR stress testing on a typical commercial real estate portfolio as captured by our mortgage analytic platform, Mobiuss. Note the significant jump at the outset in cumulative expected losses for the severe stress scenario compared with those from the other scenarios; the cumulative loss curves become nearly parallel thereafter. The initial offset between the scenario curves is due to increasingly harsh macroeconomic assumptions over the first year while periods of recovery follow that eventually return expected losses under each scenario to approximately similar growth rates. Note: for regulatory capital reporting, the first period of the forecast begins in Q4, such that the ninth-quarter measurement period occurs in Q4 4, represented by 4 in the graph. Conclusion Opera Solutions expects rigorous regulatory stress testing to be an important part of a bank s capital adequacy assessments for the foreseeable future. While arguably arbitrary, a consistent set of scenarios applied to each institution will allow relative comparisons among them, possibly enabling the regulators to identify potential problems in advance. Institutions electing to proactively run the regulator s stress tests will be in a much better position to know where they will stand in the eyes of the regulator before having to submit their results and would be in a position to remediate any capital issues that are identified well in advance of their review. Further, the mechanics presented here for conducting regulatory stress testing can be leveraged by banks to design their own stress testing scenarios to answer questions from their internal stakeholders, including risk, underwriting, finance, portfolio management, operations, and others. Jersey City Boston San Diego London Shanghai New Delhi ABOUT OPERA SOLUTIONS, LLC Opera Solutions (www.operasolutions.com, @OperaSolutions) combines advanced science, technology, and domain knowledge to extract predictive intelligence from Big Data and turn it into insights and recommended actions that help people make smarter decisions, work more productively, serve their customers better, grow revenues, and reduce expenses. Its hosted solutions, delivered as a service, are today delivering results in some of the world s most respected organizations in financial services, healthcare, hospitality, telecommunications, and government. Opera Solutions is headquartered in Jersey City, NJ, with other offices in North America, Europe, and Asia. For more information, visit the website or call -855-OPERA-. 4 by Opera Solutions, LLC. All rights reserved.