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This article focuses on model building from a bottom-up perspective of mortgages and home equity lines of credit to underscore the importance of loan-level analytics.

The role of stress testing goes beyond regulatory requirements and forms an integral component of risk management. With the right tools, a risk manager can understand, hedge, and reduce risks in their bank’s retail credit portfolio, which consist of consumer loans, primarily in the form of mortgages and home equity lines of credit, auto loans, and credit cards.

A bottom-up approach

You can perform stress testing in one of two ways – either an aggregate level “top-down” approach or an account level “bottom-up” approach. In the top-down approach, loan-level data is aggregated along a few dimensions. Models for different performance measures can be built at this aggregate or “repline” level. In the bottom-up approach, models are built at the loan level. The performance results can then be aggregated at any level of granularity. An effective stress testing program will often include multiple models using both approaches.

Modeling at the account level offers several advantages to risk managers. First, loan-level models provide capital requirements and risk assessment at the highest level of granularity. This level of detail is often useful in understanding and hedging risk. For example, loans with high capital requirements could be hedged against or traded. Risk managers can identify other dimensions of concentration risk, such as geographic risk, by determining loan-level contributions to the Value-at-Risk (VaR) of the portfolio. Second, if the portfolio is highly heterogeneous in composition, an account-level analysis allows managers to identify the outliers in the portfolio population. Often, the portfolio risk depends more on the outliers in the portfolio than on the average loan. For example, if the average Loan-to-Value (LTV) of the portfolio is 60, but a few loans have an LTV of 100, the loss of the portfolio in various scenarios depends largely on the heterogeneity of the portfolio. As the expected loss is a non-linear function of the LTV, the portfolio expected loss cannot be accurately determined by the average LTV. In cases with a large number of risk factors and their interactions, a bottom-up approach can offer a reliable means for an accurate and exhaustive risk analysis.

The complexity of mortgage modeling

There are several different types of mortgages – fixed rate loans of different terms, adjustable rate mortgages (ARM) with different fixed rate periods, underlying indices, reset frequencies, and terms, loans with Interest Only (IO) features, first and second lien loans, and loans with balloon payments. The nominal default and prepayment rates for different types of mortgages differ considerably, not only in the average value, but also through time. For example, the default rate for an ARM loan with a fixed rate period of three years is the highest when the loan is about three years old, because that is when the rate resets. On the other hand, the default rate for a fixed rate loan is the highest in the first couple of years.

There are other complexities as well in modeling defaults and prepayments. The sensitivities of defaults and prepayments to risk factors such as the LTV or mortgage premium are dependent on the FICO of the borrower. To model this behavior, we need to consider the joint interaction of FICO and LTV, or FICO and loan amount, in the default and prepayment models. The dependence of default and prepayment on each of the model factors is non-linear. Often, the default or prepayment rate “levels off” beyond a certain value of the loan or borrower characteristic.

Loans from different vintages behave very differently. The prevailing underwriting standard at origination plays a role in determining the riskiness of the loan. Moreover, the age of the loan, the home price changes since origination, the changes in unemployment rates and mortgage rates since origination, and the interest rate at origination all play an important role in determining the prepayment and default risk of a loan.

Some high LTV loans have mortgage insurance. If the loan defaults, the mortgage insurer pays a portion of the gross loss on the loan. If a pool of loans is securitized, the mortgage insurer may insure the aggregate losses on the pool. Mortgage insurance introduces significant nonlinearities in the expected loss of the portfolio.

All these features make residential mortgages one of the most difficult products to model. Moody’s Analytics has built econometric models for default, prepayment, and loss given default (LGD) using macroeconomic variables and loan and borrower characteristics. The correlation between the defaults, prepayments, and LGD of different loans is driven by the dependence on common macroeconomic variables.

Modeling at the account level offers several advantages to risk managers. First, loan-level models provide capital requirements and risk assessment at the highest level of granularity. Second, if the portfolio is highly heterogeneous in composition, an account-level analysis allows managers to identify the outliers in the portfolio population.

Stress testing a portfolio

Portfolios can be stressed in several ways. Risk managers could increase the probabilities of default (PD) and LGD for each asset or increase the default correlation between different assets. A more intuitive and consistent approach is to stress the macroeconomic environment by lowering the GDP and home prices and raising the unemployment rate. As the behavior of the borrower depends on the macroeconomic environment, stressing the economy produces an increase in the PD and LGD of the underlying loans. The default correlation increases due to the dependence on common, stressed, macroeconomic factors.

Risk managers need tools for stressing the economy and can use pre-determined stress scenarios or the Fed CCAR stress scenarios. Alternatively, they could view the behavior of a few macroeconomic variables. Moody’s Analytics has developed an approach for determining, through maximum likelihood estimation, a consistent set of values for all the other relevant macroeconomic variables. With this tool, a risk manager can create custom scenarios to stress a portfolio.

The same loan-level credit risk models can be used in simulation. Given a distribution of macroeconomic scenarios centered on a baseline scenario, a risk manager can determine distributions of losses for the portfolio. They can then determine the VaR of the portfolio and the contribution to the VaR from each loan in the portfolio.

Extending stress testing to other asset classes

The loan-level models can be used not only for analyzing portfolios of whole loans, but also for stress testing RMBS tranches. In a multi-period setting, the collateral cash flows can be generated through time under different macroeconomic conditions. The timing of these cash flows can be important when analyzing tranches of RMBS transactions. When integrated with a waterfall tool, risk managers can determine tranche-level cash flows, tranche loss distributions, and prices and expected losses on tranches.

Portfolios can be stressed in several ways… the more intuitive and consistent approach is to stress the macroeconomic environment by lowering the GDP and home prices and raising the unemployment rate.

Once loan-level models are built using macroeconomic factors, the correlations between different types of consumer loans is automatically incorporated through their dependence on common macro variables. A retail portfolio consisting of all consumer loans and structured finance securities backed by consumer loans can then be analyzed in a consistent manner by stressing the same set of macro variables. This level of consistency is an important element of an effective portfolio stress testing program.

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