Board of Governors of the Federal Reserve System

Descriptions of Supervisory Models

Pre-provision Net Revenue

PPNR is defined as net interest income (interest income minus interest expense) plus noninterest income minus noninterest expense, including losses from operational-risk events and OREO expenses.³²

Core Components of PPNR

The Federal Reserve projects components of PPNR, other than operational-risk and OREO losses, using a suite of models that generally relate specific revenue and non-provision-related expenses to firm characteristics and macroeconomic variables. These models are primarily estimated using data from the FR Y-9C and FR Y-14Q and data on historical economic conditions. When choosing the level of detail at which to model these core components of PPNR, the Federal Reserve considers the economic factors driving each component and other factors, such as the statistical properties of the individual income or the expense component and data availability. The PPNR components are projected using firm-reported data and economic conditions defined in the Federal Reserve's supervisory stress test scenarios.

The key firm characteristics that affect projected revenues and expenses include

• average historical values of the income or expense components and
• composition and size of assets and liabilities.

Revenues and expenses projected by the models vary based on changes in the economic conditions over the nine quarters of the projection horizon. Those include

• interest rates,
• stock market returns and volatility,
• corporate bond spreads, and
• GDP growth.

The Federal Reserve uses separate models to project 24 PPNR components:³³

• The eight modeled components of interest income include interest income on (1) federal funds and repurchase agreements, (2) interest-bearing balances, (3) loans, (4) mortgage-backed securities, (5) other securities, (6) trading assets, (7) U.S. Treasuries, and (8) all other interest income.
• The seven modeled components of interest expense include interest expense on (9) domestic time deposits, (10) federal funds and repurchase agreements, (11) foreign deposits, (12) other domestic deposits, (13) subordinated debt, (14) trading liabilities and other borrowed money, and (15) all other interest expenses.
• The six modeled components of noninterest income include (16) trading revenue and the following five components of noninterest, nontrading income: (17) fiduciary income and insurance and banking fees, (18) investment banking fees, (19) net servicing fees, (20) service charges on deposits, and (21) all other noninterest income.
• Finally, the three modeled components of noninterest expense include (22) compensation expense, (23) fixed asset expense, and (24) all other noninterest expense, excluding losses from operational-risk events and OREO expenses.

The types of models used to project various components of PPNR include

• autoregressive models that relate the components of a firm's revenues and non-provision-related expenses, expressed as a share of the relevant asset or liability balance, to macroeconomic variables, recent past values of the revenue or expense ratio, firm characteristics, and other controls;
• aggregate models that relate industry revenue or expense to macroeconomic variables and then allocate industry revenue or expense to each firm based on a measure of the firm's market share;
• simple nonparametric models based on recent firm-level performance; and
• structural models that use granular data on individual positions.

For all models, excluding the structural models that use granular data on individual positions, each component of PPNR is normalized by a relevant asset or liability balance (see table 1). For example, interest income on U.S. Treasuries is divided by the value of U.S. Treasuries.

The Federal Reserve models 20 of the 24 core PPNR components using an autoregressive model specification based on pro-forma historical regulatory data drawn primarily from firms' quarterly FR Y-9C filings. The pro forma data is created historically to reflect eventual acquisitions in order to create time series consistent with banks' current mix of businesses. The autoregressive term in each model is the mean of the dependent variable calculated over the past four quarters.

Each autoregressive model includes both individual firm fixed effects and a trailing multiyear fixed effect to capture each firm's average performance in recent years.³⁴ As a result, projections for these 20 PPNR components converge over time toward the firm's recent average performance for that revenue or expense category, while still allowing for variation in response to changes in macroeconomic conditions. Recent changes in a firm's business model or performance are reflected in the projections through both changes in the recent average PPNR ratios and changes in lagged revenue or expense ratios via autoregressive terms.³⁵

The models are generally specified according to the following equation:

$$Ratio\left( b,t \right)=f\left( \sum\nolimits_{j=1}^{j=4}{\tfrac{Ratio(b,t-j)}{4}},~FE\left( b \right),~FE\left( b)\text{*}Ind(T-Q<t\le T \right),~Z\left( t \right),~X\left( b,t \right) \right)$$ (1)

where b represents the firm, t represents time, Ratio(b,t) represents the component ratio, $$\sum\nolimits_{j=1}^{j=4}{\tfrac{Ratio(b,t-j)}{4}}$$ represents the mean of the lagged component ratio over the past four quarters where j is the lagged quarter, FE(b) represents the fixed effect for firm b, FE(b)* Ind(T–Q<t≤T) represents the trailing multiyear fixed effect for the last Q quarters for firm b where T is the end of the estimation period, Z(t) represents one or more of the macroeconomic variables included in the supervisory scenarios, and X(b,t) includes firm characteristics and other controls, such as seasonal factors in some equations.

The specific macroeconomic variables that enter each regression model differ across equations and are chosen based on statistical predictive power and economic theory. For example, yields on U.S. Treasuries are key variables in the models of the interest income and expense components, while GDP growth, stock market volatility, and stock returns are featured in many of the models of the noninterest expense and noninterest income components.

Some components of PPNR are estimated separately for groups of similar firms. Because these components span a relatively broad range of business lines and borrowers, the model structure for these components allows for a different relationship between macroeconomic variables and revenues across different types of firms. Regressions are estimated separately for specific groups for noninterest income from investment banking fees, interest expense on trading liabilities and other borrowed money, trading revenue, and compensation expense.

For firms subject to the global market shock, the Federal Reserve models trading revenues in the aggregate as a function of stock market returns and changes in stock market volatility and allocates revenues to each firm based on a measure of the firm's market share. Firms' trading revenues include both changes in the market value of trading assets and fees from market-making activities. Trading revenue for this group of firms is modeled using a median regression approach to lessen the influence of extreme movements in trading revenues. Trading revenues for remaining firms are modeled in an autoregressive framework similar to that of other PPNR components.

The Federal Reserve models certain components using simple, nonparametric models. These components are highly volatile from quarter to quarter but do not exhibit a clear cyclical pattern. As a result, these components are projected as the median of the firm's ratio over the most recent eight quarters.

Finally, the Federal Reserve projects interest expense on subordinated debt using a structural model that utilizes security-level data on individual positions. In contrast to the other PPNR component models, this more granular model accounts for differences across firms in the maturity, currency denomination, coupon, and rating of subordinated debt securities. The model calculates interest expense on subordinated debt as the outstanding balance multiplied by the contractual rate for each debt security collected on the FR Y-14Q, adjusted to account for unamortized costs from subordinated debt issued at a premium or discount to its face value and to account for interest rate hedging through swap agreements. Maturing debt is assumed to be refinanced using new debt with similar characteristics.

For each component that is modeled as a ratio, the Federal Reserve multiplies the projected ratios for each firm by the relevant projected asset or liability balances to transform projections into dollar amounts.³⁶

Table 1. List of variables used to construct the PPNR components

Table 2. List of key macroeconomic variables in the PPNR regression models and sources of variables

Losses Related to Operational-Risk Events

Operational-risk losses include losses stemming from events such as fraud, computer system failures, process errors, and lawsuits by employees, customers, or other parties.³⁷ The operational-risk loss model is designed to project quarterly losses over the projection horizon for each supervisory stress test scenario. The Federal Reserve estimates the model using data on economic conditions and historical data from the FR Y-14Q and FR Y-9C. The model projects losses stemming from operational-risk events using information about the size and historical operational-risk losses of the firms and economic conditions defined in the Federal Reserve's supervisory stress test scenarios. Key firm characteristics that affect projected losses include

• the size of the firm measured by total assets and
• the firm's historical operational-risk losses by operational-risk event.

The losses projected by the model vary across scenarios based on differences in the defined economic conditions over the nine quarters of the projection horizon.

Operational-risk loss estimates are derived as the average of projections from two modeling approaches: a linear regression model and a historical simulation model.³⁸ The regression model captures the sensitivity of operational-risk losses to changes in the macroeconomic environment; the simulation model captures the variation in operational-risk losses across types of operational-risk events.³⁹

The regression model projects aggregate operational-risk losses for the industry over the projection horizon and allocates those losses to firms based on their size. The model projects operational-risk losses conditional on macroeconomic factors, except for those losses due to damage to physical assets.⁴⁰ The regression model is specified as follows:

$$OpLossRatio\left( t \right)=f\left( PC\left( t \right) \right),$$ (2)

where t represents time, OpLossRatio(t) represents the industry aggregate loss divided by industry aggregate assets in quarter t, and f(PC(t)) represents the function of the first principal component of a set of macroeconomic variables, which include measures of economic activity, financial conditions, and the interest rate environment (see table 3). The share of losses allocated to a given firm is a function of the size of the firm, measured in total assets, on the effective date of the stress test.

The historical simulation model projects operational-risk losses for each firm and for each of the seven operational-risk categories identified in the Board's regulatory capital rule. The model accounts for large and infrequent operational-risk losses by projecting loss frequency (number of loss events) and severity (dollar value of each loss event) separately.⁴¹ The tails of the loss severity and the loss frequency distributions are informed by historical industry loss severity and loss frequency amounts scaled to the assets of individual firms, while the bodies of these distributions are informed by each firm's historical loss severity and loss frequency. Frequency and severity are then combined to form an unconditional loss distribution.⁴² The projected nine-quarter loss under the supervisory severely adverse scenario corresponds to the loss at a percentile related to the frequency of severe recessions.⁴³ Total projected operational-risk losses are calculated as the sum of projected losses for each operational-risk event type.

Table 3. List of key variables in the operational-risk model and sources of variables

Loan Losses and Provisions on Loans Measured at Amortized Cost

The Federal Reserve estimates losses for loans measured at amortized cost separately for different categories of loans, based on the type of obligor (e.g., consumer or commercial and industrial), collateral (e.g., residential real estate or commercial real estate), and loan structure (e.g., revolving credit lines).⁴⁴ These categories generally follow the classifications of the FR Y-9C, though some loss projections are made for more granular loan categories.

The Federal Reserve uses more than a dozen individual models to project losses on loans measured at amortized cost. The individual loan types modeled can broadly be divided into wholesale loans, such as C&I loans and CRE loans, and retail loans, including various types of residential mortgages, credit cards, student loans, auto loans, small-business loans, and other consumer loans.

For most loan types, losses in quarter t are estimated as the product of the projected PD, LGD, and EAD:

$$Loss(t)=PD(t)*LGD(t)*EAD(t).$$ (3)

The PD component measures the likelihood that a borrower enters default status during a given period t. The other two components capture the lender's loss on the loan if the borrower enters default. The LGD component measures the percent of the loan balance that the lender will not be able to recover after the borrower enters default, and the EAD component measures the total expected outstanding loan balance at the time of default.

Borrowers enter default if their recent payment history indicates that they will no longer make payments on a loan. The Federal Reserve's definition of default, for modeling purposes, may vary for different types of loans and may differ from general industry definitions or classifications. The Federal Reserve generally models PD as a function of loan characteristics and economic conditions. The Federal Reserve typically models LGD based on historical data, and modeling approaches vary for different types of loans. For certain loan types, the Federal Reserve models LGD as a function of borrower, collateral, or loan characteristics and the macroeconomic variables from the supervisory scenarios. For other loan types, the Federal Reserve assumes LGD is a fixed percentage of the loan balance for all loans in a category. Finally, the approach to modeling EAD varies by loan type and depends on whether the loan is a term loan or a line of credit.

For other loan categories, models capture the historical behavior of net charge-offs as a function of macroeconomic and financial market conditions and loan portfolio characteristics. The Federal Reserve then uses these models to project future charge-offs consistent with the evolution of macroeconomic conditions under the supervisory scenarios. To estimate projected losses, the projected net charge-off rate is applied to projected loan balances.

Wholesale Loans: Corporate Loans

Corporate loans consist of a number of different categories of loans, as defined by the FR Y-9C. These loans include graded C&I loans, agricultural loans, domestic farm loans, international farm loans, loans to foreign governments, loans for purchasing and carrying securities, other non-consumer loans, and other leases. The largest group of these loans is C&I loans, which are generally defined as loans to corporate or commercial borrowers with more than $1 million in committed balances that are graded using a firm's corporate loan rating process. The corporate loan model projects quarterly losses on these loans over the projection horizon of each stress test scenario.

The Federal Reserve estimates the model using historical data on corporate payment status and loan losses, loan characteristics, and economic conditions. The model projects these losses at the loan level in an expected-loss modeling framework, using data on firm-reported loan characteristics from the FR Y-14Q and economic conditions defined in the Federal Reserve's supervisory stress test scenarios.⁴⁵ Some of the key loan characteristics that affect projected losses include

• loan credit rating,
• the industry of the borrower,
• the country in which the borrower is domiciled, and
• whether or not the loan is secured.

The losses projected by the model for a given loan vary based on changes in the defined economic conditions over the projection horizon.⁴⁶ Those include

• GDP growth,
• unemployment rate, and
• corporate bond spreads.

The PD component assumes that the probability that a loan defaults depends on macroeconomic factors such as the unemployment rate. The Federal Reserve defines corporate loans as in default when they are 90 days or more past due or in non-accrual status as of the effective date for the stress test. The model first calculates the loan's PD at the start of the projection horizon and then projects it forward using the estimated relationship between historical changes in PD and changes in the macroeconomic environment.

The model calculates the initial PD, which is the PD at the start of the projection horizon, as the long-run average of expected default probabilities. Expected default probabilities are measures of the PD based on a structural model that links the value of a firm to credit risk. The initial PD for publicly traded borrowers reflects a borrower-specific expected default probability. The model bases the initial PD for other borrowers on the average expected default probability for the industry, country, and rating category group in which the borrower is classified. A borrower's industry and country category are directly observed in the firm-reported data, and the rating category is derived from the firm-reported internal credit rating for the borrower and firm-reported data that are used to map the internal rating to a standardized rating schedule.

The model projects PDs over the projection horizon using equations fitted to the historical relationship between changes in the expected default probabilities and changes in macroeconomic variables. The model estimates the equations separately by segments based on borrower industry, rating category, and country of borrower domicile in a regression framework.

The model specifies the change in PD for a given segment from period t-1 to t:

$$\Delta PD(t)=f(Z(t)),$$ (4)

where t represents time, ΔPD(t) represents the change in PD, and Z(t) represents changes in one or more of the macroeconomic variables included in the supervisory scenarios.

These segment-level changes in PD estimated in equation (4) are applied to the loan-level initial PDs to calculate a loan-level path of PDs over the projection horizon.

The Federal Reserve uses firm-reported data on business lines and whether a loan is secured or unsecured to set the initial LGD for performing loans at the start of the projection horizon. In cases in which the loan has already been identified as troubled the model bases initial LGD on the size of the reserve set aside and PD is set to 100 percent. For foreign loans, the model also adjusts initial LGDs based on the country in which the obligor is domiciled, capturing differences in collateral recovery rates across countries.

The model projects LGD for loan i at time t as a function of PD as follows:⁴⁷

$$LGD\left( i,t \right)=f\left( LGD\left( i,t-1 \right),~PD\left( i,t \right),PD\left( i,t-1 \right) \right),$$ (5)

where LGD represents the loss given default and PD represents the probability of default.

For closed-end loans, the EAD is the outstanding balance.⁴⁸ For standby letters of credit and trade finance credits, EADs are conservatively assumed to equal the total commitment since typically these types of credits are fully drawn when they enter default status. For lines of credit and other revolving commitments, the EAD equals the outstanding balance plus a portion of the unfunded commitment (i.e., the difference between the committed exposure and outstanding balance), which reflects the amount that is likely to be drawn down by the borrower in the event of default. The Federal Reserve calibrates the amount that is likely to be drawn down to the historical drawdown experience for defaulted U.S. syndicated revolving lines of credit that are in the Shared National Credit (SNC) database.⁴⁹ The model sets the EAD for a line of credit or other revolving product as follows:

$$EAD\left( i \right)=OB\left( i \right)+LEQ*\left( C\left( i \right)-OB\left( i \right) \right),$$ (6)

where i represents the revolving product or line of credit, EAD(i) represents the EAD, OB(i) represents the line's outstanding balance at the start of the projection horizon, LEQ represents the calibrated drawdown rate, and C(i) represents the line's committed balance at the start of the projection horizon.

Table 4. List of key variables in the corporate loan models and sources of variables

Wholesale Loans: Commercial Real Estate Loans

CRE loans are defined as loans collateralized by domestic and international non-owner-occupied multifamily or nonfarm, nonresidential properties, and C&LD, as defined by the FR Y-9C.

The Federal Reserve estimates the model using historical data on CRE payment status and loan losses, loan characteristics, and economic conditions. The model projects these losses with an expected-loss modeling framework, using data on firm-reported loan characteristics for CRE loans with $1 million or more in committed balances from the FR Y-14Q and the economic conditions defined in the Federal Reserve's supervisory stress test scenarios.⁵⁰ Some of the key loan characteristics that affect projected losses include

• the loan type (i.e., income-producing or C&LD),
• the property type (e.g., multifamily, retail, hotel, office, and other),
• loan-to-value (LTV) ratio,
• loan size, and
• loan age and the proximity of the loan to maturity.

The losses projected by the model for a given loan vary based on changes in the defined economic conditions over the projection horizon. Those include

• corporate bond spreads,
• the unemployment rate,
• vacancy rates,
• house prices, and
• CRE prices.

The PD component assumes the probability that a loan defaults depends on loan characteristics and macroeconomic factors, such as the unemployment rate. The Federal Reserve defines CRE loans as in default when they are 90 days past due or other factors in the data (e.g., non-accrual status or other evidence of weak credit quality when its maturity was last extended) indicate that the loans are significantly impaired. The PD component projects the probability that a loan transitions from current to default status. The model assumes that the loan, once in default, does not return to current status. The Federal Reserve models the probability that a loan defaults over a single quarter using a binomial logit regression model and estimates the model using data from the FR Y-14Q collection pooled with historical loan performance data on loans securitized in commercial mortgage-backed securities (CMBS).

The PD model is specified as

$$PD\left( i,t \right)=f(\lambda \left( i,t \right),~~X\left( i,t \right),~~Z\left( t \right)),$$ (7)

where i represents the loan, t represents time, PD(i,t) represents the probability of default, λ(i,t) represents a function of the age of loan i at time t, X(i,t) represents loan and property characteristics, and Z(t) represents one or more of the macroeconomic variables included in the supervisory scenarios.

The LGD model calculates the loss conditional on a default, given the characteristics of the loan as well as macroeconomic variables at the time of default, including local commercial and local residential property prices and vacancy rates by property type. The Federal Reserve estimates the LGD for CRE loans using a Tobit model, based on industry-wide realized loss data on CRE loans. This approach accounts for the possibility that no loss may be experienced on the loan. The model sets LGD as follows:

$$LGD\left( i,t \right)=f\left( X\left( i \right),Z\left( t \right) \right),$$ (8)

where i represents the loan, t represents time, X(i) represents loan and property characteristics at the loan origination date, and Z(t) represents one or more of the macroeconomic variables included in the supervisory scenarios.

The model estimates separate equations for income-producing loans and for C&LD loans. The loan-specific risk factors include factors such as origination LTV and loan size at origination. For income-producing loans, the model also includes controls for property type (i.e., apartment, hotel, industrial, office, and retail).

The PD and LGD models use unemployment rates and house prices that are projected at the state and county levels. These models also use CRE vacancies, rents, and prices that are projected by property type at the metropolitan statistical area level.

The EAD model assumes EAD for CRE loans equals the total committed exposure amount, which is the outstanding balance of the loan plus any remaining undrawn committed amount at the start of the projection horizon.

Table 5. List of key variables in the CRE loan models and sources of variables

Retail Loans: Domestic First-Lien Residential Mortgages

Domestic first-lien mortgages are closed-end exposures that are secured by one- to four-family residential real estate located in the United States, as defined by the FR Y-9C.⁵¹

The Federal Reserve estimates the model using historical data on first-lien mortgage payment status and loan losses, loan characteristics, and economic conditions. The model projects losses on first-lien mortgages at the loan level in an expected-loss modeling framework, using data on firm-reported loan characteristics from the FR Y-14M and economic conditions defined in the Federal Reserve's supervisory stress test scenarios. Some of the key loan characteristics that affect projected losses include

• interest rate type (fixed or adjustable),
• LTV ratio, and
• borrower's credit score.

The losses projected by the model for a given loan vary based on changes in the defined economic conditions over the projection horizon. Those include

• house prices,
• the unemployment rate, and
• interest rates.

The PD component for first-lien residential mortgages projects the probability that a loan transitions to a different payment status (i.e., current, impaired, default, and paid off). The Federal Reserve defines first-lien mortgages as in default when they are 180 days or more past due or when they have gone through foreclosure or have been prepaid with loss. First-lien mortgages are defined as current if they are no more than 89 days past due and are defined as impaired if they are between 90 and 179 days past due. The Federal Reserve uses separate PD models for fixed-rate mortgages and adjustable-rate mortgages. The Federal Reserve models the probability that a loan transitions from one payment status to another (e.g., from current to impaired or from impaired to default) over a single quarter using a regression framework.

The model is a system of five binomial logit models that generate a probability of default during a quarter of the projection horizon, conditional on the loan's payment status at the end of the prior quarter. Two of these models capture the transitions from a current state to other payment statuses: impaired or paid off. Three other models represent the transition from impaired status to other statuses. Impaired loans in the model may transition back to current, paid off, or default.⁵² The model assumes default and paid-off loans to be terminal states, which means that loans cannot transition out of those states in the model.⁵³ Collectively, these models are a competing risks framework for default and prepayment and are specified as

$$\text{Pr}(Tr\left( i,t+1 \right)|S\left( i,t \right))=f\left( X\left( i,t \right),~~Z\left( t \right) \right),$$ (9)

where i represents the loan, t represents time, Pr (Tr(i, t + 1)) represents the probability that the loan transitions to another status from period t to t+1, S(i,t) represents the payment status in period t, X(i,t) represents loan and borrower characteristics, and Z(t) represents one or more of the macroeconomic variables included in the supervisory scenarios.

The historical data used to estimate this model are industrywide, loan-level data on loans held in bank portfolios from many banks and mortgage loan originators. The PD model uses equation (9) to project a probability of default and prepayment for each loan in each quarter of the projection horizon.

The LGD models estimate loss at liquidation based on a number of factors, such as housing market conditions, the foreclosure legal environment, and loan characteristics.

The Federal Reserve projects the LGD for residential mortgages using two models. One model projects the length of time that elapses between default and liquidation (liquidation timeline model); the other model projects loss severity as a function of the projected liquidation timeline, as well as characteristics of the defaulted loan (loss severity model).⁵⁴

The timeline model is estimated separately for borrowers in states in which foreclosure is conducted under judicial supervision and for non-judicial foreclosure states, using an accelerated failure time framework.

For a loan that enters default, the timeline model is specified as

$$\ln \left( T\left( i \right) \right)=f\left( X\left( i,t \right),~Z\left( t \right) \right),$$ (10)

where i represents the loan, t represents the time of default, ln(T(i)) represents the log of the length of time between default and liquidation for defaulted loans i liquidated before the end of the sample period (uncensored loans) or the remaining time until the end of the sample period for those defaulted loans that have not yet been liquidated (censored loans), X(i,t) represents a set of loan and borrower characteristics, and Z(t) represents one or more of the macroeconomic variables included in the supervisory scenarios.

The loss severity model estimates separate loss severity equations for prime, Alt-A, and subprime loans using a regression framework.⁵⁵ The loss severity model is specified in the following equation:

$$LGD\left( i,t \right)=f\left( X\left( i,t \right),T(i),Z\left( T(i) \right) \right),$$ (11)

where i represents the loan, t represents the time of default, LGD(i,t) represents the loss severity rate of loan i that enters default at time t, X(i,t) represents a set of loan and borrower characteristics, T(i) represents the liquidation timeline for loan i,and Z(T(i)) represents one or more of the macroeconomic variables included in the supervisory scenarios at the time of liquidation.

Both the timeline models and loss severity models are estimated using loan-level data on loan balances, servicer advances, and losses from defaulted loans in commercially available datasets of agency and private-label mortgage-backed securities (MBS).

The Federal Reserve uses the projected time of liquidation to allocate estimated losses between credit losses on the defaulted loans and net losses arising from the eventual sale of the underlying property.⁵⁶ Finally, LGD includes unpaid accrued interest and an adjustment to reflect expected carrying costs on the loan that are not accounted for in PPNR projections (i.e., those carrying costs that would be incurred beyond the projection horizon).

The PD and LGD models use unemployment rates and house prices that are projected at the state and county levels.

The Federal Reserve assumes EAD to be the unpaid principal balance (UPB) at the start of the projection horizon.

Table 6. List of key variables in the first-lien mortgage models and sources of variables

Retail Loans: Domestic Home Equity Loans and Home Equity Lines of Credit

Domestic home equity exposures include closed-end HELs and HELOCs, which are revolving, open-ended loans. HELs and HELOCs are secured by one- to four-family residential real estate located in the United States, as defined by the FR Y-9C.

The Federal Reserve estimates the model using historical data on HEL and HELOC payment status, loan characteristics, and economic conditions. The model projects losses at the loan level in an expected-loss modeling framework using data on firm-reported loan characteristics from the FR Y-14M and economic conditions defined in the Federal Reserve's supervisory stress test scenarios. Some of the key loan and borrower characteristics that affect projected losses include

• combined LTV ratio,
• borrower's credit score, and
• utilization rate in the case of HELOCs.

The losses projected by the model for a given loan vary based on changes in the defined economic conditions over the projection horizon. Those include

• house prices,
• the unemployment rate, and
• interest rates.

The PD model for HELs and HELOCs projects the probability that a loan transitions to a different payment status (i.e., current, impaired, default, and paid off). The Federal Reserve defines home equity loans and lines of credit as in default when they are 180 days past due. The Federal Reserve also refers to accounts that reach 90 days past due as the intermediate "impaired state" in the analysis. Current and impaired loans may also transition to a paid-off state. The Federal Reserve estimates separate PD models for the two product types. At each point in time, each model uses a regression framework to estimate the probability that a loan transitions from one payment status to another status (e.g., from current to impaired or from impaired to default) over a single quarter.

The model is a system of five binomial logit equations that generates a probability of default during a quarter, conditional on the loan's payment status at the end of the prior quarter. Two of these equations capture the transitions from the current state to other payment statuses, which are either impaired or paid off. Three other equations represent the transition from impaired status to other statuses. Impaired loans in the model may transition to current, paid off, or default. The model assumes default and paid off to be terminal states and that loans in the model cannot transition out of those states. This model is specified as

$$\text{Pr}\left( Tr(i,t+1)|S(i,t) \right)=f\left( X(i,t),Z(t) \right),$$ (12)

where i represents the loan, t represents time, Pr(Tr(i, t + 1)) represents the probability that the loan transitions to another status from period t to t+1, S(i,t) represents the payment status in period t, X(i,t) represents loan and borrower characteristics, and Z(t) represents one or more of the macroeconomic variables included in the supervisory scenarios.

Collectively, these models project a probability of default, conditional on product type, initial payment status, loan and borrower characteristics, and economic conditions over the projection horizon. The top panel of tables 7 and 8 contains a list of key variables that enter the PD models.

The HELOC PD model contains an additional feature to account for the fact that, for most lines of credit, the borrower may draw on the line for a fixed period, known as the "draw period," during which repayments of principal are not required. At the end of the draw period, the outstanding line balance either becomes immediately payable or converts to a fully amortizing loan. Borrowers holding these products after the draw period ends must make higher payments than were required during the draw period. The PD model assumes HELOCs that reach the end-of-draw period pay off and default at higher rates than HELOCs that are still in their draw period.

The LGD on a loan is the UPB on the HEL or HELOC at default minus net recovery after senior-lien payout. The net recovery after senior-lien payout is calculated as the proceeds from the liquidation sale net of foreclosure costs, less the balance of any senior liens and of unpaid accrued interest on this loan. Proceeds from liquidation is calculated by subtracting the senior-lien balance from the total recovery amount estimated by the first-lien LGD timeline and loss severity models.

The PD and LGD models use unemployment rates and house prices that are projected on the state and county levels.

The Federal Reserve assumes EAD for HELs to be the UPB of the loan at the start of the projection horizon. HELOCs that have been permanently closed or have reached the end-of-draw period are essentially closed-end loans. For these HELOCs, the Federal Reserve assumes EAD to equal the UPB at the start of the projection horizon. For all other HELOCs, the Federal Reserve sets EAD to the higher of the UPB at the start of the projection horizon and the original credit limit.

Table 7. List of key variables in the HEL exposure PD and EAD models and sources of variables

Table 8. List of key variables in the HELOC exposure PD and EAD models and sources of variables

Retail Loans: Domestic Credit Cards

Domestic credit cards include general purpose, private-label, and charge cards, as defined by the FR Y-9C.⁵⁷

The model projects losses at the account level in an expected-loss modeling framework, using data on firm-reported characteristics from the FR Y-14M and economic conditions defined in the Federal Reserve's supervisory stress test scenarios.⁵⁸ Some of the key characteristics that affect projected losses include

• lending type (i.e., bank card or charge card),
• account holder's credit score,
• credit line (i.e., limit) of the account, and
• account utilization rate factor.

The losses projected by the model for a given account vary based on changes in the defined economic conditions over the projection horizon. The key macroeconomic variable that enters the model is the unemployment rate.

The PD model for credit cards estimates the probability that an account transitions to default status, given the characteristics of the account and borrower as well as macroeconomic conditions. The Federal Reserve defines credit card accounts as in default when they are 120 days or more past due, in bankruptcy, or charged off. When an account defaults, it is assumed to close and cannot return to current status in the model.

Because the relationship between the PD and its determinants can vary with the payment status of the account, the Federal Reserve estimates separate transition models for current and active accounts, current and inactive accounts, and delinquent accounts.⁵⁹ In addition, because this relationship can also vary by lending type and time horizon, the Federal Reserve uses separate models by lending type and over the short-, medium-, and long-term horizons. These transition models correspond to default in the first quarter, the second and third quarters, and the fourth through ninth quarters of the horizon, respectively. The historical data used to estimate this model are industrywide, account-level data. The probability that an account defaults in a quarter is modeled in a binomial logit regression model:

$$PD\left( i,t \right)=f\left( X\left( i,t \right),~Z\left( t \right) \right),$$ (13)

where i represents the account, t represents time, PD(i,t) represents the probability of default, X(i,t) represents account and borrower characteristics, and Z(t) represents one or more of the macroeconomic variables included in the supervisory scenarios.

The PD model uses unemployment rates that are projected at the state level. For charge cards, a simpler version of the model is estimated on data from a major credit bureau.

The LGD model assumes that LGD for credit cards is a fixed percentage of EAD. This percentage is calculated separately for bank cards and charge cards based on historical industry data of gross charge-offs and recoveries.

The EAD for credit cards is equal to the sum of the amount outstanding on the account (i.e., UPB) and the estimated amount of the credit line that is likely to be drawn down by the borrower between the beginning of the projection horizon and the time of default. The model calculates EAD for an account that defaults at a specific time as

$$EAD\left( i,t \right)=UPB\left( i \right)+LLEQ\left( i,t \right)*C\left( i \right),$$ (14)

where i represents the account, t represents time, EAD(i,t) represents the EAD, UPB(i) represents the reported unpaid balance of account i at the start of the projection horizon, C(i) represents the reported credit line of account i at the start of the projection horizon, and LLEQ(i,t) represents a utilization factor.

As shown below, LLEQ(i,t) is estimated as a function of account and borrower characteristics:

$$LLEQ\left( i,t \right)~=f\left( X\left( i,t \right) \right).$$ (15)

Because the relationship of this factor to account and borrower characteristics can vary with the payment status of the account and time to default, the Federal Reserve uses separate models to estimate the drawdown amount for current and delinquent accounts and for accounts with short-, medium-, and long-term transitions to default. For accounts that are current, the Federal Reserve estimates separate models for segments with credit lines of different sizes. The Federal Reserve adjusts estimated EAD to exclude delinquent interest and fees.⁶⁰

Table 9. List of key variables in the credit card models and sources of variables

Retail Loans: Domestic Auto Loans

Domestic auto loans are consumer loans that are extended for the purpose of purchasing new and used automobiles and light motor vehicles, as defined by the FR Y-9C.

The Federal Reserve estimates the model using historical data on auto payment status and loan losses, loan characteristics, and economic conditions. The model projects losses at the portfolio-segment level with an expected-loss framework, using data on firm-reported loan characteristics from the FR Y-14Q and economic conditions defined in the Federal Reserve's supervisory stress test scenarios.⁶¹ Some of the key loan and borrower characteristics that affect projected losses include

• product type (new or used vehicle),
• loan age,
• LTV ratio, and
• borrower's credit score.

The losses projected by the model vary based on changes in the defined economic conditions over the projection horizon. Those include

• the unemployment rate and
• house prices.

The PD model estimates the probability that a loan transitions its status from either a current or delinquent state to default status, given the characteristics of the loan and borrower and macroeconomic variables, including house prices and the unemployment rate. The Federal Reserve defines auto loans as in default if the vehicle is in repossession or if the loan is 120 days or more past due, in bankruptcy, or charged off. The model estimates the probability that a loan defaults in a quarter using historical loan-level data from a major credit bureau. Because the relationship between the PD and its determinants can vary with the payment status of the loan, the Federal Reserve estimates two separate transition models for loans that are current and for those that are delinquent.⁶² The probability that a loan defaults is modeled in a binomial logit regression framework:

$$PD\left( i,t \right)=f\left( X\left( i,t \right),~~Z\left( t \right) \right),$$ (16)

where i represents the loan, t represents time, PD(i,t) represents the probability of default, X(i,t) represents loan and borrower characteristics, such as credit score and loan age, and Z(t) represents one or more of the macroeconomic variables included in the supervisory scenarios. The model projects PDs by applying the coefficient estimates from equation (16) to specific loan segments from the FR Y-14Q regulatory report.

The Federal Reserve models the LGD for auto loans as a function of loan as well as borrower characteristics and macroeconomic variables. The historical data used to estimate this model are pooled, segment-level data provided by the firms in the FR Y-14Q report. The model estimates the LGD for defaulted loans within a segment using the following linear regression model:

$$LGD{{\left( k,t \right)}_{{}}}=f\left( X\left( k \right),~~Z\left( t \right) \right),$$ (17)

where k represents the segment, t represents time, LGD(k,t) represents the loss given default, X(k) represents characteristics of the segment k, such as product type, LTV, and loan segment age, and Z(t) represents one or more of the macroeconomic variables included in the supervisory scenarios. The model then projects LGD by applying coefficient estimates from equation (17) to segment-level data from the FR Y-14Q.

The LGD model uses projected values of a national used car price index in addition to unemployment rates and house prices that are projected on the state level.

The Federal Reserve bases the EAD for auto loans on the pattern of amortization of loans that ultimately defaulted in the data provided by a major credit bureau, as reflected in the following equation:

$$EAD\left( k,t \right)=UPB\left( k \right)*PR\left( k,t \right),$$ (18)

where k represents the loan age segment, t represents time, EAD(k,t) represents the EAD, UPB(k) represents the unpaid principal balance for loan segment k, and PR(k,t) represents a paydown ratio for loan segment k at period t. PR(k,t) is estimated as a function of loan characteristics.

Table 10. List of key variables in the auto loan models and sources of variables

Retail Loans: Other Retail Loans

The other retail loans category includes the small-business loan, other consumer loan, student loan, small-business and corporate credit card, international other consumer loan, international bank and charge card, international first mortgage, international home equity loan, international small-business loan, and international small-business and corporate credit card portfolios.⁶³ The Federal Reserve generally defines these categories based on the FR Y-9C classifications and models each of the 10 loan portfolios separately.

The Federal Reserve estimates these models using historical data on loan payment status, loan losses, loan characteristics, and economic conditions. Net charge-offs are projected at the segment level using the estimated models, firm-reported loan characteristics from the FR Y-14Q, and economic conditions defined in the supervisory stress test scenarios. The models calculate losses by applying projected net charge-off rates to balances projected by the Federal Reserve. Key portfolio characteristics that affect projected losses include

• product type within a portfolio,
• payment status,
• borrower's credit score,
• LTV ratios for certain products, and
• whether the loan is secured.

The losses projected by each model for a given portfolio vary based on changes in the defined economic conditions over the projection horizon. Those include variables such as

• unemployment rate and
• domestic and international real GDP growth.

The Federal Reserve models a net charge-off rate for each portfolio using industrywide data at the segment level. For most portfolios, the Federal Reserve collects these data at the segment level in the FR Y-14Q Retail schedule, where segments are defined based on loan characteristics.⁶⁴ The Federal Reserve defines other retail loans as in default when they are 90 days or more past due for domestic and international other consumer loans and 120 days or more past due for student loans, small-business loans, small-business and corporate credit cards, and international retail portfolios.

The models for the domestic portfolios (small-business loan, other consumer loan, student loan, and small-business and corporate credit card) project the net charge-off rate using the previous quarter's net charge-off rate:

$$Net\ charge\ off\ rate\left(b,k,t\right) = f\left(X\left(b,k,t\right), Z\left(t\right)\right),\ (19)$$

where b represents the firm, k represents a segment of loans within the portfolio, t represents time, X(b,k,t) includes the net charge-off rate in the prior period and risk-segment indicators, and Z(t) represents macroeconomic variables in different lags. The specification includes risk-segment-specific effects and macroeconomic variables.⁶⁵

The models for the international portfolios (international other consumer loan, international bank and charge card, international first mortgage, international home equity loan, international small-business loan, and international small-business and corporate credit card) project the net charge-off rate using a system of equations that also generates projections of the delinquency rate and default rate:

$$Payment~status(b,k,t)=f(X(b,k,t),Z(t)),$$ (20)

where b represents the firm, k represents a segment of loans within the portfolio, t represents time, X(b,k,t) includes the payment status in the prior period and risk-segment indicators, and Z(t) represents macroeconomic variables in different lags. The Federal Reserve models delinquency, default, and net charge-off rates using an autoregressive specification as a function of its own value in the previous period t-1 and the rate in the previous performance state to capture the transition from one state to the other. The specification also includes risk-segment-specific effects and macroeconomic variables.⁶⁶ The models use projected values of international GDP growth for certain geographic areas. By including lags of the delinquency rates and default rates in the default and net charge-off models, respectively, the models implicitly capture roll-rate dynamics.⁶⁷

Both the domestic and international models project charge-off rates by applying the estimated charge-off equation to each segment of the firm's loan portfolio, as of the effective date of the stress test. The portfolio-level charge-off rate equals the dollar-weighted average of the projected segment-level charge-off rates.⁶⁸

Table 11. List of key variables in other retail models and sources of variables

Adjustments to Losses and Calculation of Loan-Loss Provisions

Loss models focus on losses arising from loans that are measured at amortized cost as of the effective date of the stress test, but loss projections also incorporate losses on loans originated after the projection horizon begins. These incremental loan balances are calculated based on projected loan balances over the projection horizon. New balances are assumed to have the same risk characteristics as those of the loan portfolio on the effective date of the stress test, with the exception of loan age in the retail and CRE portfolios, where seasoning is incorporated.⁶⁹

New loans are assumed to be current, and firms are assumed not to originate types of loans that are no longer permitted under various regulations. Loss projections generated by the models are adjusted to account for purchase accounting treatment, which recognizes discounts on impaired loans acquired during mergers and any other write-downs already taken on loans measured at amortized cost. This latter adjustment ensures that losses related to these loans are not double-counted in supervisory projections.

Losses on loans measured at amortized cost enter net income through provisions for loan and lease losses. Provisions for loan and lease losses for each quarter equal projected loan losses for the quarter plus the change in the allowance needed to cover the subsequent four quarters of expected loan losses, taking into account the allowance established at the start of the projection horizon.

The Federal Reserve generally assumes the appropriate level of the allowance in the supervisory calculations to be the amount needed to cover projected loan losses over the next four quarters.⁷⁰ The supervisory calculation of the allowance is based on projected losses under the severely adverse scenario and may differ from a firm's established allowance at the beginning of the projection horizon, which is based on the firm's estimate of incurred losses on the effective date of the stress test. Any difference between these two measures of the allowance is linearly smoothed into the provisions projection over the nine quarters of the projection horizon. Thus, the calculation takes into account the allowance established by the firm on the effective date of the stress test. Because projected loan losses include off-balance sheet commitments, the supervisory calculation of provisions also accounts for the firm's allowance for credit losses on off-balance sheet exposures on the effective date of the stress test.

Table 12. List of key variables in the loan-loss provisions calculation for loans measured at amortized cost

Other Losses

FVO/HFS Loans

FVO/HFS loans are treated differently from loans measured at amortized cost under the accounting standards. FVO loans are valued as mark-to-market assets, while HFS loans are carried at the lower of cost or market value. As a result, FVO/HFS loans can experience gains or losses when their fair values change in response to changes in macroeconomic and financial market conditions. The Federal Reserve recognizes gains and losses related to FVO/HFS loans in earnings on the income statement at the time of the revaluation.

Fair-value gains and losses are defined as changes in the fair value of the loan or commitment. The Federal Reserve uses different models to estimate gains and losses on FVO/HFS wholesale loans and FVO/HFS retail loans. Generally, these models project gains and losses over the nine-quarter projection horizon, net of hedges, by applying the scenario-specific interest rate and credit spread shocks to loan yields.

FVO/HFS Wholesale Loans

The Federal Reserve projects gains and losses on FVO/HFS wholesale loans and commitments by revaluing each loan or commitment each quarter and computing quarterly changes in fair value in each quarter of the projection horizon. The key loan characteristics that affect projected losses include

• loan rating,
• interest rate of the loan, and
• maturity date.

The key macroeconomic variables that enter the model are

• credit spreads and
• interest rates.

The Federal Reserve models fair value using a standard bond pricing formula for fixed-rate loans and a linear approximation for floating-rate loans. For fixed-rate loans, the bond pricing formula discounts future cash flows using a discount yield that depends on loan rating and maturity. To project fair value, the model assumes that the discount yield can change due to changes in both loan-specific characteristics and macroeconomic variables.

The model infers a starting point discount yield for a loan at the start of the projection horizon using the firm-reported fair value.

The discount yield in a projection quarter tcan be written as

$$y\left( i,t,r\left( 0 \right),r\left( t \right) \right)=y\left( i,0 \right)+\text{ }\!\!\Delta\!\!\text{ }s\left( i,t,r\left( 0 \right),r\left( t \right) \right)+\text{ }\!\!\Delta\!\!\text{ }ir\left( i,t \right),$$ (21)

where i represents the loan, t represents time in the projection horizon, r(0) represents the rating at the start of the projection horizon, r(t) represents the rating in quarter t, y(i,t,r(0), r(t)) represents the discounted yield, y(i,0) represents the yield at the start of the projection horizon, Δs(i,t,r(0),r(t)) represents the rating- and maturity-specific projected change in the credit spread since the start of the projection horizon, and Δir(i,t) represents the change in the interest rate since the start of the projection horizon.

The Federal Reserve proxies credit spreads on FVO/HFS wholesale loans by those on a U.S. high-yield security index and by projected spreads calibrated to the BBB yield in the macroeconomic scenario. The Federal Reserve projects movements in spreads over the projection horizon based on their historical relationships with macroeconomic and financial variables. The model projects loan-specific discount yields for all possible rating changes in all projection periods. The model then uses the projected discount yields in equation (21) and the bond pricing formula, or linear approximation, to compute rating-specific fair values. The projected fair value is the expected fair value, over all possible ratings changes, where probabilities of rating changes are taken from a historical empirical ratings transition matrix.⁷¹

FVO/HFS Retail Loans

FVO/HFS retail loans include first- and second-lien mortgages, student loans, credit cards, and auto loans.⁷² The Federal Reserve calculates gains and losses on FVO/HFS retail loans over the nine quarters of the projection horizon using a duration-based approach. This approach uses total loan balances as reported on the FR Y-14Q, estimates of portfolio-weighted durations, and quarterly changes in stressed 5-year Treasury rates and loan spreads from the supervisory stress test scenarios. Estimates are calculated separately by vintage and loan type.

Gains and losses on FVO/HFS retail loans of a particular loan type and vintage in a projection quarter are specified as follows:

$$Loss\left( j,v,t \right)=CV\left( j,v,0 \right)*\left(D\left( j,v,r \right)*\Delta r\left(t\right)+D\left(j,v,s\right)*\Delta s\left(j,t\right)\right),\ (22)$$

where j represents loan type, v represents vintage, t represents the projection quarter, Loss(j,v,t) represents the gain or loss on the FVO/HFS retail loan, CV(j,v,0) represents the carrying value as defined in Schedule J of the FR Y-14Q, D(j,v,r) and D(j,v,s)represent measures of rate and loan spread duration, and Δr(t) and Δs(j,t) represent the change in the 5-year Treasury yield and loan spread, respectively, since the start of the projection horizon. For FVO/HFS retail loans other than mortgages, the rate duration term is assumed to be zero. The Federal Reserve projects spreads on highly rated asset-backed security indexes and uses them as a proxy for spreads on FVO/HFS retail loans. Movements in spreads over the projection horizon are based on their historical relationships with macroeconomic variables.

Hedges on FVO Loans and on Loans Measured at Amortized Cost

The Federal Reserve calculates the quarterly profit and loss (P&L) for hedges on FVO loans and on loans measured at amortized cost by combining a set of scenario-specific risk-factor projections and factor sensitivities submitted by firms. The Federal Reserve nets aggregate hedge gains and losses for each firm against projected gains and losses on wholesale and retail exposures to estimate the firm's final P&L projections.

Table 13. List of key variables in the FVO/HFS models and sources of variables

AFS and HTM Securities

Losses on securities can arise from two different sources.⁷³ For AFS debt securities, fair value reflected on the balance sheet may change due to changes in economic or financial conditions. These gains or losses are reported as OCI and are included in CET1 for firms subject to the advanced approaches. In addition, both AFS and HTM securities may be at risk of credit losses.⁷⁴

The models project credit losses and OCI for each applicable security and aggregate these losses up to the firm level in three steps. First, the models project the fair value of each security over the nine-quarter projection horizon, conditional on the supervisory stress test scenarios. Second, the models estimate security-level credit losses as a function of book value and the projected change in fair value. Finally, the models calculate OCI from AFS debt securities using projected changes in fair value, accounting for any projected credit losses.

All securities loss models are estimated using security-level information from the FR Y-14Q and economic conditions in order to project credit losses and OCI from AFS debt securities. Some of the key security characteristics that affect projected losses include

• maturity date,
• security type,
• market values and amortized costs of the securities, and
• measures of duration.

The losses projected by the model for a given security vary based on changes in economic conditions over the nine quarters of the projection horizon. Those include

• interest rates,
• stock market returns and volatility, and
• corporate bond spreads.

Fair Value of Securities

The Federal Reserve projects the fair value of fixed-income securities (i.e., bonds) over the nine-quarter projection horizon using one of three methods: a simple present-value calculation, a full revaluation based on a security-specific discounted cash flow model, or a duration-based approach.

The fair value of U.S. Treasuries is projected as a present-value calculation using a formula that defines the security price as the present value of future expected cash flows, discounted by security-specific discount rates. This formula uses yields specified in the macroeconomic scenarios, which are the paths for 3-month, 5-year, and 10-year U.S. Treasury yields. The Federal Reserve uses a term structure model to interpolate or extrapolate yields for other maturity points.⁷⁵

Full revaluation of agency MBS is projected using a discounted-cash-flow simulation model, which is an industry-standard modeling technique for agency MBS. The main drivers of change in the fair values of agency MBS are interest rates used for discounting the expected cash flows, house prices, the unemployment rate, and projected movements in an MBS option-adjusted spread (OAS) index. The Federal Reserve projects movements in spreads over the projection horizon based on their historical relationships with macroeconomic and financial variables.

The Federal Reserve projects the fair value for fixed-income securities other than U.S. Treasuries and agency MBS using a duration-based approximation. The duration-based approximation projects the quarterly price path based on a first-order approximation of the relationship between the security price and its yield, taking into account security-specific information.

The model projects the fair value for a security with a specific maturity as

$$\%\Delta FV\left( i,t \right)=-\left( D\left( i,spread \right)*\Delta OAS\left( i,t \right)+D\left( i,Rate \right)*\Delta RF\left( T,t \right) \right),$$ (23)

where i represents a security, t represents time, T represents maturity, %ΔFV(i,t) represents the percent change in fair value, D(i,spread) and D(i,Rate) represent the effective spread and rate durations for security i, ΔOAS(i,t) represents the modeled expected change in the OAS of security iin quarter t, and ΔRF(T,t) represents the change in yield on a U.S. Treasury with maturity T in quarter t. The Federal Reserve projects these expected changes in OAS using separate regression models for each asset class.

For each debt asset class, the Federal Reserve projects the OAS using regression models that relate historical values of the spreads to key macroeconomic and financial characteristics, such as the BBB corporate spread and the U.S. Dow Jones Total Stock Market Index return. OAS is projected using separate models for corporate bonds, sovereign bonds, and all other fixed-income securities. The sovereign bond OAS is projected based on high-percentile historical movements in sovereign bond spreads. This percentile is related to the frequency of severe recessions. For all debt asset classes, fair-value projections assume that duration and remaining life remain constant.

For equity securities, the Federal Reserve projects fair value using the expected return on a broad market portfolio.

Credit Losses on AFS/HTM Securities

In the supervisory stress test, the Federal Reserve assumes that U.S. Treasuries, U.S. government agency obligations, U.S. government agency or government-sponsored enterprise MBS, federally backed student loan asset-backed securities, and pre-refunded municipal bonds are not subject to credit losses.⁷⁶

For all other debt securities, the model used to project credit losses is estimated using historical data, which assumes that security-level credit losses depend on two risk factors: a term that measures the deviation of the fair value of the security from its book value, and a term that measures the recent changes in fair value. Specifically, the model takes the form:

$$\frac{CL\left( i,t \right)}{BV\left( i,t-1 \right)}=g\left( \underbrace{\frac{FV\left( i,t-1 \right)}{BV\left( i,t-1 \right)}}_{Market-to-book},\underbrace{\frac{\left( FV\left( i,t \right) \right)-FV(i,t-1)}{FV(i,t-1)}}_{Return} \right),$$ (24)

where i represents the security, t represents the year, CL(i,t) represents the credit loss taken on the security holding i in year t, BV(i,t-1) represents the amortized cost of the holding i at the end of year t-1, FV(i,t) represents the fair market value of the holding i at the end of year t, and g represents a function estimated using a fractional logit model.⁷⁷ The Federal Reserve estimates the model with historical data on securities' amortized costs, fair values, and credit write-downs obtained from the FR Y-14Q as well as from additional data from filings on the securities holdings of U.S. life insurance companies.

The Federal Reserve estimates model parameters separately for direct debt obligations and securitized obligations. The model specification accounts for different asset classes within each group using asset-class indicator variables. Securitized obligations include MBS, asset-backed securities, CLOs, and CDOs. Direct debt obligations are issued by a single issuer with recourse and include asset classes such as municipal, corporate, and sovereign debt securities.

The model computes credit losses using projections from the fair-value models and iterating on equation (24) at an annual horizon. In the first year of the horizon, the model uses the book value and market-to-book ratio for each security as of the effective date of the stress test. Annual projected credit loss is distributed equally across quarters.

Calculation of OCI

Firms subject to the advanced approaches are required to include AOCI in regulatory capital.

OCI for a given AFS debt security in a certain quarter of the projection horizon is calculated as the difference between the change in fair value for the holding in that quarter and the change in the amortized cost of the holding in that quarter. Final projections adjust for any credit loss taken and take into account applicable interest rate hedges on securities but do not account for periodic amortization or accretion.

The Federal Reserve assumes that balances at risk of credit loss do not decrease. After a security experiences a credit loss, the Federal Reserve assumes the difference between its original value and its post-credit loss value to be invested in securities with the same risk characteristics.

Table 14. List of key variables in the securities models and sources of variables

Trading and Private Equity

The trading and private equity model generates loss estimates related to trading and private equity positions held by firms that are subject to the global market shock. The trading and private equity model covers a wide range of firms' positions in asset classes such as public equity, foreign exchange, interest rates, commodities, securitized products, traded credit (e.g., municipals, auction rate securities, corporate credit, and sovereign credit), private equity, and other fair-value assets measured at mark-to-market. Trading P&L on firms' positions is determined as a function of a shock to one or more risk factors and firm-supplied information on initial positions and sensitivities to those risk-factor shocks.⁷⁸

The model applies risk-factor shocks to firm-supplied exposures in one of two ways. For certain asset classes, including securitized products, private equity, other fair-value assets, and some traded credit items, loss projections are a function of direct haircuts to the market value of the asset. For these asset classes, the trading P&L for a firm is the product of the market value of the exposure and the relevant shock.⁷⁹

For other assets in the trading book, such as foreign exchange, public equity, interest rate products, commodities, and most traded credit items, P&L is jointly determined by shocks to one or more risk factors. For these trading book assets, several risk factors may be needed to estimate P&L.⁸⁰ For cases in which the P&L is jointly determined, the model aggregates P&L over all applicable shocks.⁸¹

Total P&L projected for a firm is the sum of dollar changes associated with each shock that is relevant to the value of the position, aggregated for all trading and private equity portfolios.

Consistent with the Federal Reserve's modeling principles, losses from trading and private equity are recognized in the first quarter of the projection horizon.

Trading Exposure: Issuer Default Losses

The trading IDL model captures the losses arising over the full nine-quarter projection horizon from a jump-to-default of issuers of debt securities in the trading book. The model estimates the potential for losses in a severe stress scenario that could arise from concentration risk in credit exposures held in the trading book.

The model measures jump-to-default losses in excess of mark-to-market losses calculated by the model used to project trading P&L. The credit exposure types captured in the IDL model include corporate, sovereign, agency, municipal, and securitization positions. These exposures span single-name products (e.g., corporate bonds and single-name credit default swaps (CDS)), index products, and index-tranche products. The IDL model projects quarterly losses on those exposures over the projection horizon of each stress test scenario.

Key variables that enter the model are

• through-the-cycle default probabilities for the debt issuers,
• long-run average LGD by asset class, and
• asset value correlation.

The model assumes that an obligor defaults when its asset value falls below a certain threshold that depends mainly on the initial rating of the obligor.⁸² The model also assumes that changes in the value of an obligor's assets can be decomposed into an obligor-specific (idiosyncratic) component and a component common to all obligors. The common component enables the model to capture default correlation, as it implies that there is correlation in changes in obligor asset values and default probabilities.

The model simulates asset value paths for each obligor in a firm's portfolio. For a given simulated path, the model records a default if an obligor's stressed asset value falls below a specific model threshold. The model then calculates a loss by applying an asset-class LGD assumption to the exposure. The model repeats that process many times for each obligor, resulting in a distribution of losses.⁸³

The model measures the projected loss as the loss associated with a percentile of the generated loss distribution. This percentile is related to the frequency of severe recessions.

IDL losses are calculated net of mark-to-market trading losses under the global market shock for the portion of the relevant portfolio that is projected to default. The Federal Reserve applies the model at the level of each broad asset class.

Table 15. List of key variables in the issuer default loss model and sources of variables

Credit Valuation Adjustment

CVA is an adjustment to the mark-to-market valuation of a firm's exposures to its counterparties, taking into account PD and LGD for each counterparty. The CVA model captures the risk of credit losses arising from changes in exposures due to the effect of the global market shock on PD, LGD, and expected derivative exposures to counterparties.

The model is mainly based on firm-provided estimates of the components of stressed CVA. Those firm-provided components include

• discount factors,
• the expected exposure to counterparties,
• PD of counterparties, and
• LGD of counterparties.

The projected CVA loss in a supervisory scenario is the difference between the CVA projections in the supervisory stress scenario and those in the baseline (or unstressed) scenario. Consistent with the Federal Reserve's modeling principles, CVA losses are recognized in the first quarter of the projection horizon.

The model computes CVA by multiplying a positive expected exposure (EE) to a counterparty by its PD and LGD, and then discounts that expected valuation adjustment using a risk-free discount factor. EE is based on a 10-day margin period of risk assumption for all counterparties in cases in which margin is collected and excludes any additional margin collected due to the downgrade of a counterparty.⁸⁴ CVA is computed gross of any CVA hedges.

Specifically, in a supervisory stress scenario, the CVA model calculates a charge to a firm's derivative mark-to-market values over all the periods of contractual exposure using firm-provided inputs. These CVA charges are aggregated across all of the firm's counterparties using the following equation:

$$CVA\left( s \right)=~\sum\nolimits_{k}^{}{{}}\sum\nolimits_{t=1}^{T}{{}}DF\left( s,t,k \right)*EE\left( s,t,k \right)*PD\left( s,t,k \right)*LGD\left( s,k \right),$$ (25)

where s represents the supervisory scenario, t represents time, k represents a firm's counterparties, CVA(s) represents the stressed CVA, DF(s,t,k) represents the discount factor (DF), EE(s,t,k) represents an expected exposure, PD(s,t,k) represents the counterparty's probability of default, and LGD(s,k) represents loss given default. In general, firm-provided PDs and LGDs are market-implied and consistent with pricing observed in the CDS market. The CVA charge only takes into consideration the default probability of the counterparty. There is no consideration of debt valuation adjustment when estimating CVA losses.

The model adjusts the CVA charge computed in equation (25) in order to account for data gaps and offline reserves. The Federal Reserve collects CVA component data (i.e., EE, DF, PD, and LGD) for a subset of firms' counterparties that represent 95 percent of total unstressed CVA and 95 percent of total stressed CVA.⁸⁵ The model adjusts the value in equation (25) to account for the risk associated with remaining counterparties, based on the ratio of the firm-provided aggregate CVA and the sum of CVA for the subset of counterparties.⁸⁶ Finally, the model adjusts the CVA projection for firm-reported additional or offline scenario-specific CVA reserves to arrive at a final projection of CVA under each scenario.⁸⁷

The Federal Reserve uses the trading and private equity model to calculate gains or losses on firms' CVA hedges.⁸⁸ The calculation of gains or losses on CVA hedges uses the same methodology as the calculation for trading book positions.

Table 16. List of key variables in the credit valuation adjustment model and sources of variables

Largest Counterparty Default

The Federal Reserve applies the LCPD scenario component to firms with substantial trading or custodial operations. The LCPD captures the risk of losses due to an unexpected default of the counterparty whose default would generate the largest stressed losses for a firm.

Firms subject to the LCPD scenario apply the global market shock to their counterparty exposures across derivatives positions⁸⁹ and securities financing transactions.⁹⁰ The valuations of these positions are adjusted for any associated collateral value as of the effective date of the market shock.

The notional amount of any single-name CDS hedges on the relevant counterparty is subtracted from stressed net current exposure, and the result is then multiplied by one minus the recovery rate, which is assumed to be 10 percent of the total stressed exposure.⁹¹ Finally, the stressed CVA attributed to the counterparty is subtracted from the resulting loss. Formally, the net default loss can be expressed as

$$SN\text{ }Loss\left( s,k \right)=\left( Total~SN~CE\left( s,k \right)-CDS~Ntn\left( k \right) \right)*\left( 1-RR \right)-CVA\left( s,k \right),$$ (26)

where s represents the supervisory scenario, k represents the counterparty, SN Loss(s,k) represents a firm's stressed net default loss to counterparty k in scenario s, Total SN CE(s,k) represents stressed net current exposure to counterparty k in scenario s, CDS Ntn(k) represents the notional amount of CDS hedges on counterparty k, RR represents the assumed recovery rate, and CVA(s,k) represents the stressed CVA associated with counterparty k in scenario s.

The model calculates equation (26) for all reported counterparties and ranks stressed net losses from largest to smallest. The loss attributable to the LCPD component in scenario s is set equal to the largest counterparty-level loss.⁹²

Consistent with the Federal Reserve's modeling principles, LCPD losses are recognized in the first quarter of the projection horizon.

Table 17. List of key variables in the largest counterparty default model and sources of variables

Calculation of Regulatory Capital Ratios

The models discussed above generally project yields or loss rates, which the Federal Reserve scales by balances to arrive at levels of income and loss projections.⁹³

The final modeling step incorporates these projections of revenues, expenses, losses, and provisions into calculations of regulatory capital for each firm under the supervisory scenarios. Regulatory capital is calculated using the definitions of capital in the Board's regulatory capital rule.⁹⁴ In projecting a firm's risk-weighted assets, the Federal Reserve will account for the effect of changes associated with the calculation of regulatory capital or changes to the Board's regulations in the calculation of risk-weighted assets.⁹⁵ The Federal Reserve provides banking organizations the option to phase-in the effects on regulatory capital that may result from the adoption of the Current Expected Credit Losses methodology (CECL), the Federal Reserve does not phase-out CECL transition adjustments in place on December 31, 2021, in its projections of regulatory capital ratios.⁹⁶

Regulatory capital incorporates estimates of pre-tax net income from supervisory projections of revenues, expenses, losses, and provisions and is adjusted for tax expenses/benefits. To calculate current and deferred tax expenses/benefits, the Federal Reserve assumes all pre-tax net income to be taxable within the U.S. and subject to a consistent tax rate equal to the U.S. federal corporate tax rate of 21 percent.⁹⁷ In a specific quarter, the tax expense/benefit includes changes to the deferred tax asset (DTA) valuation allowance, which is comprised of a calculation that evaluates whether a firm will have sufficient taxable income to realize its DTAs. The model calculates tax expenses/benefits as

$$tax\left( t \right)~=21\%*PTNI\left( t \right)+\Delta VA\left( t \right),$$ (27)

where t represents time, tax(t) represents the tax expense/benefit, PTNI(t) represents pre-tax net income in projection quarter t, and ΔVA(t) represents the change in the valuation allowance, which evaluates whether a firm will have sufficient taxable income over the next year to realize its DTAs from temporary differences.⁹⁸ An increase in the valuation allowance indicates that more of the firm's DTAs cannot be used.

Two types of DTAs are projected: DTAs from net operating loss (NOL) carryforwards and DTAs from temporary differences. The Federal Reserve projects changes in net DTAs from NOLs when taxable income is negative.⁹⁹ Tax law imposes an 80 percent limit on the use of NOL carryforwards to offset current taxes, and the Federal Reserve imposes that limitation in the supervisory calculations. The Federal Reserve projects changes in net DTAs from temporary differences when there is a temporary difference between the GAAP and tax basis for income. In the supervisory calculation, the Federal Reserve projects net DTAs from temporary differences from OCI associated with AFS securities and the difference between the amount of loan losses booked for GAAP (i.e., loan-loss provisions) and the amount of loan losses recognized for tax purposes (i.e., net charge-offs). In accordance with stress test principles, supervisory models do not account for any firm-specific, inter-company tax sharing agreements that may be in place.

The quarterly change in CET1 capital before adjustments and deductions equals projected after-tax net income minus certain capital distributions (i.e., preferred dividends) plus other changes in equity capital, such as OCI and income attributable to minority interest.¹⁰⁰

Projected regulatory capital levels are calculated under the applicable regulatory capital framework to incorporate, as appropriate, projected levels of non-common capital and certain items that are subject to adjustment or deduction in capital.¹⁰¹ The Federal Reserve assumes most items that are subject to adjustment or deduction in capital and non–common capital remain constant at their starting value over the projection horizon. A similar approach is taken for income attributable to minority interest. The Federal Reserve projects other items subject to deduction, including DTAs, under each supervisory scenario. The Federal Reserve adjusts its projection of certain deduction items to reflect the impact of the global market shock.

The Federal Reserve combines projections of regulatory capital levels with projections of total assets for the leverage ratio, total assets and off-balance sheet exposures for the supplementary leverage ratio, and RWAs to calculate regulatory capital ratios. The risk-based regulatory capital ratios use RWAs calculated under the standardized approach.¹⁰² The Federal Reserve assumes that a firm's RWAs and leverage ratio denominators remain unchanged over the projection horizon, except for changes primarily related to items subject to deductions from regulatory capital. The Federal Reserve adjusts the starting capital ratio denominators for items subject to adjustment or deduction from capital, consistent with the projection of each item in the numerator of the regulatory capital ratios and the regulatory capital requirements. Projected capital levels and ratios are not adjusted to account for any differences between projected and actual performance of firms observed at the time the supervisory stress test results are produced.

The Federal Reserve will not adjust RWA projections to include the standardized approach for counterparty credit risk (SA-CCR) for firms that adopt in the projection horizon.

Table 18. Treatment of key regulatory capital deductions and adjustments

 

References

 

 32. OREO expenses are based on losses projected by the first-lien mortgage model, which is discussed in the "Loan Losses and Provisions on Loans Measured at Amortized Cost" section. Return to text

 33. In modeling PPNR, the Federal Reserve makes adjustments to eliminate or minimize potential double-counting of losses. For example, in the models of core PPNR components, the Federal Reserve adjusts historical data series to exclude losses from operational-risk events and OREO expenses. In addition, the modeling approach for trading revenue limits the influence of severe market events that are separately captured in the global market shock. Return to text

 34. The trailing multiyear fixed effect interacts a firm-specific fixed effect with an indicator variable that takes the value of 1 for the past several years. Firm-specific fixed effects used in the PPNR models are indicator variables that account for unobserved characteristics of the individual firm. These fixed effects aim to capture individual firm characteristics and differences in business models that cannot be accounted for by firm balance sheet variables. Return to text

 35. PPNR models incorporate historical net interest income trends to forecast post-stress revenues. These models do not include separate adjustments to incorporate accretion schedules for fair-value marks, as this accretion is captured in income forecasts through historical net interest income trends. Similarly, model coefficients reflect the historical impact of hedging behavior on PPNR components. Return to text

 36. This process is not necessary for aggregating interest expense on subordinated debt, which is projected by a security-level model. Return to text

 37. See Basel Committee on Banking Supervision, International Convergence of Capital Measurement and Capital Standards (Basel, Switzerland: BCBS, June 2004), 149, https://www.bis.org/publ/bcbs107.pdf. Return to text

 38. The Federal Reserve adjusts loss projections in order to account for reported losses that fall below the modeling threshold. Firms subject to the supervisory stress test have different data collection and reporting thresholds. In order to treat firms consistently, loss events below a common modeling threshold (i.e., common across firms) are excluded before estimating the regression and historical simulation models. An additional model generates add-on estimates to account for losses excluded from modeling. Return to text

 39. These types of operational-risk events include internal fraud; external fraud; employment practices and workplace safety; clients, products, and business practice; damage to physical assets; business disruption and systems failures; and execution, delivery, and process management. Return to text

 40. Losses due to damage to physical assets are generally not dependent on the macroeconomic environment and therefore are modeled separately only as a function of firm size. Return to text

 41. Stuart A. Klugman, Harry H. Panjer, and Gordon E. Willmot (May 1998), "Loss Models," AgSTIN Bulletin: The Journal of the IAA, vol. 28, pp. 163–66; Paul Embrechts, Roger Kaufmann, and Gennady Samorodnitsky, (Dec 2002), "Ruin Theory Revisited: Stochastic Models for Operational Risk," ORIE Technical Reports. Return to text

 42. Patrick De Fontnouvelle, Virginia DeJesus-Rueff, John S. Jordan, and Eric S. Rosengren (Oct 2006), "Capital and Risk: New Evidence on Implications of Large Operational Losses," Journal of Money, Credit and Banking, vol. 38, no. 7, pp. 1819–46. Return to text

 43. The quarterly frequency of events is calculated as the cumulative number of events observed divided by the number of quarters for which operational-risk data are available for the relevant firm. In addition, the tail of frequency distribution is also informed by the historical industry loss frequency. The quarterly frequency is multiplied by nine to arrive at a nine-quarter frequency. Event-level severities are calculated as the ratio of losses from a given event to the assets of the firm at the time that it experienced the event. Return to text

 44. The Federal Reserve models loans measured under fair-value accounting separately. Return to text

 45. The Federal Reserve does not require firms to report information about loans with less than $1 million in overall facility committed balances on schedule H.1 of the FR Y-14Q. Return to text

 46. "Real disposable income growth" was removed from the models key variable list because it is not used in the updated model implemented in the 2022 supervisory stress test. Please see "Appendix A: Model Changes for the 2022 Supervisory Stress Test."  Return to text

 47. Jon Frye and Michael Jacobs Jr. (Mar 2012), "Credit Loss and Systematic Loss Given Default," Journal of Credit Risk, vol. 8, no. 1, pp. 109–40. Return to text

 48. The Federal Reserve collects information about a loan's outstanding balance in the item "Utilized Exposure Global" on the FR Y-14Q Schedule H.1. Return to text

 49. For additional information, see "Shared National Credit Program," Board of Governors of the Federal Reserve System, last modified March 9, 2017, https://www.federalreserve.gov/supervisionreg/snc.htm. Return to text

 50. The Federal Reserve does not require firms to report information about loans with less than $1 million in overall facility committed balances on schedule H.2 of the FR Y-14Q. Return to text

 51. Loans are limited to first-lien, conventional home-purchase and refinance mortgages (excluding those insured by the Federal Housing Administration, guaranteed by the Department of Veterans Affairs, or backed by other government agencies) held in banks' portfolios, inclusive of loans that have been sold but subsequently returned to the seller. Return to text

 52. The binomial logit models in each subgroup approximate a multinomial logit model that models the competing risks of, for example, delinquency and paid off. To ensure that the transition probabilities to all states sum to 1, the Federal Reserve first models the conditional probabilities of each transition and then converts the conditional probabilities to unconditional probabilities when the binomial logit models are combined. Return to text

 53. The model captures the effects of loan modification and evolving modification practices in the probability that an impaired loan transitions back to current status. Return to text

 54. The Federal Reserve does not incorporate private mortgage insurance recovery into the LGD models. Return to text

 55. The Federal Reserve classifies a loan as prime, Alt-A, or subprime depending on the borrower's credit score, LTV, and loan characteristics. Return to text

 56. Net losses arising from the eventual sale of the underlying property are OREO expenses, which are a component of PPNR. Return to text

 57. The Federal Reserve includes credit card loans extended to individuals in the retail credit cards model. Credit card loans extended to businesses and corporations are modeled separately. Return to text

 58. These losses are adjusted to reflect agreements with private entities to share a portion of both revenues and losses generated by a specific credit card portfolio. Return to text

 59. The Federal Reserve defines credit card accounts as active and current if they have had activity in the past 12 months and are no more than 29 days past due, delinquent if they are between 30 and 119 days past due, and inactive if they have had no activity in the past 12 months and are no more than 29 days past due. Return to text

 60. Delinquent interest and fees are often reversed upon default and reflected in reduced PPNR rather than as credit losses. Return to text

 61. The Federal Reserve specifies loan segments in the FR Y-14Q Schedule, Section A.2 – US Auto Loan. Return to text

 62. The Federal Reserve defines auto loans as current if they are no more than 29 days past due and as delinquent if they are between 30 and 119 days past due (unless subject to bankruptcy or repossession). Return to text

 63. Please see Appendix A: Model Changes for the 2022 Supervisory Stress Test for additional detail on the 2022 model change for the Other Retail Loans model. Return to text

 64. Business and corporate credit card portfolio data, previously collected in the FR Y-14Q Retail schedule, are now collected at the loan level on the FR Y-14M Credit Card schedule and are subsequently aggregated to the segment level. Return to text

 65. The risk segments are based on product type, borrower's credit score, collateral status, and other characteristics that describe different loan types. Return to text

 66. The risk segments are based on product type, borrower's credit score, geographic location, and other characteristics that describe different loan types. Return to text

 67. Roll-rate dynamics refers to the transition of delinquent loans to defaulted loans in one period and the transition of defaulted loans to net charge-offs in the next period. Return to text

 68. The models base the dollar weights used on the distribution reported during the previous observation period. This method assumes that the distribution of loans across risk segments, other than delinquency status segments, remains constant over the projection period. Return to text

 69. Seasoning is defined as the age of the loan. Return to text

 70. For loan types modeled in a charge-off framework, the Federal Reserve adjusts the appropriate level of the allowance to reflect the difference in timing between the recognition of expected losses and that of charge-offs. Return to text

 71. For loans that are projected to transition into default, a loss given default assumption is applied to the fully drawn committed exposures. Return to text

 72. The Federal Reserve assumes zero losses for residential mortgages under forward contract with GSEs. Return to text

 73. The Federal Reserve separately projects losses on securities held in firms' trading books in the Trading and Private Equity models. See "Trading and Private Equity" below. Return to text

 74. For firms that have adopted ASU 2016-13 in 2020, expected credit losses relating to AFS and HTM debt securities are recorded through the allowance for credit losses. Return to text

 75. Jens H. E. Christensen and Jose A. Lopez (Oct 2012), "Common Risk Factors in the US Treasury and Corporate Bond Markets: An Arbitrage-Free Dynamic Nelson-Siegel Modeling Approach," Federal Reserve Bank of San Francisco (unpublished paper), https://www.frbsf.org/economic-research/files/Treasury-risk-AFDNS.pdf. Return to text

 76. "Federally backed student loan asset-backed securities" was formerly known as "Federal Family Education Loan Program asset backed securities" in previous disclosures. This change does not reflect a change to the model. Return to text

 77. Prior to the adoption of ASU 2016-13 (see note 18), securities credit losses were realized through other-than-temporary impairment (OTTI). For firms under the CECL standard, credit losses are measured as an allowance rather than as a write-down. Return to text

 78. The risk factors typically relevant for a large institution's trading portfolio include those relating to interest rates, currencies, energy and other commodity prices, equity prices, and credit spreads shocks for both advanced and emerging market economies. Return to text

 79. An adjustment is made to the estimate of losses on private equity investments in affordable housing that qualify as Public Welfare Investments (PWI). For PWIs made at the bank holding company level, an affordable housing private equity investment is recognized by the Federal Reserve if it also qualifies under 12 C.F.R. § 225.28(b)(12) and 12 C.F.R. § 225.127. For PWIs made at the bank level, an affordable housing private equity investment is recognized by the Federal Reserve if it also qualifies under the applicable PWI criteria of the bank's primary Federal regulator. Return to text

 80. For example, for foreign exchange positions, the relevant shocks would include shocks to the spot level of the exchange rate pair and to the volatility of the exchange rate. Return to text

 81. The Federal Reserve collects aggregated data that capture changes in value of the positions with respect to many different values of each specified risk-factor shock. For example, firms may report sensitivities to a negative 30 percent, negative 25 percent, and 30 percent shock to a foreign exchange rate. Return to text

 82. Oldrich Alfons Vasicek (Dec 2002), "The Distribution of Loan Portfolio Value," Risk, vol. 15, pp. 160–62. Return to text

 83. In cases in which the firm's obligor data are collected in aggregate by rating for a given asset class, instead of granular obligor-level data on the FR Y-14Q schedule, the simulation uses obligor-size assumptions to proxy for obligor-level exposures. Return to text

 84. The 10-day margin period of risk assumption implies that no margin payments are made for a 10-day period. Return to text

 85. A data collection relevant to 95 percent of total stressed CVA began in 2Q 2020, as an addition to the prior data collection on 95 percent of total unstressed CVA. Return to text

 86. This subset of counterparties reported at the counterparty level includes the firm's top counterparties, as ranked by unstressed CVA and by stressed CVA, and comprises 95 percent of total unstressed CVA and 95 percent of total stressed CVA. Return to text

 87. The model does not take the funding valuation adjustment into account in the CVA loss estimation process. Return to text

 88. The Federal Reserve collects information on these positions separately from and in the same format as information on other trading positions. Return to text

 89. A firm's direct or indirect credit exposure to a client arising from centrally cleared derivatives is excluded from the LCPD loss estimation. This includes either the case in which the firm is acting as a financial intermediary on behalf of the client and enters into an offsetting transaction with a central counterparty (CCP) or an exchange (referred to as a back-to-back derivative) or the case in which the firm guarantees the client's performance to a CCP or an exchange (referred to as a guaranteed derivative). Return to text

 90. SFTs include securities lending and borrowing positions and repo-style transactions. Return to text

 91. The current assumption is an estimate of a potential stressed recovery rate for an undiversified credit exposure under severe market conditions. Return to text

 92. Certain entities are excluded from the selection of a firm's largest counterparty, including Canada, France, Germany, Italy, Japan, the United Kingdom, the United States, and central counterparties. For an intermediate holding company (IHC), affiliate counterparties, as they are defined in the U.S. final rule for single counterparty credit limits pursuant to the Dodd-Frank Wall Street Reform and Consumer Protection Act, 83 FR 38460 (Aug. 6, 2018) are also excluded from the selection of its largest counterparty. Return to text

 93. The Federal Reserve generally projects that a firm takes actions to maintain its current level of assets, including its securities, trading assets, and loans, over the projection horizon. The Federal Reserve assumes that a firm's risk-weighted assets and leverage ratio denominators remain unchanged over the projection horizon, except for changes primarily related to items subject to deduction from regulatory capital or due to changes to the Board's regulations. Return to text

 94. See 12 C.F.R. pt. 217. Return to text

 95. 12 C.F.R. pt. 252., Appx. B at 3.4(b). Return to text

 96. The Federal Reserve and other federal bank regulatory agencies in 2018 approved a final rule modifying their regulatory capital rules and providing an option to phase in over three years the day-one regulatory capital effects of updated accounting standard known as the "Current Expected Credit Losses" (CECL) methodology.
See https://www.federalregister.gov/documents/2019/02/14/2018-28281/regulatory-capital-rule-implementation-and-transition-of-the-current-expected-credit-losses. Additionally, in 2020, these agencies approved a final rule providing banking organizations that implement CECL during the 2020 calendar year the option to delay for two years an estimate of CECL's effect on regulatory capital, relative to the incurred loss methodology's effect on regulatory capital, followed by a three-year transition period.
See https://www.federalregister.gov/documents/2020/09/30/2020-19782/regulatory-capital-rule-revised-transition-of-the-current-expected-credit-losses-methodology-for  Return to text

 97. For a discussion of the effect of changing this tax rate assumption, see Board of Governors of the Federal Reserve System, Dodd-Frank Act Stress Test 2013: Supervisory Stress Test Methodology and Results (Washington: Board of Governors, March 2013), 11, box 2, https://www.federalreserve.gov/newsevents/press/bcreg/dfast_2013_results_20130314.pdf. For an explanation of modifications to the calculation of projected capital to account for the passage of the Tax Cuts and Jobs Act in December 2017, see Board of Governors of the Federal Reserve System, Dodd-Frank Act Stress Test 2018: Supervisory Stress Test Methodology and Results (Washington: Board of Governors, June 2018), 16, box 2, https://www.federalreserve.gov/publications/files/2018-dfast-methodology-results-20180621.pdf. Return to text

 98. This one-year look-ahead is equal to the look forward period for determining the appropriate level of allowance for expected credit losses on loans, as loan timing differences are the primary driver of projected temporary differences. DTAs from net operating losses (NOLs) are not evaluated for a potential valuation allowance because DTAs from NOLs are fully deducted from regulatory capital. Return to text

 99. The Federal Reserve calculates taxable income as PPNR less credit losses on HTM and AFS securities, net charge-offs on loans measured at amortized cost, and other losses, including trading and counterparty losses and losses on HFS and fair-value option loans. Return to text

 100. The Federal Reserve uses the following capital action assumptions in projecting post-stress capital levels and ratios: (1) no dividends on any instruments that qualify as common equity tier 1 (CET1) capital; (2) all payments on instruments that qualify as additional tier 1 capital or tier 2 capital are equal to the stated dividend, interest, or principal due on such instruments; (3) no redemption or repurchase of any capital instrument that is eligible for inclusion in the numerator of a regulatory capital ratio; and (4) no issuances of common stock or preferred stock. Return to text

 101. See 12 C.F.R. pt. 217. Return to text

 102. See 12 C.F.R. pt. 217. Return to text