Appendix B: Models to Project Net Income and Stressed Capital

This appendix describes the models used to project stressed capital ratios and pre-tax net income and its components for the 33 bank holding companies (BHCs) subject to DFAST 2016.³⁵ The models fall into five broad categories:

1. Models to project losses on loans held in the accrual loan portfolio; loans in the accrual loan portfolio are those measured under accrual accounting, rather than fair-value accounting.
2. Models to project other types of losses, including those from changes in fair value on loans held for sale or measured under the fair-value option; losses on securities, trading, and counterparty exposures; losses related to operational-risk events; and mortgage repurchase/put-back losses.
3. Models to project the components of pre-provision net revenue (PPNR) (revenues and non-credit-related expenses).
4. Models to project balance sheet items and risk-weighted assets (RWAs).
5. The calculations to project capital ratios, given projections of pre-tax net income, assumptions for determining provisions into the allowance for loan and lease losses (ALLL), and prescribed capital actions.

The Federal Reserve has updated its model descriptions to increase clarity and consistency in the amount of detail provided across these supervisory models but has either made only incremental refinement or re-estimated model parameters with additional data for a majority of the models described here. The Federal Reserve enhanced its methods for estimating operational risk and components of MRWA, as well as the calculation of regulatory capital and capital ratios (see box 1).

The supervisory models also incorporate material changes in a BHC's business plan, such as a planned merger, acquisition, consolidation, or divestiture, where applicable.

Losses on the Accrual Loan Portfolio

More than a dozen individual models are used to project losses on loans held in the accrual loan portfolio. The individual loan types modeled can broadly be divided into wholesale loans, such as commercial and industrial (C&I) loans and commercial real estate (CRE) loans, and retail loans, including various types of residential mortgages, credit cards, student loans, auto loans, small business loans, and other consumer lending. In some cases, these major categories comprise several subcategories, each with its own loss projection model, but the models within a subcategory are similar in structure and approach. The models project losses using detailed loan portfolio data provided by the BHCs on the Capital Assessments and Stress Testing (FR Y-14) report.

Two general approaches are taken to model losses on the accrual loan portfolio. In the first approach--an approach broadly used for DFAST 2016--the models estimate expected losses under the macroeconomic scenario; that is, they project the probability of default (PD), loss given default (LGD), and exposure at default (EAD) for each quarter of the planning horizon. Expected losses in quarter t are the product of these three components:

Loss t = PD t * LGD t * EAD t

PD is generally modeled as part of a transition process in which loans move from one payment status to another (e.g., from current to delinquent) in response to economic conditions. Default is the last possible transition, and PD represents the likelihood that a loan will default during a given period. The number of payment statuses and the transition paths modeled differ by loan type.

LGD is typically defined as a percentage of EAD and is based on historical data. For some loan types, LGD is modeled as a function of borrower, collateral, or loan characteristics and the macroeconomic variables from the supervisory scenarios. For other loan types, LGD is assumed to be a fixed percentage for all loans in a category. Finally, the approach to EAD varies by loan type and depends on whether the outstanding loan amount can change between the current period and the period in which the loan defaults (e.g., for lines of credit).

In the second approach, the models capture the historical behavior of net charge-offs relative to changes in macroeconomic and financial market variables and loan portfolio characteristics.

The loss models primarily focus on losses arising from loans in the accrual loan portfolio as of December 31, 2015. The loss projections also incorporate losses on loans originated after the planning horizon begins. These incremental loan balances are calculated based on the Federal Reserve's projections of loan balances over the planning horizon. These new balances are assumed to have the same risk characteristics as those of the loan portfolio as of December 31, 2015, with the exception of loan age in the retail and CRE portfolios, where seasoning is incorporated. Where applicable, new loans are assumed to be current, and BHCs are assumed not to originate types of loans that are no longer allowed under various regulations. Loss projections also incorporate losses on loans acquired through mergers or purchase after the planning horizon begins. Additional information provided by the BHCs about the size and composition of acquired loan portfolios is used to estimate losses on acquired portfolios.

Loss projections generated by the models are adjusted to take account of purchase accounting treatment, which recognizes discounts on impaired loans acquired during mergers and any other write-downs already taken on loans held in the accrual loan portfolio. This latter adjustment ensures that losses related to these loans are not double counted in the projections.

Wholesale Lending: Corporate Loans

Losses stemming from default on corporate loans are projected at the loan level using an expected loss modeling framework. Corporate loans consist of a number of different categories of loans, as defined by the Consolidated Financial Statements for Holding Companies--FR Y-9C report (FR Y-9C). The largest group of these loans includes 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 BHC's corporate loan rating process.³⁶

The PD for a C&I loan is projected over the planning horizon by first calculating the loan's PD at the beginning of the planning horizon and then projecting it forward using an equation that relates historical changes in PD to changes in the macroeconomic environment. The PD as of December 31, 2015, is calculated for every C&I loan in a BHC's portfolio using detailed, loan-level information submitted by the BHC. For publicly traded borrowers, a borrower-specific PD, based on the expected default frequency, is used. For other borrowers, the PD is estimated based on the borrower's industry category and the BHC's internal credit rating for the borrower, which is converted to a standardized rating scale and then mapped to a PD. Loans that are 90 days past due, in non-accrual status, or that have a Financial Accounting Standards Board Accounting Standards Codification Subtopic 310-10 (ASC 310-10) reserve as of December 31, 2015, are considered in default.

Quarterly changes in the PD after the fourth quarter of 2015 are projected over the planning horizon using a series of equations that relate historical changes in the average PD as a function of changes in macroeconomic variables, including changes in real gross domestic product (GDP), the unemployment rate, and the spread on BBB-rated corporate bonds. The equations are estimated separately by borrower industries, credit quality categories, and whether the borrower is foreign or domestic.

The LGD for a C&I loan at the beginning of the planning horizon is determined by the line of business, seniority of lien (if secured), country, and ASC 310-10 reserve, if applicable. The LGD is then projected forward by relating the change in the LGD to changes in the PD. In the model, the PD is used as a proxy for economic conditions, and, by construct, increases in PD generally lead to higher LGDs.

The EAD for C&I loans equals the sum of the funded balance and a portion of the unfunded commitment, which reflects the amount that is likely to be drawn down by the borrower in the event of default. This drawdown amount was estimated based on the historical drawdown experience for defaulted U.S. syndicated revolving lines of credit that are in the Shared National Credit (SNC) database.³⁷ In the case of closed-end C&I loans, the funded balance and the corresponding EAD equals the outstanding balance. The EAD for standby letters of credit and trade finance credit are conservatively assumed to equal the total commitment.

Other corporate loans that are similar in some respects to C&I loans are modeled using the same framework. These loans include owner-occupied CRE loans, capital equipment leases, loans to depositories, and other loans.³⁸ Projected losses on owner-occupied CRE loans are disclosed in total CRE losses, while projected losses for the remaining other corporate loans are disclosed in the other loans category.

Wholesale Lending: CRE Mortgages

CRE mortgages are loans collateralized by domestic and international multifamily or nonfarm, nonresidential properties, and construction and land development loans (C&LD), as defined by the FR Y-9C report. Losses stemming from default on CRE mortgages are projected at the loan level using an expected-loss modeling framework.

The PD model for CRE mortgages is a hazard model of the probability that a loan transitions from current to default status, given the characteristics of the loan as well as macroeconomic variables, including commercial and residential property price indices and unemployment rates, at both the geographic market and national level. Once defaulted, the model assumes the loan does not re-perform; the effect of re-performance on the estimated loan loss is captured in the LGD model. A CRE mortgage loan is considered in default if it is 90 days past due, in non-accrual status, has an ASC 310-10 reserve, or had a very low internal credit rating at the most recent time its maturity was extended. The PD model also incorporates a nonlinear increase in PD as the loan maturity nears. The effect of loan maturity on the PD is estimated to be different for income-producing and C&LD loans, and is estimated separately for each loan type using historical Capital Assessments and Stress Testing (FR Y-14Q) data. However, the proportional effect of other loan characteristics and the macroeconomic variables is assumed to be the same for income-producing properties and C&LD loans and is estimated using a single model for both types of loans using historical commercial mortgage-backed security data.

The LGD for CRE mortgages is estimated using FR Y-14Q data on ASC 310-10 reserves. The model first estimates the probability that a defaulted loan will have losses as a function of loan characteristics and macroeconomic variables including commercial property prices, residential house prices, and the unemployment rate. Then, using loans with losses, the model estimates the loss on the CRE mortgage as a function of the expected probability of loss, characteristics of the loan, and residential house prices and the unemployment rate. Finally, the EAD for CRE mortgages is assumed to equal the loan's full committed balance for both income producing and C&LD loans.

Retail Lending: Residential Mortgages

Residential mortgages held in BHC portfolios include first and junior liens--both closed-end loans and revolving credits--that are secured by one- to four-family residential real estate as defined by the FR Y-9C report. Losses stemming from default on residential mortgages are projected at the loan level using an expected-loss modeling framework.³⁹

The PD model for first-lien residential mortgages estimates the probability that a loan transitions to different payment statuses, including current, delinquent, servicing transfer, default, and paid off. Separate PD models are estimated for three types of closed-end, first-lien mortgages: fixed-rate, adjustable-rate, and option adjustable-rate mortgages. The PD model specification varies somewhat by loan type; however, in general, each model estimates the probability that a loan transitions from one payment state to another (e.g., from current to delinquent or from delinquent to default) over a single quarter, given the characteristics of the loan, borrower, and underlying property as well as macroeconomic variables, including local house prices, the statewide unemployment rate, and interest rates.⁴⁰

Origination vintage effects are also included in the estimation in part to capture unobserved characteristics of loan quality. The historical data used to estimate this model are industrywide, loan-level data from many banks and mortgage loan originators. These estimated PD models are used to simulate default for each loan reported by each BHC under the supervisory scenarios. Loans that are 180 days or more past due as of December 31, 2015, are considered in default.

The LGD for residential mortgages is estimated using two models. One model estimates the amount of time that elapses between default and real estate owned (REO) disposition (timeline model), while the other relates characteristics of the defaulted loan, such as the property value at default, to one component of losses net of recoveries--the proceeds from the sale of the property net of foreclosure expenses (loss model).⁴¹

These net proceeds are calculated from historical data on loan balances, servicer advances, and losses from defaulted loans in private-label, residential mortgage-backed securities (RMBS). These RMBS data are also used to estimate the LGD loss model separately for prime jumbo loans, subprime, and alt-A loans.⁴²

Finally, using the elapsed time between default and REO disposition estimated in the timeline model, total estimated losses are allocated into credit losses on the defaulted loans, which are fully written down at the time of default, or net losses arising from the eventual sale of the underlying property (other real estate owned--or OREO--expenses), which flow through PPNR. House price changes from the time of default to foreclosure completion (REO acquisition) are captured in LGD, while house price changes after foreclosure completion and before sale of the property are captured in OREO expenses. The LGD for loans already in default as of December 31, 2015, includes further home price declines through the point of foreclosure.

Home equity loans (HELs) are junior-lien, closed-end loans, and home equity lines of credit (HELOCs) are revolving open-end loans extended under lines of credit. Both are secured by one- to four-family residential real estate as defined by the FR Y-9C report. Losses stemming from default on HELs and HELOCs are projected at the loan level in an expected loss framework that is similar to first-lien mortgages, with a few differences. The PD model for HELOCs estimates the probability that the loan transitions from its status as of December 31, 2015, to payment statuses including current, impaired, default, prepaid, and paid off. At each point in time, each transition model is a function of account characteristics, customer characteristics, economic environment, and past delinquency history. Economic drivers include interest rates, home prices, and the unemployment rate.

For second-lien HELs and HELOCs that are current as of December 31, 2015, but are behind a seriously delinquent first-lien, the model assumes elevated default rates under the supervisory scenarios. In addition, most HELOC contracts require only payment of interest on the outstanding line balance during the period when the line can be drawn upon (draw period). When the line reaches the end of its draw period (end-of-draw), the outstanding line balance either becomes immediately payable or converts to a fully amortizing loan. HELOCs that reach the end-of-draw period are assumed to prepay at a higher rate just prior to end-of-draw and to default at a higher rate just after end-of-draw than HELOCs that are still in their draw period.

The LGD for HELs and HELOCs is estimated using data from private-label mortgage-backed securities, using the same models used for closed-end first-lien mortgages, but the estimated total mortgage losses for properties with a defaulted HEL or HELOC are allocated based on the lien position. Finally, for HELOCs, EAD is assumed to equal the credit limit.

Retail Lending: Credit Cards

Credit cards include both general purpose and private-label credit cards, as well as charge cards, as defined by the FR Y-9C report. Credit card loans extended to individuals are included in retail credit cards, while credit cards loans extended to businesses and corporations are included in other retail lending and are modeled separately. Losses stemming from defaults on credit cards are projected at the loan level using an expected-loss modeling framework.

The PD model for credit cards estimates the probability that a loan transitions from delinquency status to default status, given the characteristics of the account and borrower as well as macroeconomic variables, including unemployment. When an account defaults, it is assumed to be closed and does not return to current status. Credit card loans are considered in default when they are 120 days past due. Because the relationship between the PD and its determinants can vary with the initial status of the account, separate transition models are estimated for accounts that are current and active, current and inactive accounts, and delinquent accounts. In addition, because this relationship can also vary with time horizons, separate transition models are estimated for short-, medium-, and long-term horizons. The historical data used to estimate this model are industrywide, loan-level data from many banks, and separate models were estimated for bank cards and charge cards. The PD model is used to forecast the PD for each loan reported by each BHC in the Capital Assessments and Stress Testing (FR Y-14M) report.

The LGD for credit cards is assumed to be a fixed percentage and is calculated separately for bank cards and charge cards based on historical industry data on LGD during the most recent economic downturn. The EAD for credit cards equals the sum of the amount outstanding on the account and a portion of the credit line, which reflects the amount that is likely to be drawn down by the borrower between the beginning of the planning horizon and the time of default. This drawdown amount is estimated as a function of account and borrower characteristics. Because this relationship can vary with the initial status of the account and time to default, separate models are estimated for current and delinquent accounts and for accounts with short-, medium-, and long-term transition to default. For accounts that are current, separate models were also estimated for different credit-line-size segments.

Retail Lending: Auto

Auto loans are consumer loans extended for the purpose of purchasing new and used automobiles and light motor vehicles as defined by the FR Y-9C report. Losses stemming from default in auto retail loan portfolios are projected at the portfolio segment level using an expected loss framework.

The PD model for auto loans estimates the probability that a loan transitions from either a current or delinquent status to default status, given the characteristics of the loan and borrower as well as macroeconomic variables, including house prices and the unemployment rate. Default on auto loans is defined based on either the payment status (120 days past due), actions of the borrower (bankruptcy), or actions of the lender (repossession). Because the relationship between the PD and its determinants can vary with the initial status of the account, separate transition models are estimated for accounts that are current and delinquent accounts. The historical data used to estimate this model are loan-level, credit bureau data.

The LGD for auto loans is estimated given the characteristics of the loan as well as macroeconomic variables, such as the unemployment rate and used car prices. The historical data used to estimate this model are pooled, segment-level data provided by the BHCs on the FR Y-14Q reports. The EAD for auto loans is based on the typical pattern of amortization of loans that ultimately defaulted in historical credit bureau data. The estimated EAD model captures the average amortization by loan age for current and delinquent loans over nine quarters.

Retail Lending: Other Retail Lending

Other retail lending includes the small business loan portfolio, the other consumer loan portfolio, the student loan portfolio, the business and corporate credit card portfolio, and international retail portfolio. Losses due to default on other retail lending are forecast by modeling net charge-off rates as a function of portfolio risk characteristics and macroeconomic variables. This model is then used to predict future charge-offs consistent with the macroeconomic variables provided in the supervisory scenarios.⁴³ The predicted net charge-off rate is applied to balances projected by the Federal Reserve to estimate projected losses. Default is defined as 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, corporate cards, and international retail portfolios. The net charge-off rate is modeled in a system of equations that also includes the delinquency rate and the default rate.

In general, each rate is modeled in an autoregressive specification that also includes the rate in the previous delinquency state, characteristics of the underlying loans, macroeconomic variables, such as changes in the unemployment rate and disposable personal income growth, and, in some cases, seasonal factors. The models are specified to implicitly capture roll-rate dynamics. In some cases, the characteristics of the underlying loans, such as dummy variables for each segment of credit score at origination, are also interacted with the macroeconomic variables to capture differences in sensitivities across risk segments to changes in the macroeconomic environment. Each retail product type is modeled separately and, for each product type, economic theory and the institutional characteristics of the product guide the inclusion and lag structure of the macroeconomic variables in the model.

Because of data limitations and the relatively small size of these portfolios, the net charge-off rate for each loan type is modeled using industrywide, monthly data at the segment level. For most portfolios, these data are collected on the FR Y-14Q Retail schedule, which segments each portfolio by characteristics such as borrower credit score; loan vintage; type of facility (e.g., installment versus revolving); and, for international portfolios, geographic region.⁴⁴

Charge-off rates are projected by applying the estimated system of equations to each segment of the BHC's loan portfolio as of December 31, 2015. The portfolio-level charge-off rate equals the dollar-weighted average of the segment-level charge-off rates.⁴⁵ These projected charge-off rates are applied to the balances projected by the Federal Reserve to calculate portfolio losses.

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Loan-Loss Provisions for the Accrual Loan Portfolio

Losses on the accrual loan portfolio flow into net income through provisions for loan and lease losses. Provisions for loan and lease losses equal projected loan losses for the quarter plus the amount needed for the ALLL to be at an appropriate level at the end of the quarter, which is a function of projected future loan losses. The appropriate level of ALLL at the end of a given quarter is generally assumed to be the amount needed to cover projected loan losses over the next four quarters.⁴⁶ Because this calculation of ALLL is based on projected losses under the adverse or severely adverse scenarios, it may differ from a BHC's actual level of ALLL at the beginning of the planning horizon, which is based on the BHC's assessment of future losses in the current economic environment. Any difference between these two measures of ALLL is smoothed into the provisions projection over the nine quarters of the planning horizon. Because projected loan losses include off-balance sheet commitments, the BHC's allowance at the beginning of the planning horizon for credit losses on off-balance sheet exposures (as reported on the FR Y-9C report) is subtracted from the provisions projection in equal amounts each quarter.

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Other Losses

Loans Held for Sale or Measured under the Fair-Value Option

Certain loans are not accounted for on an accrual basis. Loans to which the fair-value option (FVO) is applied are valued as mark-to-market assets. Loans that are held-for-sale (HFS) are carried at the lower of cost or market value.

FVO/HFS loan portfolios are identified by BHCs and reported on the FR Y-14Q report. Losses related to FVO/HFS loans are recognized in earnings on the income statement at the time of the devaluation and are estimated by applying scenario-specific interest rate and credit spread projections.

Losses on C&I and CRE loans and commitments are estimated by revaluing each loan or commitment each quarter using a stressed discount yield. The initial discount yield is based on the loan or commitment's initial fair value, settlement date, maturity date, and interest rate. Quarterly movements in the discount yield over the planning horizon are assumed to equal the stressed change in corporate bond yields of the same credit rating and maturity, adjusted for potential changes in credit ratings. The models estimate changes in the fair value of the loan in a given scenario on a committed-balance basis.

Losses on retail loans held under FVO/HFS accounting are estimated over the nine quarters of the planning horizon using a duration-based approach. This approach uses balances on these loans reported on the FR Y-14Q report, estimates of portfolio-weighted duration, and quarterly changes in stressed spreads from the macroeconomic scenario. Estimates are calculated separately by vintage and loan type. No losses are assumed for residential mortgage loans under forward contract with the government-sponsored enterprises (GSEs).

Gains and losses on FVO loan hedges are modeled on a quarterly basis, using a set of scenario-specific factor projections and factor sensitivities submitted by BHCs. Profits and losses are calculated for a variety of hedge types, including corporate credit, rates, equities, and commercial mortgage-backed securities (CMBS). These profits and losses are netted from estimated losses on the FVO loans.

Projections of fair value losses assume that each position has a constant maturity over the projection horizon. Aggregate gains and losses on hedges at the firm level are netted against projected gains and losses on wholesale and retail exposures in order to arrive at final estimates.

Securities in the Available-for-Sale and Held-to-Maturity Portfolios

Securities in the available-for-sale and held-to-maturity (AFS/HTM) portfolios include U.S. Treasury, U.S. Agency, municipal, mortgage-backed, asset-backed, corporate debt, and equity securities. The AFS/HTM portfolio does not include securities held for trading; losses on these securities are projected separately. Changes in the value of the AFS/HTM portfolio can potentially impact a BHC's capital in two ways. First, other-than-temporary impairment (OTTI) losses on AFS/HTM securities and other realized gains and losses are recognized in the net income of all BHCs. Second, under regulatory capital rules, advanced approaches BHCs and other BHCs that opt into advanced approaches treatment for AOCI must incorporate into Common Equity Tier 1 (CET1) capital the accumulated other comprehensive income (AOCI) that arises, in part, from changes in the value of AFS securities. Both OTTI and unrealized gains and losses on AFS securities are projected at the security level, based on FR Y-14Q data, and aggregated up to the BHC level.

OCI associated with AFS securities arises from changes in the unrealized gains and losses on those securities, which are calculated as the difference between each security's fair value and its amortized cost. The amortized cost of each AFS security is collected by the Federal Reserve and equals the purchase price of a debt security periodically adjusted if the debt security was purchased at a price other than par or face value or has had a prior impairment recognized in earnings. The fair value of each AFS security is projected over the nine-quarter planning horizon using one of three methods: a present-value calculation, a full revaluation, or a duration-based approach. The simple present-value calculation is used to directly re-price U.S. Treasury securities. This calculation incorporates both the timing and amount of contractual cash flows and quarterly Treasury yields from the macroeconomic scenario. Full revaluation uses a security-specific discounted cash flow model to re-price agency MBS. Finally, the duration-based approach is used for all other securities. The duration-based approach forecasts the quarterly price path based on an approximation of the relationship between the securities price and its yield, taking into account security-specific information. Separate spread projections are estimated for securities in each asset class using projections of interest rates, corporate credit spreads, volatility, and asset prices included in supervisory scenarios. Final projections of OCI take into account applicable interest hedges on the securities.

Securities experiencing an impairment over the forecast horizon may be at risk of an OTTI, which affects earnings and regulatory capital.⁴⁷ An impairment occurs when the fair value of a security falls below its amortized cost. If the BHC intends to sell a security, or if it is more likely than not that the BHC will have to sell without recovering its investment, then any impairment on that security will flow through the BHC's earnings and the full write-down to fair value is recognized periodically as OTTI until the quarter in which the security is sold. Otherwise, a BHC must recognize as a charge to earnings only the credit component of OTTI, which reflects a non-temporary decline in present value below amortized cost. The supervisory OTTI models are designed to incorporate the credit component only, unless the firm will be required to sell the security.⁴⁸

U.S. Treasury and U.S. government agency obligations and U.S. government agency or GSE mortgage-backed securities are assumed not to be at risk for the kind of credit impairment that results in credit-related OTTI charges. The supervisory OTTI models test all other securities for the potential for OTTI impairment under the stress scenario. For all securities at risk for impairment that would result in credit-related OTTI charges, future balances are assumed to have risk characteristics similar to those of the initial balances.

Securities at risk of an impairment that would result in credit-related OTTI charges can be grouped into three categories: securitizations, direct debt obligations, and equity securities.

Securitized obligations include CMBS, U.S. non-agency RMBS, collateralized loan obligations (CLOs), auto asset-backed securities (ABS), credit card ABS, and foreign RMBS. The present value of security-level cash flows is calculated based on the projected collateral cash flows and the structure of the security using the contractual rate of interest on the security as the discount rate. The projected collateral cash flows of securitized obligations depend on the performance of the collateral pool, which is projected using internally developed or third-party models that are conditioned on macroeconomic variables such as the unemployment rate, real estate prices, GDP, and interest rates. The CMBS, U.S. non-agency RMBS, and CLO models project the performance of each loan in the pool. These models are broken into PD and LGD components and include applicable loan-specific variables, such as loan-to-value ratio, issuer credit rating, and loan geography. Other models project the performance of the overall portfolio. All models consider variables specifying the type of loan and loan delinquency status.

Direct debt obligations are issued by a single issuer with recourse and include corporate bonds and sovereign bonds. In the models, whether a credit-related OTTI charge is taken on these securities is based on the potential for a rating downgrade. The potential of a rating downgrade is determined by projected changes in the one-year PD of the issuer for corporate bonds and the credit default swap (CDS) spread for sovereign bonds in response to changes in macroeconomic drivers, such as interest rates, spreads, and regional GDP. If the projected value of either the PD or the CDS spread crosses a threshold level consistent with a "CCC/Caa" rating or below, then the security is considered to have an OTTI, to the extent the projected present value of cash flow is below amortized cost. If a security is considered OTTI, then the present value of cash flows is projected using historical data on bond recovery rates given default.

Projected OTTI charges on other direct debt obligations, including municipal bonds and security types with smaller levels of exposure, are based on the statistical relationship between observed OTTI write-downs and the evolution of unrealized losses over the scenario as projected by the fair value model. The probability of an OTTI write-down and the severity of the write-down are estimated separately. Observed OTTI write-downs are based on data reported on FR Y-14Q and unrealized loss is estimated based on the initial amortized cost and projections of the fair value model for the security. Projected OTTI charges on equity securities are based on the projected fair value of each security as determined by the path of the U.S. equities index and the sensitivity of each security's returns to the overall returns of the index.

Balances at risk of OTTI are assumed not to decrease. After a security is written down as OTTI, the difference between its original value and its post-OTTI value is assumed to be invested in securities with the same risk characteristics. Similarly, the fair value projections assume that duration and remaining life remain constant. Net increases projected by the Federal Reserve in a BHC's securities portfolio after December 31, 2015, are assumed to be in short-term, riskless assets, and no OTTI or OCI are projected on these securities.

Trading and Private Equity

Losses related to trading positions that are included in the supervisory stress test are of two primary types. The first type arises from changes in the mark-to-market value of the trading positions. The second type is associated with either the potential or the realized default of obligors and counterparties. The models used to project losses on trading positions under the global market shock account for both types of losses and rely on the market values and stressed revaluation of positions provided by BHCs on the FR Y-14Q.

Mark-to-market gains and losses on trading positions are estimated by applying the movements in the global market shock factors to the associated market values or market value movements provided by BHCs. The global market shock specifies movements in numerous market factors, such as equity prices, foreign exchange rates, interest rates and spreads, commodity prices, securitized product prices, and private equity values. BHCs provide the market value of their securitized products and private equity positions. For all other market factors, BHCs provide the estimated market value change (i.e., the profit or loss) across the trading book associated with a single, limited movement in a market factor (e.g., +1 basis point movement in a foreign exchange rate) or a range of positive and negative movements in a market factor (e.g., -30 percent, -25 percent, +30 percent for a foreign exchange rate). These market values and market value changes are collected for the same factors specified in the global market shock. The computation of gains and losses is performed by applying the market factor movements specified in the global market shock to the information reported by BHCs. For securitized products and private equity positions, the market values are multiplied by the global market shock market value movements. For all other market factors the gains and losses are computed by either multiplication of the global market shock movement and a single associated market value change or by interpolation using the range of associated market value changes. The ranges are used to capture the non-linear market value changes associated with certain assets.

Losses that are related to the potential adverse changes in credit quality of a counterparty to derivatives transactions are captured through credit valuation adjustments (CVA). CVA is an adjustment to the mark-to-market valuation of a BHC's trading positions that accounts for the risk of adverse changes in counterparty credit quality prior to default on its obligations. BHCs report their baseline and stressed CVA on a counterparty-level on the FR Y-14Q as well as the associated baseline and stressed values of the components of CVA: expected exposure, PD, and LGD. The loss estimate is computed as the difference between the baseline and the stressed CVA for all counterparties.

In addition to mark-to-market and CVA losses on trading positions, the losses associated with the default of issuers of credit instruments is captured through an incremental default risk (IDR) model that estimates the losses in excess of mark-to-market losses. The exposure types captured through this issuer default-loss estimate include single-name products (e.g., corporate bonds and single name CDS), index and index-tranche products, and securitized products, which are distinct from the bilateral derivatives agreements and securities financing transactions included in the largest counterparty default scenario component (described below). A distribution of simulated sets of issuer defaults is created through a random jump-to-default framework that is based on factors such as probability of default and obligor correlations. Default distributions are simulated at the level of individual obligors or at the instrument and rating level, depending on exposure type. Losses associated with each default are derived from exposure at default, which is based on position information reported on the FR Y-14Q, and loss given default, which is based on historical information. The loss estimate is the loss associated with a tail percentile of the distribution, which is calibrated to the severity of the macroeconomic scenario.

Largest Counterparty Default

To estimate losses from the default of counterparties to derivatives and securities financing transactions, the Federal Reserve applied a counterparty default scenario component to the eight BHCs that have substantial trading or custodial operations. The loss is based on the assumed instantaneous and unexpected default of a BHC's largest counterparty, defined as the counterparty that would produce the largest total net stressed loss if it were to default on all of its derivatives and securities financing transactions. Net stressed loss was estimated using net stressed current exposure (CE), which is derived by applying the global market shock to the unstressed positions as well as any collateral posted or received and reported by BHCs. For derivative agreements, applicable CDS hedges and CVA are netted from the net stressed current exposure. A recovery rate of 10 percent is assumed for both net stressed CE and applicable CDS hedges.

Similar to the global market shock component, the loss associated with the counterparty default component occurs in the first quarter of the projection and is an add-on to the macroeconomic conditions and financial market environment in the supervisory scenarios. Certain sovereign entities (Canada, France, Germany, Italy, Japan, the United Kingdom, and the United States) and designated clearing counterparties were excluded when selecting the largest counterparty.

Losses Related to Operational-Risk Events

Losses related to operational-risk events are a component of PPNR and include losses stemming from events such as fraud, employee lawsuits, or computer system or other operating disruptions. Operational-risk loss estimates include the average of loss estimates from two modeling approaches and estimates of potential costs from unfavorable litigation outcomes, which reflect elevated litigation risk and the associated increase in legal reserves observed in recent years. In both modeling approaches--a panel regression model and a historical simulation approach--projections of operational-risk-related losses for the 33 BHCs are modeled for each of seven operational-risk categories identified in the Board's advanced approaches rule.⁴⁹ Both models are based on historical operational-loss data submitted by the BHCs on the FR Y-14Q report.

In the panel regression model, projections of losses related to operational-risk events are the product of two components: loss frequency and loss severity. Loss frequency is modeled as a function of macroeconomic variables and BHC-specific characteristics. Macroeconomic variables, such as the real GDP growth rate, stock market return and volatility, and the unemployment rate, are included directly in the panel regression model and/or used to project certain firm-specific characteristics. Loss is projected as a product of projected loss frequency from the panel regression model and loss severity, which equals the average historical dollar loss per event in each operational-risk category. Total operational loss estimates equal the sum of loss forecasts for each operational-risk category. Because the relationship between the frequency of operational-risk events and macroeconomic conditions varies across the categories, separate models were estimated for each
category.⁵⁰

In the historical simulation model, losses at different percentiles of simulated, nine-quarter loss distributions are used as a proxy for the expected operational losses conditional on the macroeconomic scenarios. The loss frequency is assumed to follow a Poisson distribution, in which the estimated intensity parameter of the Poisson distribution is specific to event type and informed by historical industry loss frequency scaled to the assets of individual BHCs. The tail of loss severity is also informed by historical industry loss severity scaled to the assets of individual BHCs.

The distribution of aggregate annual losses is simulated by repeatedly drawing the annual event frequency from this frequency distribution, and the severity of those events is drawn from historical realized loss data for all BHCs. The percentiles of loss distributions, which are used to estimate stressed losses, are tied to the frequency of severe recessions for the severely adverse scenario and the frequency of recessions of all types for the adverse scenario. Loss forecasts for an individual BHC are the sum of the BHC's loss estimates for each event type.

Mortgage Repurchase Losses

Mortgage repurchase expenses are a component of PPNR. Mortgage loans sold to investors (GSEs, private-label security (PLS) investors, or whole loan buyers) typically include certain representations and warranties describing characteristics of the loan and its underwriting. If these representations and warranties are proven to have been breached, the loan is "put back" to the seller of the loan, who is contractually obligated to repurchase the loan at par and incur any credit loss the loan may suffer. Breaches of representations and warranties may also be settled by settlement (or make-whole) payments from the seller to the investor, and disputes may in some cases be resolved through litigation.

Mortgage repurchase losses for loans sold with representations and warranties liability are estimated in two parts. The first part is the estimation of credit losses for all loans sold by a BHC that have outstanding representations and warranties liability, including loans sold as whole loans, into private-label securities or to Fannie Mae and Freddie Mac, or loans insured by the government. Credit loss rates for each vintage of mortgage loans are estimated by applying the scenario projections of house prices to a third-party model. This part takes into account both losses recognized to date and future losses projected over the remaining lifetime of the loans. For loans sold to Fannie Mae and Freddie Mac, industrywide credit loss rates are adjusted to reflect the relative credit performance of loans sold by each BHC and are applied to the BHC's outstanding balances. These estimates are based on vintage-level data on original and current unpaid balances, current delinquency status, and losses recognized to date. Estimated credit loss rates are applied to each BHC's repurchase-eligible sold loan population, as determined by Y-14A data.

The second part is the estimation of the share of this credit loss that may be ultimately put back to the selling BHC (whether through contractual repurchase, a settlement agreement, or litigation loss). Put-back rates are estimated by investor as follows, based on either historical information on settlement payments or data on the volume of put-backs to mortgage sellers:

• Whole loans and loans sold into PLS--The estimated put-back rate is based on information from recent settlement activities in the banking industry and incorporates adjustments for supervisory assessments of BHC-specific put-back risk.
• Government-insured loans--The estimated put-back rate is also based on information from recent settlement activities.
• GSE loans--The estimated put-back rate is based on historical information on the settlements and repurchases of loans sold to Fannie Mae or Freddie Mac, with consideration given to the relative seasoning of each vintage and the time interval between default and demand.

Mortgage repurchase expenses are netted against actual mortgage put-back reserves as reported by the BHCs.

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Pre-provision Net Revenue

PPNR is forecast with a mix of models: structural using granular data on individual positions; autoregressive models that relate the components of a BHC's revenues and non-credit-related expenses, expressed as a share of relevant asset or liability balances, to BHC characteristics and to macroeconomic variables; and simple nonparametric models based on recent firm-level performance.

When choosing the level of detail at which to model the components of PPNR, consideration is given both to the BHCs' business models and the ability to accurately model components of revenue. Movements in PPNR stemming from operational-risk events, mortgage repurchases, or OREO are modeled in separate frameworks, described earlier in this document.

The PPNR model estimates and projections are adjusted where appropriate to avoid double counting movements associated with these items. In addition, gains or losses associated with debt valuation adjustments (DVA) for firms' own liabilities are removed from the historical PPNR data series used to estimate the model, and, as a result, PPNR projections do not include DVA gains or losses under the supervisory scenarios.

Separate models are estimated for 22 different components of PPNR. Components of interest income modeled include income on loans, Treasury securities, mortgage-backed securities, federal funds and repurchase agreements, other securities, trading assets, and all other interest income. The five components of interest expense modeled include interest expense on deposits, federal funds and repurchase agreements, trading liabilities and other borrowed money (OBM), subordinated debt, and all other interest expenses. Noninterest, non-trading income modeled include service charges on deposits, fiduciary income, income from insurance, investment banking and net servicing fees, and all other noninterest income. Finally, the three components of noninterest expense (compensation expense, fixed asset expense, and all other noninterest expense) as well as trading revenue are modeled as part of PPNR. Autoregressive models are estimated using historical, merger-adjusted data from the FR Y-9C report. The autoregressive model specifications vary by PPNR component. But, in general, each component is related to BHC-specific characteristics, including, in some cases, total assets, asset composition, funding sources, and liabilities. In some PPNR components, these measures of BHC portfolio and business activity do not adequately capture the significant variation across BHCs, so BHC-specific controls are included in the models for these components. Macroeconomic variables used to project PPNR include yields on Treasury securities, corporate bond yields, mortgage rates, real GDP, and stock market price movements and volatility. The specific macroeconomic variables differ across equations based on statistical predictive power and economic interpretation.

For other volatile components of PPNR, the Federal Reserve follows alternative approaches to the autoregressive model. For example, some noninterest income and noninterest expense components that are highly volatile quarter-to-quarter but do not exhibit a clear cyclical pattern are modeled as a constant forecast ratio to reflect a most recent eight-quarter median performance. Finally, the forecast of interest expenses on subordinated debt is based on security-level information and takes into account differences across firms in their maturity schedule and debt pricing in each of the supervisory scenarios.

Trading revenues are volatile because they include both changes in the market value of trading assets and fees from market-making activities. Forecasts of PPNR from trading activities at the six BHCs subject to the global market shock are modeled in the aggregate and then allocated to each BHC based on a measure of the BHC's market share. In addition, because forecasts of trading revenues are intended to include the effect of the relevant macroeconomic variables and to exclude the effect of the global market shock, net trading revenue is modeled using a median regression approach to lessen the influence of extreme movements in trading revenue associated with the recent financial crisis. Trading revenues for the remaining BHCs are modeled in an autoregressive framework similar to that of other PPNR components.

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Balance-Sheet Items and Risk-Weighted Assets

The BHC balance sheet is projected based on a model that relates industrywide loan and non-loan asset growth to each other and to broader economic variables including a proxy for loan supply. The model allows for both long-run relationships between the industry aggregates and macroeconomic variables, as well as short-term dynamics that cause deviations from these relationships. It is estimated using aggregate data from the Federal Reserve's Financial Accounts of the United States (Z.1) and the Bureau of Economic Analysis's National Income and Product Accounts.

Industry loan and asset growth rates are projected over the planning horizon using the macroeconomic variables prescribed in the supervisory scenario. Over this horizon, each BHC is assumed to maintain a constant share of the industry's total assets, total loans, and total trading assets. In addition, each BHC is assumed to maintain a constant mix within their loan and trading asset categories. These assumptions are applied as follows

• Each category of loans at a BHC is assumed to grow at the projected rate of total loans in the industry.
• Each category of trading assets at a BHC is assumed to grow as a function of both the projected rate of total assets and the projected market value of trading assets in the industry.
• All other assets of a BHC, including securities, are assumed to grow at the projected rate of non-loan assets in the industry.
• A BHC's cash holdings level, the residual category, is set such that the sum of cash and noncash assets grows at the projected rate of total assets.
• Growth in securities is assumed to be in short-term, riskless assets.

Balance sheet projections incorporate expected changes to a BHC's business plan, such as mergers, acquisitions, and divestitures that are likely to have a material impact on its capital adequacy and funding profile. BHC-submitted data are used to adjust the projected balance sheet in the quarter when the change is expected to occur. Once adjusted, assets are assumed to grow at the same rate as the pre-adjusted balance sheet. Only submitted divestitures that are either completed or contractually agreed upon before April 5, 2016, are incorporated.

The projection of RWAs is accomplished in two parts and is based on the tenets of the standardized approach and market risk rule in the Board's Regulation Q.⁵¹ The first part requires estimating the path of credit risk-weighted assets based on exposures from loans and securities.⁵² The second requires estimating the path of MRWA based on exposures under the market risk rule.⁵³

Credit RWA projection is a straightforward implementation of the standardized approach. Most risk weights are imputed from the FR Y-9C report and held fixed throughout the projection horizon. Risk weights are applied to appropriate balance paths and summed across categories. This treatment is consistent with the assumption that the general features of the credit portfolio and non-trading book assets remain constant during the projection period.

MRWA projections incorporate the assumption that market risk is sensitive to the economic scenario. In particular, the path of MRWAs is sensitive to changes in the projected volatility of the underlying mix of trading assets. While the underlying mix of exposures subject to the market risk rule is assumed to remain constant throughout the scenario, some elements of MRWAs are affected by changes in market conditions assumed in supervisory scenarios. For example, projected value-at-risk (VaR) calculations--an important element of MRWAs--rise as the volatility of the portfolio's underlying assets increases. Similarly, a firm's incremental risk charge and its comprehensive risk measure are affected by the volatility of credit products. The remaining categories of MRWAs are assumed to evolve according to projections of a BHC's trading assets. These properties make the trajectory of MRWAs more dynamic than credit RWAs because both the underlying path of trading assets and the volatility associated with the portfolio evolve.

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Regulatory Capital

The final modeling step translates the projections of revenues, expenses, losses, provisions, balances, and RWAs from the models described above into estimates of regulatory capital for each BHC under the supervisory scenarios. Regulatory capital is calculated using the definition of capital in the Board's Regulation Q.⁵⁴ Regulatory capital is calculated consistent with the requirements that will be in effect during the projected quarter of the planning horizon.⁵⁵ The definition of regulatory capital changes throughout the planning horizon in accordance with the transition arrangements in the revised regulatory capital framework.⁵⁶

Estimated regulatory capital incorporates estimates of net income and taxable income based on supervisory projections of total losses and revenues. A consistent tax rate across all BHCs is applied to taxable income to calculate after-tax net income over the projection period.⁵⁷ The consistent tax rate is also used to generate projections of deferred tax assets (DTAs) from temporary timing differences and net operating losses. DTA projections are also based on a firm's starting tax position, including net operating loss carrybacks and tax history. Then, a valuation allowance is estimated to determine whether a BHC will have sufficient taxable income in the future to realize its DTAs. Changes in the valuation allowance are factored into after-tax net income. Finally, projected after-tax income incorporates each BHC's reported one-time revenue and expense items and adjusts for income attributable to minority interests. Projected after-tax net income is employed to project quarter-by-quarter changes in retained earnings.⁵⁸

The quarterly change in CET1 capital before adjustments and deductions equals projected after-tax net income minus capital distributions (dividends and any other actions that disperse equity), plus any issuance or other corporate actions that increase equity, plus other changes in equity capital such as other comprehensive income, and changes incident to business combinations.

Projected regulatory capital levels are calculated using the applicable capital rules to incorporate, as appropriate, projected levels of non-common capital and certain items that are subject to adjustment or deduction in capital. Some items, such as DVA, goodwill, and intangible assets (other than mortgage servicing assets), and components of AOCI other than unrealized gains (losses) on AFS securities, are assumed to remain constant at their starting value over the planning horizon. For other items, BHC projections--with supervisory adjustments--were factored into the regulatory capital calculation. Those items include the reported path of additional tier 1 and tier 2 capital and significant investments in the capital of unconsolidated financial institutions in the form of common stock. Other items subject to deduction, including DTAs and mortgage servicing assets, are projected under each supervisory scenario. The Federal Reserve also includes the effects of certain planned mergers, acquisitions, or divestitures in its projections of capital and the components of capital.

The projections of regulatory capital levels are combined with Federal Reserve projections of total assets for the leverage ratio and risk-weighted assets to calculate regulatory capital ratios. The risk-based regulatory capital ratios incorporate the standardized approach for calculating risk-weighted assets.⁵⁹ Risk-weighted assets and total assets for the leverage ratio are projected based on supervisory projections of each firm's balance sheet. The capital ratio denominators are adjusted 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 the BHCs during the time the supervisory stress test results were being produced in the second quarter of 2016.

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References

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