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 31 bank holding companies (BHCs) subject to DFAST 2015.³³ 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 (RWA).
5. The model 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.

A majority of the models described here were refined incrementally over the past year. However, the Federal Reserve enhanced its methods for estimating PPNR and regulatory capital and capital ratios (see box 1).

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 2015--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 September 30, 2014. 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 balances are assumed to have the same risk characteristics as those of the loan portfolio as of September 30, 2014, 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. This is a simple, but generally conservative, assumption. 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 was 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 include 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.³⁴

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 September 30, 2014, 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 BHC's internal credit rating, which is converted to a standardized rating scale. 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 September 30, 2014, are assigned a PD of 100 percent.

Quarterly changes in the PD after the third quarter of 2014 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 countries.

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.³⁵ 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.³⁶ 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 such as house prices and CRE vacancy 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 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, and then, using loans with losses, estimates the loss on the CRE mortgage as a function of the expected probability of loss, characteristics of the loan, and macroeconomic variables. Finally, the EAD for CRE mortgages is assumed to equal the loan's full committed balance for both income producing and C&LD loans. As was the case with closed-end C&I loans, for amortizing income-producing loans the EAD equals the outstanding balance.

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.³⁷

The PD model for first-lien residential mortgages estimates the probability that a loan transitions to different payment statuses, including current, delinquent, 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 such as local house prices, the statewide unemployment rate, and interest rates.³⁸

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 September 30, 2014, are considered in default and are assigned a PD of 100 percent.

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).³⁹

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.⁴⁰

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 September 30, 2014, 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 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.

For second-lien HELs and HELOCs that are current as of September 30, 2014, 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, 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 conservatively 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 such as 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 such as house prices and the unemployment rate (which, in some cases, are interacted with loan and borrower characteristics to allow for greater sensitivity to stressful conditions in high-risk segments). Default on auto loans is defined based on either the payment status (120 days past due), actions of the borrower (bankruptcy), or 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. 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.⁴¹ 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 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.⁴²

Charge-off rates are projected by applying the estimated system of equations to each segment of the BHC's loan portfolio as of September 30, 2014. The portfolio level charge-off rate equals the dollar-weighted average of the segment-level charge-off rates.⁴³ 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.⁴⁴ 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 under the held-for-sale (HFS) and some loans under the held-for-investment (HFI) accounting classifications are carried at the lower of cost or market value. FVO, HFS, and HFI loan portfolios are identified by the BHCs and reported on the FR Y-14Q report. Losses related to FVO, HFS, and HFI loans are recognized in the income statement at the time of the devaluation.

Losses are estimated by applying the macroeconomic scenario to loans held in portfolio under FVO, HFS, and HFI accounting. Losses on C&I and CRE loans and commitments are estimated by revaluing each loan or commitment each quarter using a stressed discount yield (and spread for floating rate loans). The initial discount yield is based on the loan or commitment's initial fair value, settlement date, maturity date, and interest rate for fixed rate loans and the fair value, settlement date, maturity date, and interest rate spread for floating rate loans. 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. Gains on FVO loan hedges were modeled using a similar methodology as one used for comparable assets in the trading portfolio, using the FVO-specific sensitivities reported by the BHC, and were netted from estimated losses on the FVO loans.

Losses on retail loans held under FVO, HFS, and HFI 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).

In addition, under the revised regulatory capital rules, the difference between the amortized cost (accounting for any OTTI charges) and fair value of AFS securities as well as HTM securities that have taken OTTI is phased into the calculation of tier 1 capital for advanced approaches BHCs.⁴⁵ To address this issue, a separate fair-value model is used to project quarterly changes in the prices of AFS securities under the supervisory scenarios, as described below.

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

If a security becomes OTTI, then all or a portion of the difference between the fair value and amortized cost of the security must be recognized in earnings.⁴⁶ Losses on OTTI securities are projected using a suite of models reflecting differences in the basic structure of the securities (i.e., securitized versus direct obligation) and differences in underlying collateral and obligor type.

The OTTI models are designed to incorporate other-than-temporary differences between amortized cost and fair market value due to credit impairment but not differences reflecting changes in liquidity or market conditions unless the firm will be required to sell the security. Some AFS/HTM securities, including 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 OTTI charges. The remaining securities can be grouped into three basic categories: securitizations, where the value of the security depends on the value of an underlying pool of collateral; direct debt obligations, such as corporate and sovereign bonds, where the value of the security depends primarily on the credit quality of the issuer; and equity securities.⁴⁷

For securitized obligations, credit and prepayment models estimate delinquency, default, severity, and prepayment vectors on the underlying pool of collateral under the supervisory scenarios. Where feasible, these projections incorporate detailed information on the underlying collateral characteristics for each individual security, derived from commercial databases that contain collateral and security structure information. Delinquency, default, severity, and prepayment vectors are projected either using econometric models developed by the Federal Reserve or third-party models used by Federal Reserve analysts that are designed to project these estimates in stressed economic environments. The models used vary with the type of underlying collateral but generally estimate the relationship between the collateral's performance vectors and economic variables, such as the unemployment rate and house prices. These vectors are then applied to a cash flow engine that captures the specific structure of each security (e.g., tranche, subordination, and payment rules) to calculate the present value of the cash flows (intrinsic value) for that security. If the projected intrinsic value is less than amortized cost, then the security is considered to be other than temporarily impaired, and OTTI is calculated as the difference between amortized cost and intrinsic value.

For direct obligations, the predominant approach is to assess the PD or severe credit deterioration for each security issuer or group of security issuers over the planning horizon. PD is either modeled directly or inferred by modeling changes in expected frequency of default or CDS spreads for the bonds in question. A security is considered other than temporarily impaired if the projected value of the PD or CDS spread crosses a predetermined threshold level--generally the level consistent with a CCC/Caa rating--at any point during the planning horizon. LGD on these securities is based on historical data on bond recovery rates. OTTI is calculated as the difference between the bond's amortized cost and its projected recovery value under the supervisory scenarios.

For certain securitized obligations with smaller levels of exposure and municipal bonds, the OTTI is estimated as a fraction of projected unrealized losses on the security from the fair-value model.

After a security is written down as OTTI, the difference between its original value and the post-OTTI value is assumed to be invested in securities with the same risk characteristics. Increases projected by the Federal Reserve in a BHC's securities portfolio after September 30, 2014, are assumed to be in short-term, riskless assets, and no OTTI charges are assigned to these securities.

In addition, under the revised regulatory capital rules, the difference between the amortized cost (accounting for any OTTI charges) and fair value of AFS securities as well as non-credit-loss OTTI on HTM securities is phased into the calculation of tier 1 capital for advanced approaches BHCs.⁴⁸ To address this issue, a separate fair-value model is used to project quarterly changes in the prices of AFS and HTM securities under the supervisory scenarios, as described below.

In order to project fair-value changes for AFS securities, each security is re-priced using one of three methods depending on the asset class of the security--a duration-based approach, generic revaluation, or model-based revaluation.

• Duration-based approach--The duration-based approach is taken for all AFS securities except Treasury securities and agency RMBS. This approach approximates the quarterly price path for a security over a nine-quarter planning horizon using projected changes in the security's yield and its initial interest rate and spread durations. The yields used in the approximation vary over the projection period with changes in Treasury yields and the securities' option-adjusted spread. Separate yield projections were estimated for securities in different asset classes and with different credit ratings and maturities.
• Generic revaluation--U.S. Treasury securities are directly re-priced using a simple present-value calculation that incorporates the timing and amount of contractual cash flows and quarterly Treasury yields from the macroeconomic scenario.
• Model-based revaluation--Agency RMBS are revalued using a security-specific pricing model to capture the effect of embedded options on the cash flows of each security.

Trading and Private Equity

Total potential mark-to-market losses stemming from trading positions under a stressed market environment can be broken into two primary types. The first type of loss arises from a decrease in the market value of trading positions, regardless of the default of credit instruments (e.g., loans or bonds) or the BHC's counterparties. The second type is the loss associated with the risk of default--both the risk of the default of obligors and the counterparty credit risk associated with changes in counterparty exposures as well as the deterioration of counterparties' creditworthiness under stressed market conditions, which adversely affects the riskiness of positively valued trading positions. The models used to project losses on trading positions under the global market shock account for both sources of potential losses, generally relying on information provided by firms on estimated sensitivities of their exposures to specific risk-factor shocks. Because positions in the trading account are marked to market on a daily basis, the approach used to generate loss projections on trading positions is intended to capture the market-value effect of the global market shock. Losses on trading positions as a result of a global market shock were estimated only for the six BHCs with large trading operations, since trading operations determine risk and performance to a larger extent at these firms than at any other BHCs participating in DFAST 2015.

Losses on trading positions, such as equities, foreign exchange, interest rates, commodities, credit products, private equity, and other fair-value assets arising from the global market shock are calculated using position values or the BHCs' own estimates of the sensitivity of the position values to changes in a wide range of market rates, prices, spreads, and volatilities. Trading losses are calculated by multiplying these sensitivities by the risk-factor changes included in the global market shock developed by the Federal Reserve or by interpolating the change in position values from BHC-supplied profit/(loss) grids. These shocks are assumed to be instantaneous and no additional hedging, recovery in value, or changes in positions are incorporated into the loss calculation.

Losses in the global market shock include losses from credit valuation adjustments (CVA) and trading incremental default risk (IDR) of the six BHCs with large trading positions. CVAs are adjustments above and beyond the mark-to-market valuation of the BHCs' trading portfolios that capture changes in the risk that a counterparty to derivatives transaction or other trading position will default on its obligations. Using detailed data provided by the six trading BHCs on the FR Y-14Q Counterparty schedule, each trading firm's baseline and stressed CVA for each counterparty is calculated as a function of unstressed and stressed values of exposure, PD, and LGD. CVA losses equal the difference between the baseline and the stressed CVAs.

In addition to CVA and other mark-to-market losses on trading positions, default risk of credit instruments in the trading book is captured through IDR. IDR estimates the potential additional loss stemming from the default of issuers in excess of the mark-to-market losses in the trading book. IDR estimates the losses from jump-to-default in the tail of the distribution of defaults, where the tail percentile is calibrated to the severity of the macroeconomic scenario.

The IDR models estimate losses from jump-to-default for various exposure types, including single-name, index and index-tranche, and securitizations, at different levels of granularity depending on exposure type. The loss estimates are based on simulation models of issuer-level defaults. The IDR loss models rely on position and exposure data provided by the firms. IDR losses occur over nine quarters.

Largest Counterparty Default

To estimate losses from the default of counterparties to derivatives and securities financing agreements, 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 derivative and securities financing agreements. 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. For derivative agreements, applicable CDS hedges and CVA were netted from the net stressed current exposure. A recovery rate of 10 percent was 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 historically based loss estimates, based on the average of three 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 all three models--a panel regression model, a loss distribution approach, and a historical simulation approach--projections of operational-risk-related losses for the 31 BHCs are modeled for each of seven operational-risk categories identified in the Board's advanced approaches rule.⁴⁹ All three 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 primary components: loss frequency and loss severity. The expected loss frequency is the estimated number of operational-loss events in the supervisory scenario, while loss severity is the estimated loss per event in each category. 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, credit spread, 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 losses related to operational-risk events equal losses summed across operational-risk categories. 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 loss distribution approach model, losses at different percentiles of simulated, annualized loss distributions are used as a proxy for the expected losses related to operational risk 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 each event type and BHC. A loss severity distribution is also fit to each event type for each BHC.⁵¹ The distribution of aggregate annual losses is simulated, and the macroeconomic scenario is implicitly incorporated in the results through the percentile choice, which was based on analysis of historical loss data for all BHCs taken together. The approach used to choose the percentile for each scenario essentially targets the total loss forecast for all BHCs and allows the loss distribution approach to split this loss among the individual BHCs and event types. Loss forecasts for an individual BHC are the sum of the BHCs' loss estimates for each event type.

In the third approach--the historical simulation approach--the distribution of aggregate annual losses are simulated by repeatedly drawing the annual event frequency from the same distribution used in the loss distribution approach, but the severity of those events was drawn from historical realized loss data rather than an estimated loss severity distribution. Losses from the same percentile of the distribution as in the loss distribution approach are used to approximate the supervisory scenarios.

Mortgage Repurchase Losses

Mortgage repurchase expenses are a component of PPNR and are related to litigation, or to demands by mortgage investors to repurchase loans deemed to have breached representations and warranties, or to loans insured by the U.S. government for which coverage could be denied if loan defects are identified. Mortgage repurchase losses for loans sold with representations and warranties liability are estimated in two parts.

The first part is to estimate 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 (PLS) or to a GSE (Fannie Mae and Freddie Mac) or loans insured by the government. This part takes into account both losses recognized to date and future losses projected over the remaining lifetime of the loans.

The second part is to estimate 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).

Future credit loss rates for mortgages (grouped by vintage and investor type) are projected using industrywide data and models that incorporate the house price assumptions in the supervisory scenario.⁵² For GSE loans, 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.

The share of past and future credit losses likely to be ultimately put back to the selling BHCs (the put-back rate) is estimated separately for each investor type.

• 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 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 structural models 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 models based on recent firm-level performance.

Autoregressive models are estimated using historical, merger-adjusted data from the FR Y-9C report. Separate models are estimated for 22 different components of PPNR, including eight components of interest income, five components of interest expense, five components of noninterest non-trading income, three components of noninterest expenses, and trading revenue.

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 small 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.

The autoregressive model specifications vary somewhat by PPNR component. But, in general, each component is related to characteristics of the BHCs, 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.

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 a framework similar to that of other PPNR components.

For other volatile components of PPNR, we follow 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.

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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 is the residual category, and its level 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 incorporated expected changes to a BHC's business plan, such as mergers, acquisition, and divestitures, that are likely to have a material impact on the its capital adequacy and funding profile.

BHC-submitted data were used to adjust the projected balance sheet in the quarter when the change was expected to occur. Once adjusted, assets were assumed to grow at the same rate as the pre-adjusted balance sheet. Only divestitures that were either completed or contractually agreed upon before January 5, 2015, were incorporated.

Estimating RWA under the two different regulatory capital regimes in place over the planning horizon requires the calculation of four RWA components: market risk-weighted assets (MRWA) and credit RWA as computed under both the general approach that was in effect as of October 1, 2014, and the standardized approach of the revised regulatory capital framework.

For asset categories subject to the market risk rule, the seven components of MRWA are value at risk (VaR), stressed VaR (SVaR), incremental risk charge, correlation trading, non-modeled securitization, specific risk charge, and other risk charge.

VaR and the incremental risk charge are updated using the estimated volatility of the trading portfolio, which is a function of stock market volatility in the supervisory scenarios, and the projected change in trading assets. The remaining categories are assumed to evolve according to projections of a BHC's trading assets.

For all asset categories not subject to the market risk rule, generalized risk weights are imputed from FR Y-9C report data. These weights are held fixed throughout the forecast horizon to reflect an assumption that the credit portfolio's underlying risk features remain constant throughout the horizon. In computing standardized RWA, we apply the generalized RWA growth path to the standardized RWA as-of date value reported by the BHCs. Estimates of the additional capital requirements for past-due exposures under the standardized approach are consistent with the estimated loss forecast for that exposure.

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Equity Capital and 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 tier 1 common and regulatory capital for each BHC under the supervisory scenarios. The supervisory projections of total losses and revenues are combined to estimate taxable income.

A consistent tax rate across all BHCs is applied to taxable income to calculate after-tax net income over the projection period.⁵³ The consistent tax rate is also used to generate projections of deferred tax assets (DTAs) from temporary timing differences and net operating losses. A valuation allowance is estimated to determine whether a BHC will have sufficient taxable income in the future to realize the DTAs, with changes in the valuation allowance 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, combined with common capital action assumptions, are used to project quarter-by-quarter changes in equity capital components.⁵⁴

The quarterly change in the components of equity capital equals projected after-tax net income minus capital distributions (dividends and any other actions that disperse equity), plus any employee compensation-related issuance or other corporate actions that increase equity, plus other reported changes in equity capital such as other comprehensive income, where applicable, and changes incident to business combinations.

Projected changes in equity capital components determine changes in equity capital (for tier 1 common and regulatory capital ratios) and common equity tier 1 capital before adjustments and deductions (for regulatory capital ratios), which in turn drive changes in tier 1 common and regulatory capital. Tier 1 common capital is calculated using the definition of capital in the Board's prior capital adequacy guidelines.⁵⁵ Regulatory capital is calculated consistent with the requirements that are in effect during the projected quarter of the planning horizon.⁵⁶ The definition of regulatory capital changes throughout the planning horizon in accordance with the transition arrangements in the revised regulatory capital framework.⁵⁷

Projected 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 and non-mortgage servicing assets), and components of accumulated other comprehensive income (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 were factored into capital calculations. 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. The Federal Reserve also included the effects of certain planned mergers, acquisitions, or divestitures in its projections of capital and the components of capital.

The projections of capital levels are combined with Federal Reserve projections of average total assets and risk-weighted assets to calculate capital ratios after adjusting for capital deductions. The tier 1 common ratio is calculated based on the general approach for calculating risk-weighted assets in all quarters of the planning horizon. All other risk-based capital ratios incorporate the general approach for calculating risk-weighted assets in projections of the first quarter of the planning horizon (fourth quarter 2014) and the standardized approach for calculating risk-weighted assets in projections of the following eight quarters of the planning horizon (first quarter 2015 through fourth quarter 2016). 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 fourth quarter of 2014 and the first quarter of 2015.

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References

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