Board of Governors of the Federal Reserve System

Overview of Modeling Framework

The Federal Reserve estimates the effect of supervisory scenarios on the regulatory capital ratios of firms participating in the stress test by projecting net income and other components of regulatory capital for each firm over a nine-quarter projection horizon. Projected net income, adjusted for the effect of taxes, is combined with non-common capital action assumptions and other components of regulatory capital to produce post-stress capital ratios. The Federal Reserve's approach to modeling post-stress capital ratios generally follows U.S. generally accepted accounting principles (GAAP) and the regulatory capital framework.¹⁴ Figure 2 illustrates the framework used to calculate changes in net income and regulatory capital.

Projecting Pre-tax Net Income

The Federal Reserve calculates projected pre-tax net income for the firms subject to the stress test by combining projections of revenue, expenses, provisions for credit losses, and other losses, including

• PPNR;
• provisions for credit losses;
• losses on loans held for sale (HFS) or for investment and measured under the fair-value option (FVO), losses or gains on hedges for fair-value loans, and losses or gains on hedges for loans measured at amortized cost;
• credit losses on investment securities in the available-for-sale (AFS) and held-to-maturity (HTM) portfolios;¹⁵
• losses or gains on market risk exposures, credit valuation adjustment (CVA), and issuer default losses (IDL) for firms subject to the global market shock; and
• losses from a default of the largest counterparty for firms with substantial trading, processing, or custodial operations.

The Federal Reserve projects these components of pre-tax net income using supervisory models that take the Board's scenarios and firm-provided data as inputs. The projections are based on the assumption that firms' balance sheets remain unchanged throughout the projection period. Macroeconomic variables used in select supervisory models vary across geographic locations (e.g., by state or by county). The Federal Reserve projects the paths of these variables as a function of aggregate macroeconomic variables included in the Board's scenarios.

Pre-provision Net Revenue

PPNR is defined as net interest income (interest income minus interest expense) plus noninterest income minus noninterest expense. Consistent with U.S. GAAP, the projection of PPNR includes projected losses due to operational-risk events and expenses related to the disposition of real-estate-owned properties.¹⁶

The Federal Reserve models most components of PPNR using models that relate specific revenue and non-provision-related expenses to the characteristics of firms and to macroeconomic variables. These include eight components of interest income, seven components of interest expense, six components of noninterest income, and three components of noninterest expense.

The Federal Reserve separately models losses from operational risk and other real-estate-owned (OREO) expenses. Operational risk is defined as "the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events."¹⁷ OREO expenses are those expenses related to the disposition of real-estate-owned properties and stem from losses on first-lien mortgages.

Loan Losses and Provisions on Loans Measured at Amortized Cost

The Federal Reserve projects 13 quarters of losses on loans measured at amortized cost using one of two modeling approaches: the expected-loss framework or the net charge-off approach.¹⁸

For certain loans, expected losses under the macroeconomic scenario are estimated by projecting the probability of default (PD), loss given default (LGD), and exposure at default (EAD) for each quarter of the projection horizon. Expected losses in each quarter are the product of these three components.

Losses are modeled under the expected-loss framework for the following loan categories:

• corporate loans, including graded commercial and industrial (C&I) loans, agricultural loans, domestic farm loans, international farm loans, loans to foreign governments, loans for purchasing and carrying securities, other non-consumer loans, and other leases
• commercial real estate (CRE) loans, including domestic and international non-owner-occupied multifamily or nonfarm, nonresidential property loans and construction and land development (C&LD) loans
• domestic first-lien residential mortgages
• domestic home equity loans (HELs) and home equity lines of credit (HELOCs)
• domestic credit cards
• domestic auto loans

The net charge-off approach projects losses over the projection horizon using models that capture the historical behavior of net charge-offs as a function of macroeconomic and financial market conditions and loan portfolio characteristics. The Federal Reserve models losses under the net charge-off approach for other consumer loans, business and corporate credit card loans, small-business loans, student loans, and international retail loans.

Losses on loans measured at amortized cost flow into net income through provisions for loan and lease losses. Generally, provisions for loan and lease losses for each quarter equal projected loan losses for the quarter plus the change in the allowance needed to cover the subsequent four quarters of expected loan losses, taking into account the allowance established by the firm as of the effective date of the stress test exercise.¹⁹

The Federal Reserve assumes that the allowance at the end of each quarter covers projected loan losses for four quarters into the future. The supervisory estimate of the allowance at the start of the projection horizon, which is based on projected losses under the severely adverse scenario, may differ from a firm's established allowance at the beginning of the projection horizon, which is based on the firm's estimate of losses on the effective date of the stress test. Any difference between the supervisory calculation of the allowance and the firm's reported allowance at the beginning of the projection horizon is linearly smoothed into the Federal Reserve's provisions projection over the nine quarters.

Losses on Loans Measured on a Fair-Value Basis

Certain loans are accounted for on a fair-value basis instead of on an amortized cost basis. For example, if a loan is accounted for using the FVO, it is marked to market, and the accounting value of the loan changes as market risk factors and fundamentals change. Similarly, loans that are held for sale are accounted for at the lower of cost or market value.

The models for these asset classes project gains and losses on the banks' FVO/HFS loan portfolios over the nine-quarter projection horizon, net of any hedges, by applying the scenario-specific path of interest rates and credit spreads.

Losses are modeled under this approach for the following loan categories:

• FVO/HFS C&I loans
• FVO/HFS CRE loans
• FVO/HFS residential mortgages, student loans, auto loans, and credit cards

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

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

The Federal Reserve estimates two types of losses on AFS or HTM securities related to investment activities.²⁰ First, for debt securities classified as AFS, projected changes in the fair value of the securities due to changes in interest rates and other factors will result in unrealized gains or losses that are recognized in capital for some firms through other comprehensive income (OCI).²¹ Second, credit losses on the security may be recorded. With the exception of certain government-backed obligations, both AFS and HTM securities are at risk of incurring credit losses.²² The models project security-level credit losses, using as an input the projected fair value for each security over the nine-quarter projection horizon under the macroeconomic scenarios.

Securities at risk of credit losses include the following securitizations and direct debt obligations:

• corporate debt securities
• sovereign debt securities (other than U.S. government obligations)
• municipal debt securities
• mortgage-backed, asset-backed, collateralized loan obligation (CLO), and collateralized debt obligation (CDO) securities

Unrealized Gains or Losses on the Fair Value of Available-for-Sale Debt Securities

The fair value of securities in the AFS portfolio may change in response to the macroeconomic scenarios. Under U.S. GAAP, unrealized gains and losses on AFS debt securities are reflected in accumulated OCI (AOCI) and do not flow through net income.²³ Under the regulatory capital rule, AOCI must be incorporated into common equity tier 1 capital (CET1) for certain firms.²⁴ The incorporation of AOCI in regulatory capital is described in "Calculation of Regulatory Capital Ratios" below.

Unrealized gains and losses are calculated as the difference between each security's fair value and its amortized cost. The amortized cost of each AFS debt security is equivalent to the purchase price of a debt security, which is periodically adjusted if the debt security was purchased at a price other than par or face value, has a principal repayment, or has an impairment recognized in earnings.²⁵

OCI losses from AFS debt securities are computed directly from the projected change in fair value, taking into account credit losses and applicable interest-rate hedges on securities. All debt securities held in the AFS portfolio are subject to OCI losses, including

• U.S. Treasuries;
• U.S. agency securities;
• corporate debt securities;
• sovereign debt securities;
• municipal debt securities; and
• mortgage-backed, asset-backed, CLO, and CDO securities.

Losses on Trading and Private Equity Exposures and Credit Valuation Adjustment

The trading and private equity model covers a wide range of firms' exposures to asset classes such as public equity, foreign exchange, interest rates, commodities, securitized products, traded credit (e.g., municipals, auction rate securities, corporate credit, and sovereign credit), private equity, and other fair-value assets. Loss projections are constructed by applying movements specified in the global market shock scenario²⁶ to market values of firm-provided positions and risk factor sensitivities.²⁷ In addition, the global market shock is applied to firm counterparty exposures to generate losses due to changes in CVA.

Trading, private equity, and CVA losses are calculated only for a relevant subset of firms.²⁸ Different from the nine-quarter evolution of losses for other parts of the stress test, these losses are estimated and applied in the first quarter of the projection horizon. This timing is based on the observation that market dislocations can happen rapidly and unpredictably any time under stress conditions and ensures that potential losses from trading and counterparty exposures are incorporated into trading companies' capital ratios at all points in the projection horizon.

Trading Exposure: Issuer Default Losses

The Federal Reserve separately estimates the risk of losses arising from a jump-to-default of issuers of debt securities in the trading book, in excess of mark-to-market losses calculated by the trading model. Trading losses associated with IDL account for concentration risk in agency securities, trading book securitization positions, and corporate, sovereign, and municipal bonds. These losses are applied in each of the nine quarters of the projection horizon.

Largest Counterparty Default Losses

The largest counterparty default (LCPD) scenario component is applied to firms with substantial trading or custodial operations. The LCPD captures the risk of losses due to an unexpected default of the counterparty whose default on derivatives and SFTs would generate the largest stressed losses for a firm.

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

Balance Projections and the Calculation of Regulatory Capital Ratios

Balance Sheet Items and Risk-Weighted Assets

The Federal Reserve generally projects that a firm takes actions to maintain its current level of assets, including its securities, trading assets, and loans, over the projection horizon. The Federal Reserve assumes that a firm's RWAs and leverage ratio denominators remain unchanged over the projection horizon except that the Federal Reserve will account for changes primarily related to the calculation of regulatory capital or due to changes to the Board's regulations.²⁹

Calculation of Regulatory Capital Ratios

The five regulatory capital measures that are included in the stress test are the (1) CET1 risk-based capital, (2) tier 1 risk-based capital, (3) total risk-based capital, (4) tier 1 leverage, and (5) supplementary leverage ratios. A firm's regulatory capital ratios are calculated in accordance with the Board's regulatory capital rule using Federal Reserve projections of pre-tax net income and other scenario-dependent components of the regulatory capital ratios.

Pre-tax net income and the other scenario-dependent components of the regulatory capital ratios are combined with additional information, including assumptions about taxes and capital distributions, to calculate post-stress regulatory capital. In that calculation, the Federal Reserve first adjusts pre-tax net income to account for taxes and other components of net income, such as income attributable to minority interests, to arrive at after-tax net income.³⁰

The Federal Reserve calculates the change in equity capital over the projection horizon by combining projected after-tax net income with changes in OCI, assumed capital distributions, and other components of equity capital. The path of regulatory capital over the projection horizon is calculated by combining the projected change in equity capital with the firm's starting capital position and accounting for other adjustments to regulatory capital specified in the Board's regulatory capital framework.³¹

The denominator of each firm's regulatory capital ratios, other than the leverage ratios, is calculated using the standardized approach for calculating RWAs for each quarter of the projection horizon.

 

References

 

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

 15. For firms that have adopted ASU 2016-13, the Federal Reserve incorporates its projection of expected credit losses on securities in the allowance for credit losses, in accordance with Financial Accounting Standards Board (FASB), Financial Instruments–Credit Losses (Topic 326), FASB Accounting Standards Update (ASU) 2016-13 (Norwalk, Conn.: FASB, June 2016). Return to text

 16. PPNR projections do not include debt valuation adjustment, which is not included in regulatory capital. Return to text

 17. See 12 C.F.R. § 217.101 ("Operational Risk"). Return to text

 18. "Loans measured at amortized cost" were formerly referred to as "accrual loans" in previous disclosures. The name change does not reflect a change to the model, but rather an enhancement to improve consistency with accounting terminology. Return to text

 19. To reduce uncertainty, allow for better capital planning at affected firms, and gather additional information on the impact of the current expected credit loss methodology (CECL), the Federal Reserve plans to maintain the framework used prior to the adoption of CECL for calculating allowances on loans in the stress test through the 2023 stress test cycle while continuing to evaluate appropriate future enhancements. See Board of Governors of the Federal Reserve System, "Statement on the Current Expected Credit Loss Methodology (CECL) and Stress Testing," December 9, 2021, https://www.federalreserve.gov/supervisionreg/files/cecl-in-stress-testing-public-statement-20211209.pdf. Return to text

 20. This portfolio does not include securities held for trading. Losses on these securities are projected by the model that projects gains and losses on trading exposures. Return to text

 21. Other comprehensive income is accounted for outside of net income. Under the Board's regulatory capital rule, accumulated OCI (AOCI) that arises from unrealized changes in the value of AFS securities must be incorporated into common equity tier 1 capital for firms subject to the advanced approaches and other firms that do not opt out of including AOCI in regulatory capital. Return to text

 22. Certain government-backed securities, such as U.S. Treasuries, U.S. government agency obligations, U.S. government agency or government-sponsored enterprise (GSE) mortgage-backed securities, federally backed student loan asset-backed securities, and pre-refunded municipal bonds, are assumed not to be subject to credit losses. Return to text

 23. Unrealized gains and losses on equity securities are recognized in net income and affect regulatory capital for all firms. See Financial Accounting Standards Board (FASB), Financial Instruments—Overall (Subtopic 825-10), FASB Accounting Standards Update (ASU) 2016-01 (Norwalk, Conn.: FASB, January 2016). Return to text

 24. The Board amended its prudential standards to allow firms with total consolidated assets of less than $700 billion and cross-jurisdictional activity of less than $75 billion to opt out of including AOCI in regulatory capital (84 Fed. Reg. 59,230 (November 1, 2019)). Return to text

 25. The fair value of each AFS security is projected over the nine-quarter projection horizon using either a present-value calculation, a full revaluation using a security-specific discounted cash flow model, or a duration-based approach, depending on the asset class. Return to text

 26. The global market shock scenario is a set of hypothetical shocks to a large set of risk factors reflecting general market distress and heightened uncertainty. See Board of Governors of the Federal Reserve System, "Global Market Shock Component for Supervisory Severely Adverse Scenario," 2023 Stress Test Scenarios (Washington: Board of Governors, February 2023), 8, https://www.federalreserve.gov/newsevents/pressreleases/files/bcreg20230209a1.pdf. Return to text

 27. The trading model is also used to calculate gains or losses on firms' portfolios of hedges on credit valuation adjustment exposures (CVA hedges). Return to text

 28. The global market shock scenario in the 2023 stress test applies to Category I, II, and III firms that have aggregate trading assets and liabilities of $50 billion or more, or trading assets and liabilities equal to or greater than 10 percent of total consolidated assets. Return to text

 29. See 12 C.F.R. pts. 217, 225, and 252; the Federal Register notice is available on the Board's website at https://www.federalreserve.gov/newsevents/pressreleases/files/bcreg20200304a2.pdf. For additional information, see also Board of Governors of the Federal Reserve System, "Federal Reserve Board Approves Rule to Simplify Its Capital Rules for Large Banks, Preserving the Strong Capital Requirements Already in Place," press release, March 4, 2020, https://www.federalreserve.gov/newsevents/pressreleases/bcreg20200304a.htm. Return to text

 30. The Federal Reserve applies a consistent tax rate of 21 percent to pre-tax net income and accounts for deferred tax assets. Return to text

 31. The regulatory capital framework specifies that regulatory capital ratios account for items subject to adjustment or deduction in regulatory capital, limits the recognition of certain assets that are less loss-absorbing, and imposes other restrictions. Return to text