Financial Risk Manager (FRM) Operational, Liquidity, and Integrated Risk Management Syllabus

What is liquidity stress testing and what types of scenarios should it cover?

Liquidity stress testing projects a firm's liquidity position under adverse scenarios to assess survival horizon. It should cover idiosyncratic (firm-specific, e.g., rating downgrade/deposit run), market-wide (systemic), and combined scenarios, modeling deposit outflows, drawdowns on credit lines, collateral calls, and reduced asset liquidity.

Define the Basel III Liquidity Coverage Ratio (LCR), including its formula and minimum standard.

$$\text{LCR} = \frac{\text{High-Quality Liquid Assets (HQLA)}}{\text{Total Net Cash Outflows over 30 days}} \geq 100\%$$ It ensures a bank holds enough unencumbered HQLA to survive a 30-day severe liquidity stress scenario.

How are HQLA categorized in the LCR (Level 1, Level 2A, Level 2B), and what haircuts/caps apply?

Level 1 (cash, central bank reserves, high-quality sovereigns): no haircut, no cap. Level 2A (e.g., certain sovereign/agency and high-rated corporates): 15% haircut, and Level 2 assets capped at 40% of HQLA. Level 2B (e.g., lower-rated corporates, certain RMBS, equities): 25-50% haircuts, capped at 15% of HQLA.

Define the Basel III Net Stable Funding Ratio (NSFR), including its formula, horizon, and minimum.

$$\text{NSFR} = \frac{\text{Available Stable Funding (ASF)}}{\text{Required Stable Funding (RSF)}} \geq 100\%$$ It promotes resilient funding over a one-year horizon by requiring stable funding sources to support the liquidity profile of assets and off-balance-sheet exposures.

Contrast the LCR and NSFR in terms of objective and time horizon.

LCR is a short-term measure (30-day stress survival) ensuring sufficient HQLA. NSFR is a structural, longer-term measure (one-year) ensuring assets are funded with sufficiently stable liabilities/equity. LCR addresses acute liquidity shocks; NSFR addresses chronic funding mismatch.

What is model risk, and what are its two primary sources?

Model risk is the potential for adverse consequences from decisions based on incorrect or misused models. Its two primary sources are (1) the model having fundamental errors (wrong specification, flawed assumptions, programming bugs) and (2) the model being used incorrectly or inappropriately (misapplication, bad inputs/calibration).

What are the three core components of model validation per supervisory guidance (e.g., SR 11-7)?

(1) Evaluation of conceptual soundness (assessing the model's design, theory, and assumptions); (2) Ongoing monitoring (verifying the model works as intended, including process verification and benchmarking); and (3) Outcomes analysis (backtesting model outputs against actual results).

What is benchmarking in model validation, and how does it differ from backtesting?

Benchmarking compares a model's outputs against those of alternative models or challenger approaches to identify discrepancies. Backtesting compares model predictions against realized outcomes over time. Benchmarking is a relative cross-model check; backtesting is an absolute comparison to actual outcomes.

Why is independence emphasized in the model validation process?

Effective challenge requires validators to be independent of model developers and users, with the authority, incentives, and competence to critically assess and override. Independence reduces conflicts of interest and confirmation bias, ensuring genuine scrutiny rather than rubber-stamping.

What is enterprise-wide stress testing, and how does it differ from sensitivity analysis?

Enterprise-wide (firm-wide) stress testing applies coherent, often macroeconomic, scenarios across all risk types and business lines simultaneously to assess aggregate impact on capital and liquidity. Sensitivity analysis varies a single risk factor in isolation; enterprise stress testing captures correlated, multi-factor scenario effects.

Distinguish a scenario analysis from a sensitivity (single-factor) stress test.

Sensitivity testing shifts one risk factor (e.g., +200 bps rates) holding others constant—quick but ignores interactions. Scenario analysis applies a consistent set of simultaneous shocks to multiple factors reflecting a plausible (often historical or hypothetical macro) event, capturing correlations and feedback effects.

What is CCAR (Comprehensive Capital Analysis and Review)?

CCAR is the Federal Reserve's annual supervisory exercise assessing whether the largest US bank holding companies have adequate capital and robust, forward-looking capital-planning processes to absorb losses under stress while continuing operations and meeting obligations. It includes both quantitative (stress-test) and qualitative assessments and reviews planned capital actions (dividends/buybacks).

What is DFAST (Dodd-Frank Act Stress Test), and how does it differ from CCAR?

DFAST is a mandated, standardized supervisory stress test using prescribed scenarios and standardized capital-action assumptions to project losses, revenues, and capital. Unlike CCAR, DFAST uses fixed/standardized capital assumptions and is purely quantitative, whereas CCAR incorporates a firm's own planned capital actions and a qualitative assessment.

What supervisory scenarios are typically prescribed in DFAST/CCAR, and how is post-stress capital adequacy judged?

Regulators prescribe baseline, adverse, and severely adverse macroeconomic scenarios (and a global market shock for trading firms). Adequacy is judged by whether projected post-stress regulatory capital ratios (e.g., CET1, tier 1 leverage) remain above required minimums plus buffers throughout the projection horizon.

What is reverse stress testing, and how does it differ from conventional stress testing?

Reverse stress testing starts from a defined adverse outcome (e.g., the firm becoming non-viable/insolvent) and works backward to identify the scenarios and combinations of events that could cause it. Conventional stress testing starts from a scenario and computes the impact; reverse stress testing fixes the impact and finds the breaking-point scenarios.

What qualities define a good stress-test scenario?

A good scenario is severe but plausible, internally consistent (factor moves cohere), relevant to the firm's material risk exposures, forward-looking (not just replaying history), and granular enough to translate into risk-factor and P&L impacts. It should also be actionable for management decisions.

Define economic capital.

Economic capital is the amount of capital a firm internally estimates it needs to remain solvent over a given horizon at a chosen confidence level, given its actual risk profile. It is typically measured as the unexpected loss—the difference between a high-percentile loss (e.g., 99.9% VaR) and expected loss—covered by capital.

How are expected loss, unexpected loss, and economic capital related?

Expected loss (EL) is covered by reserves/pricing. Unexpected loss (UL) is the deviation of losses above EL up to a confidence level. Economic capital is held against unexpected loss: $$\text{Economic Capital} = \text{VaR}_{\alpha} - \text{EL}$$ i.e., the high-percentile loss minus expected loss.

What is the difference between economic capital and regulatory capital?

Regulatory capital is the minimum capital mandated by supervisors using standardized rules (Basel). Economic capital is the firm's own internal estimate of capital needed given its actual risk profile and chosen solvency standard. They can differ because regulatory rules are standardized while economic capital is risk-sensitive and firm-specific.

What is the RAROC formula?

$$\text{RAROC} = \frac{\text{Risk-Adjusted Return}}{\text{Economic Capital}} = \frac{\text{Revenues} - \text{Costs} - \text{Expected Loss} + \text{Return on Economic Capital}}{\text{Economic Capital}}$$ It measures return per unit of risk-based capital, allowing comparison of activities with different risk profiles.

How is RAROC used in decision-making relative to the hurdle rate?

A business or transaction creates value (is accepted/retained) if its RAROC exceeds the firm's hurdle rate, typically the cost of equity capital. If RAROC < hurdle rate, the activity destroys shareholder value. This aligns capital allocation with risk-adjusted profitability.

What is the distinction between RAROC, RORAC, and RARORAC?

RORAC (return on risk-adjusted capital) divides return by risk-based (economic) capital. RAROC (risk-adjusted return on capital) divides a risk-adjusted return (net of expected loss) by capital. RARORAC adjusts both numerator (for risk/expected loss) and denominator (risk-based capital). In practice terms are often used interchangeably for risk-adjusted performance.

What is 'adjusted RAROC,' and why might raw RAROC be misleading when comparing businesses?

Raw RAROC ignores systematic (beta) risk. Adjusted RAROC corrects for it: $$\text{Adjusted RAROC} = \text{RAROC} - \beta_{E}\,(R_{M} - R_{F})$$ A project is accepted if adjusted RAROC > risk-free rate. This prevents over-accepting high-beta projects that have high RAROC but also high systematic risk.

What is risk budgeting?

Risk budgeting is the process of allocating a firm's total risk capacity (e.g., total VaR or economic capital) across business lines, strategies, or asset classes in line with strategic objectives and risk appetite, then monitoring usage against those allocations to optimize risk-adjusted return.

Why does diversification cause the sum of standalone risks to exceed total firm risk, and what is the diversification benefit?

Because risks across business lines are imperfectly correlated, the aggregate risk is less than the sum of standalone risks. The diversification benefit equals: $$\text{Diversification Benefit} = \sum_{i}\text{EC}_{i} - \text{EC}_{\text{total}}$$ This 'saved' capital must be allocated back to units, typically via marginal/component contributions.

What is the difference between standalone, incremental (marginal), and component (diversified) capital contributions?

Standalone capital ignores diversification (unit measured alone). Incremental/marginal capital is the change in total capital from adding or removing the unit. Component (diversified) capital allocates total firm capital to each unit such that contributions sum to the total firm capital, accounting for correlation; it is preferred for performance measurement.

Why can't market, credit, and operational economic capital simply be summed to get total firm capital?

Summing assumes perfect (+1) correlation among risk types, which overstates capital. Because the risk types are not perfectly correlated, integrated capital is lower than the simple sum. Aggregation methods include the variance-covariance/correlation-matrix approach and copula-based simulation to capture dependence and tail co-movement.

Write the variance-covariance aggregation formula for total economic capital across risk types.

$$\text{EC}_{\text{total}} = \sqrt{\sum_{i}\sum_{j}\rho_{ij}\,\text{EC}_{i}\,\text{EC}_{j}}$$ where $\rho_{ij}$ is the correlation between risk types $i$ and $j$. With $\rho_{ij}=1$ for all pairs this reduces to the simple sum; lower correlations yield diversification benefits.

Summarize the main focus of Basel I, Basel II, and Basel III.

Basel I (1988): minimum capital (8%) focused on credit risk via crude risk weights. Basel II (2004): three pillars (minimum capital, supervisory review, market discipline), more risk-sensitive credit/operational capital, internal models. Basel III (post-2008): higher and better-quality capital (CET1), capital buffers, leverage ratio, and liquidity standards (LCR, NSFR).

What is the leverage ratio under Basel III, and why was it introduced?

$$\text{Leverage Ratio} = \frac{\text{Tier 1 Capital}}{\text{Total Exposure (on- and off-balance-sheet, non-risk-weighted)}} \geq 3\%$$ It is a non-risk-based backstop to the risk-weighted ratios, constraining excessive leverage and guarding against model risk and risk-weight gaming. G-SIBs face an additional leverage buffer.

What is the Basel III 'output floor' introduced in the Basel III endgame/finalization, and what is its calibrated level?

The output floor limits the capital benefit a bank can gain from internal models by requiring risk-weighted assets computed under internal models to be at least 72.5% of the RWA that would result from the standardized approaches. It reduces variability in RWAs across banks and caps model-based capital reductions; it is phased in to the 72.5% level.