Sections 1–4 explain methods. Sections 5–15 connect the risk metrics to worked bank examples. Use Sections 17–18 for the interactive laboratory and Excel calculations. Expand the classroom answers after attempting each question.
LEARNING SECTION 01
What is financial stress testing?
Stress testing asks how a bank, portfolio or financial system would behave under unusually adverse conditions. A useful test states the shock, its timing, the affected exposures and the point at which management must act. Financial stress testing examines earnings, capital and cash flows. This article focuses on banking rather than software performance testing.
A bank may remain solvent on paper but run out of usable cash. Conversely, it may have enough cash today while loan losses erode its capital. Capital stress and liquidity stress therefore need separate calculations and a connected narrative.
| Question | What the test measures | Example of a management decision |
|---|---|---|
| Can we absorb losses? | Capital ratios and capital depletion | Reduce distributions or raise equity |
| Can we meet payments? | Cash gaps, buffers and survival horizon | Lengthen funding or pre-position collateral |
| Can we exit or hedge positions? | Stressed valuation and market depth | Reduce concentrations before market liquidity disappears |
LEARNING SECTION 02
Sensitivity, scenario and reverse stress tests
| Method | Starting point | Illustration | Main limitation |
|---|---|---|---|
| Sensitivity analysis | One risk factor changes, others remain fixed | Immediate +200 basis points in yields | Misses interactions across risk factors |
| Scenario analysis | A coherent combination of shocks | Recession, wider spreads, falling collateral and deposit withdrawals | Depends on scenario design and transmission models |
| Historical scenario | A past episode applied to current exposures | 2008 financial crisis or March 2020 disruption | Today’s positions and market structure differ |
| Hypothetical scenario | A forward-looking adverse narrative | Stagflation and a funding-market freeze | Needs an explicit severity and plausibility rationale |
| Reverse stress testing | A specified failure or viability threshold | Find combinations that push capital below an 8% internal threshold | Many different scenarios can produce the same failure |
A basis point (bp) equals 0.01 percentage point. A rise from 6% to 8% is +200 basis points. Sensitivity tests can be instantaneous. A scenario can be instantaneous or span several periods, depending on its purpose.
Historical replay should apply relevant shock dynamics to the bank’s current exposures. It should not simply reuse the past institution’s reported loss.
LEARNING SECTION 03
Designing an adverse scenario
Start with the institution’s vulnerabilities. A bank concentrated in commercial property needs a scenario that stresses property values, rental income, refinancing and collateral recovery. A deposit-funded bank with long-duration securities also needs rate and withdrawal shocks.
| Design step | What to specify |
|---|---|
| Objective and perimeter | Legal entities, currencies, portfolios and the business decision |
| Starting position | Balance sheet date, capital, allowances, encumbered assets and funding profile |
| Narrative and path | Trigger, severity, persistence and quarterly or daily time path |
| Risk-factor translation | Rates, credit spreads, asset prices, defaults, recoveries and run-off assumptions |
| Feedback effects | Margin calls, forced sales, collateral haircuts and loss of confidence |
| Management response | Actions, execution time, capacity and costs |
| Review and challenge | Data checks, independent challenge and documented limitations |
Correlated shocks means that the assumptions fit an economic narrative, rather than every risk factor receiving its worst historical value at once. In a recession, government yields may fall while corporate spreads widen. In stagflation, both inflation and government yields may rise.
LEARNING SECTION 04
One-factor calculations and joint shocks
Consider a hypothetical bond position with a dollar value of one basis point (DV01) of ₹0.04 crore per basis point. Here DV01 is the positive magnitude of loss from a one-basis-point rise in yield for this long position.
A separate ₹40 crore equity holding loses ₹8 crore under a 20% equity fall. If both shocks occur together, a first-order sum is ₹16 crore. The sum assumes no overlap in positions, no hedges and no additional cross-effects.
| Risk measure | Meaning | How to use it in stress |
|---|---|---|
| DV01 | Dollar value of one basis point | Signed rate sensitivity × change in basis points |
| CS01 | Credit spread sensitivity for a one-basis-point move | Spread sensitivity × spread widening |
| Delta | First derivative of instrument value with respect to the underlying price | Delta × price change |
| Vega | Sensitivity to implied volatility | Vega × volatility change, with matching units |
Large shocks require full instrument revaluation. Bond convexity, changing option sensitivities, basis risk and funding costs can make the linear estimate inaccurate. Sensitivity labels alone are not regulatory capital charges.
LEARNING SECTION 05
Five groups of stress metrics
| Group | Core question | Examples |
|---|---|---|
| Capital adequacy and solvency | How much loss-absorbing capacity remains? | Common Equity Tier 1 capital, leverage ratio, depletion |
| Liquidity and funding | How long can the institution meet payments? | Liquidity Coverage Ratio, cash gaps, survival horizon |
| Asset quality and credit | How do defaults and recoveries change? | Probability of Default, Loss Given Default, provisions |
| Market and trading | What does repricing do to the portfolio? | Stressed loss, Value at Risk and Expected Shortfall |
| System-wide indicators | What does the external stress environment show? | Volatility, credit spreads and composite stress indices |
These five groups organise the discussion. They are not a universal regulatory classification. Market indices provide context and possible scenario inputs. They do not measure an individual bank’s capital or cash shortfall directly.
LEARNING SECTION 06
Capital adequacy and solvency metrics
| Metric | Definition or formula | Interpretation |
|---|---|---|
| Common Equity Tier 1 (CET1) ratio | CET1 capital / Risk-Weighted Assets (RWA) | Core equity capital after regulatory adjustments relative to risk-weighted exposures |
| Tier 1 capital ratio | (CET1 + Additional Tier 1 capital) / RWA | Going-concern capital under the applicable eligibility rules |
| Total capital ratio | (Tier 1 + Tier 2 capital) / RWA | Adds qualifying Tier 2 capital |
| Leverage ratio | Tier 1 capital / regulatory leverage exposure measure | A non-risk-based backstop that includes specified off-balance-sheet exposures |
| Capital depletion | Starting or peak ratio less stressed trough ratio | Report percentage points or basis points and identify the reference point |
Additional Tier 1 (AT1) capital and Tier 2 capital have distinct eligibility and loss-absorption features. Tier 2 is not part of Tier 1. The leverage exposure measure uses prescribed treatments for derivatives, securities financing and off-balance-sheet items. It is not simply the accounting balance sheet total.
The denominator can change under stress because borrowers migrate to riskier categories, credit lines draw down or other exposures change. A ratio can deteriorate even without a proportionate fall in capital.
LEARNING SECTION 07
Worked capital stress: a bank under pressure
All amounts are in ₹ crore. Assume opening Common Equity Tier 1 (CET1) capital of 120 and Risk-Weighted Assets (RWA) of 1,000. Opening CET1 ratio is 12%. The one-year stress uses the following simplified assumptions.
| Input | Stress assumption |
|---|---|
| Loan Exposure at Default (EAD) | 600 |
| Probability of Default (PD) | 8% |
| Loss Given Default (LGD) | 45% |
| Pre-loss earnings | 15 |
| Market loss | 12 |
| Other loss | 5 |
| Stressed RWA | 1,100 |
Starting-to-end depletion is 12.00% − 8.76% = 3.24 percentage points, approximately 324 basis points. Against an assumed 8% internal trigger, the capital headroom is 96.40 − (8% × 1,100) = ₹8.40 crore.
This is a teaching capital bridge. It assumes the entire stated credit loss hits the horizon’s earnings, no opening loss allowance offsets it, and no taxes, dividends, regulatory deductions or capital issuance apply. A real bank must reconcile accounting provisions, write-offs and capital adjustments to avoid counting the same loss twice.
LEARNING SECTION 08
Reverse stress testing: starting from failure
A reverse stress test begins with an explicit adverse outcome. It can be a capital-trigger breach, inability to make payments, loss of a critical funding channel or a business model becoming unviable. Complete insolvency or total exhaustion of cash is not required.
- Choose the failure metric, threshold and horizon.
- Calculate the remaining loss or cash capacity.
- Find combinations of risk-factor shocks that exhaust that capacity.
- Challenge the economic plausibility and timing.
- Identify early warnings and preventative actions.
Reverse testing often produces a boundary of failure combinations rather than a unique scenario. For instance, a milder credit deterioration may cause failure if it arrives alongside larger market losses and a funding run.
LEARNING SECTION 09
Worked reverse test: the default rate at the boundary
Retain the previous bank’s assumptions, including stressed Risk-Weighted Assets (RWA) of ₹1,100 crore and an 8% internal Common Equity Tier 1 (CET1) trigger.
Holding every other input fixed, a default probability above approximately 11.11% breaches the assumed trigger. Exactly at the boundary, the CET1 ratio equals 8%.
| Probability of Default | Credit loss (₹ crore) | Closing capital (₹ crore) | CET1 ratio |
|---|---|---|---|
| 8% | 21.60 | 96.40 | 8.76% |
| 10% | 27.00 | 91.00 | 8.27% |
| 11.11% (rounded) | 30.00 (boundary) | 88.00 | 8.00% |
| 12% | 32.40 | 85.60 | 7.78% |
A model that lets default rates, recoveries, earnings and risk weights deteriorate together will have a different failure boundary. The 11.11% result is a conditional threshold, not a forecast or a probability that the bank fails.
LEARNING SECTION 10
Liquidity buffers, stable funding and survival
The Liquidity Coverage Ratio (LCR) compares eligible, unencumbered High-Quality Liquid Assets (HQLA), after applicable regulatory adjustments, with stressed 30-day net cash outflows.
The Basel normal-times minimum is 100%. During actual stress, banks may use the buffer and fall below the minimum, subject to the supervisory framework. Regulatory asset eligibility, haircuts, caps and operational availability matter.
The Net Stable Funding Ratio (NSFR) compares weighted Available Stable Funding (ASF) with weighted Required Stable Funding (RSF) over a one-year horizon. Basel requires at least 100% on an ongoing basis.
The weights depend on funding stability, maturity and asset characteristics. This is not simply deposits divided by loans.
| Additional metric | What it measures |
|---|---|
| Survival horizon | First date at which usable cash and credible inflows fail to cover cumulative outflows |
| Cash burn rate | Net use of cash per day or other stated period |
| Deposit run-off | Withdrawals by deposit type and concentration under the scenario |
| Collateral haircut | Discount applied to collateral value when estimating borrowing capacity |
| Encumbrance | Assets already pledged and unavailable for an alternative use |
Cash-flow projections should distinguish contractual and behavioural flows, currencies and legal entities. Report separately whether a survival horizon includes ordinary central bank facilities, emergency support or neither.
LEARNING SECTION 11
Worked liquidity stress and a reverse run-off test
| 30-day measure (₹ crore) | Initial case | More severe case |
|---|---|---|
| Eligible High-Quality Liquid Assets (HQLA) | 150 | 130 |
| Gross cash outflows | 240 | 300 |
| Eligible inflows before cap | 100 | 70 |
| Inflow cap: 75% of gross outflows | 180 | 225 |
| Net cash outflows | 140 | 230 |
| Liquidity Coverage Ratio (LCR) | 107.14% | 56.52% |
In the severe case, restoring the ratio to 100% would require ₹100 crore more eligible liquid assets if net outflows stay at 230, or an equivalent reduction in net outflows. This arithmetic does not show whether either action is executable in stress.
A separate one-year example has Available Stable Funding (ASF) of ₹850 crore and Required Stable Funding (RSF) of ₹900 crore. The Net Stable Funding Ratio (NSFR) is 94.44%. With RSF fixed, ₹50 crore more weighted stable funding is needed.
Reverse cash test
Assume ₹150 crore of usable cash resources, ₹50 crore of credible inflows and ₹80 crore of non-deposit payments over the horizon. A ₹1,000 crore deposit base can then sustain at most (150 + 50 − 80)/1,000 = 12% aggregate run-off before this simplified cash balance reaches zero.
This is a cash-budget illustration, rather than a regulatory LCR calculation. Timing can cause an earlier failure even when end-of-horizon cash is positive.
Survival under constant burn
Daily cash gaps are preferable when burn rates vary. Do not count the same asset both as sale proceeds and as collateral for borrowing.
LEARNING SECTION 12
Credit deterioration, provisions and asset quality
| Metric | Expanded name | Stress interpretation |
|---|---|---|
| PD | Probability of Default | Likelihood of default over a stated horizon |
| LGD | Loss Given Default | Fraction of exposure lost conditional on default |
| EAD | Exposure at Default | Outstanding exposure when default occurs, including stressed drawdowns |
| ECL | Expected Credit Loss | Accounting loss estimate under the relevant recognition framework |
| NPA / NPL ratio | Non-Performing Asset / Non-Performing Loan ratio | Non-performing balances divided by the specified gross loan base |
For ₹600 crore exposure, 2% default probability and 40% loss given default, expected loss is ₹4.80 crore. At 8% and 45%, it is ₹21.60 crore, an increase of ₹16.80 crore. Expected loss is not a worst-case loss.
International Financial Reporting Standard 9 (IFRS 9) uses probability-weighted, discounted expected cash shortfalls, including 12-month or lifetime loss recognition as applicable. The US Current Expected Credit Losses (CECL) framework has a different recognition approach. The simple product is a teaching building block, not a complete calculation for either framework.
For lifetime calculations, default timing, survival probabilities, changing exposures, recoveries, scenarios and discounting matter. Multiplying an unconditional average default probability by unrelated average loss and exposure inputs can miss dependence.
Classification rules for non-performing loans or assets vary across jurisdictions. Such ratios are related to credit quality but are not interchangeable with modelled default probabilities.
LEARNING SECTION 13
Market risk: stressed losses and tail measures
A scenario loss is the change in portfolio value under a specified shock. A statistical tail measure instead summarises a modelled loss distribution. Both can be useful, but they answer different questions.
| Measure | Expanded definition | Important distinction |
|---|---|---|
| VaR | Value at Risk | A loss quantile at a stated confidence and horizon |
| ES | Expected Shortfall | Average loss in the worst tail of the loss distribution |
| Stressed VaR | Value at Risk calibrated to stressed conditions | In the legacy Basel market-risk approach, stressed calibration used a relevant continuous 12-month stress period |
| Stressed ES | Expected Shortfall calibrated to stressed conditions | The Basel internal-models market-risk framework uses 97.5% one-tailed expected shortfall with stress calibration and liquidity-horizon adjustments |
For a continuous loss distribution, Expected Shortfall at confidence α is the average loss beyond the corresponding Value at Risk quantile. For discrete distributions, quantile-based tail averaging needs appropriate treatment of probability mass at the threshold.
The legacy Basel Value at Risk and stressed Value at Risk measures used a 99% confidence level and a 10-trading-day horizon. The current framework’s 97.5% Expected Shortfall specification should not be replaced casually by a 99% number. National implementation and the applicable capital method must be checked.
A transparent tail-loss illustration
Suppose 100 equally weighted simulated daily losses have worst five outcomes of ₹8, ₹10, ₹12, ₹15 and ₹20 crore. The average of the worst 5% is (8+10+12+15+20)/5 = ₹13 crore. This is a teaching 95% tail average. A Value at Risk number depends on the quantile convention and the full ordered sample.
LEARNING SECTION 14
System-wide stress indicators
| Indicator | Primary focus | What to read carefully |
|---|---|---|
| Cboe Volatility Index (VIX) | Option-implied, annualised 30-day expected volatility of the Standard & Poor’s 500 index | A volatility gauge, not a forecast of return direction or a bank failure probability |
| Historical LIBOR–OIS spread | London Interbank Offered Rate minus a matched-maturity Overnight Index Swap rate | Historically reflected unsecured term bank credit and liquidity conditions. LIBOR has ceased as a mainstream benchmark. |
| SOFR-based funding and basis measures | Secured Overnight Financing Rate versus comparable swap or funding benchmarks | SOFR is Treasury-collateralised. A SOFR-based spread is not a like-for-like replacement for unsecured LIBOR–OIS credit stress. |
| CISS | Composite Indicator of Systemic Stress | A European Central Bank measure combining stress across financial segments and their dependence |
| High-yield credit spreads | Speculative-grade corporate bond yields or option-adjusted spreads versus a benchmark | Reflect default risk, risk premia and liquidity. State the index and spread definition. |
Foreign exchange (FX), money, bond, equity and financial-intermediary measures can enter a systemic-stress dashboard. Correlation across segments matters: simultaneous stress in several markets is different from an isolated equity-volatility spike.
For an Overnight Index Swap (OIS), specify the reference overnight rate and maturity. Comparing an overnight secured cash rate with a term swap rate also introduces maturity and market-structure differences.
LEARNING SECTION 15
Regulatory exercises: CCAR, DFAST and EBA
Comprehensive Capital Analysis and Review (CCAR) refers to the Federal Reserve’s capital-planning review framework. Dodd–Frank Act Stress Tests (DFAST) refers to statutory stress-testing requirements. They are related concepts with different legal and supervisory roles. Terminology, coverage and mechanics have evolved over time.
The Federal Reserve’s supervisory stress test estimates losses, revenues, expenses and capital under hypothetical adverse conditions. It can include market-shock and counterparty-default components for relevant firms. The European Banking Authority (EBA) coordinates the European Union (EU)-wide stress exercise with participating authorities.
| Issue | How to interpret it |
|---|---|
| Capital focus | Regulatory solvency exercises centre on stressed capital and related financial projections. They are not a substitute for dedicated liquidity stress tests. |
| Scenario meaning | A severely adverse scenario tests resilience. It is not the regulator’s economic forecast. |
| Comparability | Common assumptions support comparison, but institution-specific risks still matter. |
| Management actions | Exercises prescribe how actions, balance sheets and distributions enter the calculations. Follow the applicable methodology. |
| Local applicability | US and EU exercises do not directly specify the rules for an Indian bank. Check Reserve Bank of India requirements and the institution’s own framework. |
For current-year details, use the official sources linked below. An old CCAR pass/fail description should not be assumed to explain every current capital-setting mechanism.
REGULATORY CONTEXT
Dodd–Frank: why the law matters for stress testing
The Dodd–Frank Wall Street Reform and Consumer Protection Act became United States federal law on 21 July 2010, following the 2007–2008 Global Financial Crisis. It was a major overhaul of financial regulation, comparable in scope to the broad reform periods associated with the 1930s New Deal.
The Act sought to reduce systemic risk and expectations of “too big to fail” support, improve oversight and transparency in derivatives markets, strengthen consumer protection and provide a framework for resolving failing financial groups. These are policy objectives, rather than proof that bailouts or financial crises have become impossible.
| Mechanism | Expanded meaning and purpose | Connection to risk management |
|---|---|---|
| FSOC | Financial Stability Oversight Council, an inter-agency body monitoring threats to financial stability. It can designate qualifying nonbank financial companies for Federal Reserve supervision under statutory criteria. | Systemic importance depends on activities, interconnectedness and potential spillovers. “Systemically Important Financial Institution” (SIFI) is a descriptive label, not a claim that every large firm has the same legal designation. |
| Volcker Rule, Title VI | Section 619 added Section 13 to the Bank Holding Company Act. It generally restricts banking entities’ proprietary trading and ownership or sponsorship of covered funds. | Limits certain activities and exposures. The dedicated sections below explain permitted activities and qualifications. |
| DFAST and capital planning | Dodd–Frank Act Stress Tests (DFAST) implement statutory stress-testing requirements. Comprehensive Capital Analysis and Review (CCAR) is the related Federal Reserve capital-planning review framework. | Tests capital resilience under adverse assumptions. Dodd–Frank did not create every element of CCAR. Frequency, scope and thresholds have changed since 2010. |
| Orderly Liquidation Authority, Title II | Orderly Liquidation Authority (OLA) provides a special resolution backstop for qualifying financial companies when statutory conditions apply. | Orderly resolution aims to contain systemic harm. It is distinct from keeping the existing shareholders or management in place. |
| Living wills, Title I | Specified large banking organisations and certain other firms periodically submit resolution plans to the Federal Reserve and the Federal Deposit Insurance Corporation (FDIC). | Plans explain how a firm could undergo rapid and orderly resolution. Recovery planning seeks to restore viability before failure and is a different exercise. |
| Derivatives reform, Title VII | Over-the-Counter (OTC) derivatives reform introduced clearing, trading, reporting and dealer requirements. A Central Counterparty (CCP) intermediates cleared trades. A Swap Execution Facility (SEF) is a regulated trading venue. | Clearing and execution obligations apply to specified products and counterparties, subject to conditions and exemptions. Not every OTC transaction must be centrally cleared or traded on a SEF. |
| CFPB, Title X | The Consumer Financial Protection Bureau (CFPB) was created to administer and enforce federal consumer-financial protection laws within its jurisdiction. | Consumer-product design, disclosure and conduct can create legal, operational and reputational risk. |
| Executive compensation and governance | Say-on-pay voting, compensation recovery policies and pay-ratio disclosures strengthen shareholder information and accountability under implementing rules. | Say-on-pay is generally advisory. Recovery of erroneously awarded compensation can apply after specified accounting restatements. Chief Executive Officer (CEO)-to-median-employee pay disclosure has coverage rules and exemptions. |
Sources: Public Law 111–203, Treasury designation framework, FDIC resolution authority, Securities and Exchange Commission implementation overview and Commodity Futures Trading Commission derivatives overview. The Securities and Exchange Commission (SEC) regulates security-based swaps, while the Commodity Futures Trading Commission (CFTC) regulates swaps, with joint treatment for mixed swaps.
REGULATORY CONTEXT
The Volcker Rule: trading and covered-fund restrictions
The Volcker Rule, named after former Federal Reserve Chairman Paul Volcker, is Section 619 of Dodd–Frank and Section 13 of the Bank Holding Company Act. It generally applies to defined banking entities, including covered banks and affiliates, with statutory exclusions and regulatory exemptions.
Its purpose is to limit certain speculative activities and fund relationships within banking groups benefiting from the banking safety net. It is not a ban on every trade made for a bank’s own account, nor a rule that every bank trading loss breaches the law.
The two core restrictions
| Restriction | What it generally addresses | What must be checked |
|---|---|---|
| Proprietary trading | Trading as principal in a defined trading account, including certain short-term dealing in financial instruments. | Trading-account definitions, instrument scope and applicable exclusions or exemptions. Securities, derivatives and commodity futures can fall within scope. |
| Covered-fund relationships | Acquiring or retaining ownership interests in, or sponsoring, a covered fund. | Whether the vehicle is a covered fund under the rules and whether a permitted activity or exclusion applies. Hedge funds and private equity funds are central examples, but labels alone do not decide the classification. |
Covered-fund rules contain exclusions, permitted activities and conditions. A banking entity cannot assume it may invest in any hedge fund merely because its proposed holding is less than 3%.
Sources: Federal Reserve: Volcker Rule and Regulation VV, Section 248.12. Coverage and permitted activities depend on current law and the applicable facts.
REGULATORY CONTEXT
Permitted activities: market making, underwriting and hedging
| Activity | Purpose and conditions | Teaching illustration |
|---|---|---|
| Market making | Permits qualifying customer-facing market making. Inventory should relate to reasonably expected near-term demand (RENTD) of clients, customers or counterparties, subject to the applicable controls. | A desk holds corporate-bond inventory to meet documented customer demand. An unrelated directional bet cannot become market making simply through its label. |
| Underwriting | Permits qualifying underwriting and distribution activity, with requirements concerning demand, inventory and risk management. | A bank temporarily holds securities while distributing an issuer’s bond offering. |
| Risk-mitigating hedging | Permits qualifying hedges designed to reduce or significantly mitigate specific, identifiable risks, subject to the rule’s requirements. | A desk hedges an identified exposure and monitors whether the hedge actually reduces the risk. |
| Government obligations | Permits trading in specified government obligations, including qualifying United States government, agency, state and municipal obligations. Other sovereign activity has its own conditions. | A qualifying Treasury transaction falls under the relevant permission. This is not a blanket exemption for every sovereign-linked product. |
Permitted activities remain subject to applicable limits on material conflicts of interest, high-risk exposures and threats to safety and soundness or financial stability. The particular requirements vary by activity and institution.
A hedge can still create a stress loss
Assume a customer portfolio loses $10 million in a scenario, while its hedge gains $8 million. The net loss is $2 million before funding and execution costs. The hedge’s risk-reducing purpose and compliance conditions are separate from the question of whether it eliminates every stress loss.
Source: Federal Reserve rulemaking and implementation materials. The figures above are hypothetical.
REGULATORY CONTEXT
The 3% covered-fund limits: a worked illustration
For qualifying permitted fund investment under the organising-and-offering framework, the rules generally impose a per-fund ownership limit after the permitted seeding period and an aggregate capital-based limit. Special provisions apply, including to certain securitisation vehicles and fund structures.
| Limit | Simplified teaching interpretation |
|---|---|
| Per-fund limit | Generally no more than 3% of the total number or value of outstanding ownership interests of an individual covered fund, under the relevant provision. |
| Aggregate limit | The aggregate value of relevant ownership interests held by the banking entity and its affiliates must not exceed 3% of the applicable Tier 1 capital measure. |
| Capital treatment | Specified investments also require capital deductions. Passing a percentage limit does not remove capital consequences or other compliance conditions. |
Example: each limit needs its own check
Assume a banking group has $10 billion of applicable Tier 1 capital. Its simplified aggregate cap is 3% × $10 billion = $300 million. A qualifying Fund A has $1 billion of outstanding ownership value, giving a simplified per-fund cap of $30 million.
| Proposed position | Per-fund test | Aggregate test | Result under the simplified inputs |
|---|---|---|---|
| $25 million in Fund A, with $250 million already in other relevant funds | 25 / 1,000 = 2.5% | (250 + 25) / 10,000 = 2.75% | Within both numerical caps, assuming the activity otherwise qualifies. |
| $40 million in Fund A, with $250 million in other relevant funds | 40 / 1,000 = 4.0% | (250 + 40) / 10,000 = 2.9% | Fails the per-fund cap despite meeting the aggregate cap. |
| $25 million in Fund A, with $290 million in other relevant funds | 25 / 1,000 = 2.5% | (290 + 25) / 10,000 = 3.15% | Fails the aggregate cap despite meeting the per-fund cap. |
These are independent hypothetical cases with fixed denominators. Actual calculations follow prescribed valuation, attribution and capital rules, and consider seeding-period treatment and applicable permissions. The limits are not a general investment allowance for all funds.
Why this belongs in a stress-testing guide
Fund value changes, ownership changes, capital depletion, redemption constraints and collateral demands can interact. A stress programme should track both economic losses and regulatory headroom. Even a legally permitted investment can create liquidity or concentration risk.
Sources: Federal Reserve: permitted investment limits and Capital treatment of covered-fund investments. This worked example illustrates the basic constraints rather than every calculation provision.
LEARNING SECTION 16
Management actions, governance and model risk
Results matter only if the institution can act on them. Management should see the unmitigated outcome first, then the outcome after credible actions. An asset sale that assumes normal liquidity during a crisis can overstate resilience.
| Control | Practical check |
|---|---|
| Data ownership | Reconcile exposures, collateral, allowances and starting capital |
| Independent challenge | Question assumptions and benchmark outcomes against alternative models |
| Action feasibility | Specify timing, decision authority, market capacity and execution cost |
| Aggregation | Avoid double counting credit losses, collateral use and hedge benefits |
| Limits and escalation | Link breaches to named owners, deadlines and board reporting |
| Model limitations | Test parameter sensitivity and disclose missing feedback channels |
Stressed correlations can change, models can extrapolate poorly and historical data can omit plausible future shocks. Reverse testing helps expose gaps, but it also depends on the chosen failure definition.
A practical report identifies the main vulnerability, the failure boundary, leading indicators and the date by which action must start. It should not present a single ratio as proof that every material risk is under control.
LEARNING SECTION 17
Interactive bank stress laboratory
Change the inputs to reproduce the capital bridge, calculate a reverse default-rate boundary and assess a separate 30-day liquidity ratio. Amounts are in ₹ crore. Percentages are entered as percentage numbers, so 8 means 8%.
LEARNING SECTION 18
Excel setup and classroom questions
| Cell | Input or formula | Default example |
|---|---|---|
| B2 | Opening capital | 120 |
| B3 | Pre-loss earnings | 15 |
| B4 | Exposure at Default | 600 |
| B5 | Probability of Default | 8% |
| B6 | Loss Given Default | 45% |
| B7 | Market loss | 12 |
| B8 | Other loss | 5 |
| B9 | Stressed Risk-Weighted Assets | 1100 |
| B10 | Internal trigger | 8% |
| B12 | =B4*B5*B6 | Credit loss: 21.60 |
| B13 | =B2+B3-B12-B7-B8 | Closing capital: 96.40 |
| B14 | =B13/B9 | Capital ratio: 8.76% |
| B15 | =(B2+B3-B7-B8-B10*B9)/(B4*B6) | Reverse default-rate boundary: 11.11% |
Excel percentage cells use decimal values internally. Enter 8% or 0.08 in B5, rather than 8. Check that the reverse boundary lies between 0% and 100%. A negative value means the threshold already fails before credit loss. A value above 100% means default probability alone cannot reach it under the fixed assumptions.
Why can a bank’s capital ratio fall when capital changes only slightly?
Risk-Weighted Assets can rise. Both the numerator and denominator drive the ratio.
Does passing a capital stress test guarantee survival?
No. A bank can suffer an earlier cash shortfall, a currency-specific funding gap or an operational disruption.
Why can a reverse test yield several answers?
Different combinations of defaults, recoveries, market losses and funding withdrawals can produce the same failure threshold.
What is the first check on a proposed management action?
Whether the action can occur in the assumed market conditions before the failure date, at a credible cost and without double counting its benefits.
EXTENDED LEARNING
Core and peripheral variables: completing the scenario
A scenario usually specifies a few core variables directly, such as an equity-index decline or a rate shock. Other peripheral variables, such as related equity indices or sector spreads, must also receive consistent shocks. Leaving every unspecified variable unchanged can materially understate loss.
A simple linear conditional-mean model for changes in two variables is:
Here E denotes expectation, Δ denotes a change, ρ (rho) is correlation and σ (sigma) is standard deviation. With negligible mean changes over the chosen interval:
Suppose the core equity index falls 30%, its volatility is 18%, a related mid-cap index has volatility 24%, and correlation is 0.85. The conditional estimate is 0.85 × (24/18) × (−30%) = −34%.
Volatility and correlation must use compatible definitions, units and sampling horizons. The result is a conditional mean, not a worst-case peripheral shock. Under a joint normal linear model, conditional residual standard deviation is σY√(1−ρ²), about 12.64% with these inputs. That normal assumption may be unreliable for an extreme shock.
Use stress-period relationships, alternative correlations and residual shocks to challenge the estimate. With several core variables, multiple regression or a covariance-based conditional model can help, but unstable relationships still need judgement.
EXTENDED LEARNING
Static, dynamic and path-dependent stress tests
| Design choice | Meaning | Risk of a careless assumption |
|---|---|---|
| Static balance sheet | The exercise constrains balance-sheet evolution using prescribed assumptions. Maturing positions may be replaced to maintain the defined balance sheet. | It need not mean every position remains literally unchanged. State the replacement rules. |
| Dynamic balance sheet | Business volumes, funding and management actions can change through the scenario. | Optimistic new business or asset sales can hide stress. |
| Top-down exercise | A central team or supervisor applies common models to institutions or portfolios. | Common data and models can miss institution-specific features. |
| Bottom-up exercise | Business units or banks project their own exposures and outcomes using common scenario inputs. | Model and assumption differences can reduce comparability. |
Daily liquidity can fail before a quarterly capital trough
| Day | Hypothetical event | Usable cash after event (₹ crore) |
|---|---|---|
| 0 | Initial cash buffer | 100 |
| 1 | Margin call of 45 | 55 |
| 2 | Deposit withdrawals of 70 | −15 |
| 5 | Expected collections of 40 | 25, only if the day-2 gap was funded |
The end-of-week arithmetic is positive, but the institution faces a ₹15 crore shortfall on day 2. A later inflow cannot pay an earlier obligation without bridging finance.
A second-round loss illustration
Suppose a bank must raise ₹18 crore by selling securities that initially carry a marked value of ₹20 crore. A 10% sale discount raises ₹18 crore but adds a ₹2 crore loss. If similar sales lower remaining collateral values, new margin calls may follow. Model the sale proceeds, realised loss and reduced asset stock consistently.
The same idea applies to dynamic option hedging: after a shock changes delta, rebalancing creates trades, funding needs and execution costs. Repeated shocks can be costly even when the final market price returns near its starting value.
EXTENDED LEARNING
Bank Kaveri: an integrated multi-risk case
This case extends the capital bridge to bonds, equities, currency exposure and incremental credit provisions. All amounts are hypothetical ₹ crore. Opening Common Equity Tier 1 (CET1) capital is 1,200 and Risk-Weighted Assets (RWA) are 10,000, so the opening ratio is 12%.
| Position | Exposure | Shock | Loss calculation |
|---|---|---|---|
| Bonds, modified duration 4 | 3,000 | Yield +200 basis points | 3,000 × 4 × 0.02 = 240 |
| Equities | 400 | Price −30% | 400 × 30% = 120 |
| Unhedged US-dollar borrowing | Rupee value 500 | Rupees per dollar rise 10% | 500 × 10% = 50 |
| Loan book | 8,000 | Default probability 2% to 6%, loss given default 45% to 55% | Stressed expected loss 264 less opening allowance 72 = 192 |
Against assumed teaching comparison levels of 5.5% and 8%, capital remains above the first but below the second. The result does not establish survival: liquidity, total capital and institution-specific requirements must also pass.
Two important conventions
Currency quotation: the ₹50 crore loss assumes the rupee price of a dollar rises 10%. If instead “the rupee falls 10%” means dollars per rupee fall 10%, the inverse exchange rate rises 11.111%, producing a ₹55.56 crore liability increase. Define the quote before calculating.
Opening provisions: this case deducts only the ₹192 crore increase above an assumed ₹72 crore existing allowance. The earlier ₹120 crore capital example assumed no opening allowance. Do not transfer one case’s provision convention into the other.
Bond loss uses a modified-duration approximation and omits convexity. The bridge also omits tax, distributions and regulatory adjustments. Profit must be measured consistently before the additional loss charges.
EXTENDED LEARNING
Combined-shock reverse testing: the failure frontier
Retain Bank Kaveri’s opening capital of ₹1,200 crore, but use a separate reverse-test experiment: fixed Risk-Weighted Assets of ₹10,000 crore, no profit, only credit and bond shocks, and an assumed 5.5% Common Equity Tier 1 trigger. Loss capacity is 1,200 − 0.055 × 10,000 = ₹650 crore.
Let p be the stressed Probability of Default (PD), with Loss Given Default fixed at 55%. Retain the opening credit allowance of ₹72 crore. Let Δy be the bond-yield rise in decimal units.
| Stressed PD | Incremental credit loss | Yield rise at the boundary |
|---|---|---|
| 2% | ₹16 crore | 528.33 basis points |
| 6% | ₹192 crore | 381.67 basis points |
| 10% | ₹368 crore | 235.00 basis points |
| 14% | ₹544 crore | 88.33 basis points |
| 16.4091% | ₹650 crore | 0 basis points |
At a 10% default probability and a 300-basis-point yield rise, loss is 368 + 360 = ₹728 crore. Closing capital is ₹472 crore, or 4.72% of fixed risk-weighted assets, below the assumed 5.5% trigger.
The 2% row still produces a ₹16 crore incremental loss because loss given default has increased from 45% in the opening allowance to 55%. Every row uses that same stressed loss fraction.
The boundary identifies combinations that reach the trigger. It is not a probability distribution. Very large yield shocks make duration approximations unreliable, so full bond revaluation should replace the linear formula in implementation.
EXTENDED LEARNING
Reverse liquidity testing: a refinancing freeze
A hypothetical Non-Banking Financial Company (NBFC) has ₹800 crore usable cash and liquid investments, ₹300 crore credible collections and ₹2,000 crore maturing short-term debt over 30 days. Assume no other payments, no asset haircuts and inflows available before obligations fall due.
At 55% non-renewal, the simplified end-of-horizon cash buffer is exactly exhausted. Above 55%, the company has a shortfall. A 60% non-renewal rate requires ₹1,200 crore but resources are ₹1,100 crore, leaving a ₹100 crore gap.
Commercial Paper (CP) is one form of short-term borrowing. Rollover means replacing maturing debt with new funding. A capital-adequate lender can still fail to pay when lenders refuse renewal.
If only half the expected collections arrive, the threshold becomes (800 + 150)/2,000 = 47.5%. If asset sales incur discounts or other payments occur, survival capacity falls further. This cash test is separate from a bank’s regulatory Liquidity Coverage Ratio.
EXTENDED LEARNING
Reverse scenario search with constraints
When several risk factors can change, a spreadsheet or numerical optimiser can search for a large loss or for a threshold breach. Begin with an explicit objective, economic constraints and a reliable valuation model.
| Component | Example specification |
|---|---|
| Changing cells | Equity return, yield change, volatility and default probability |
| Objective | Maximise loss within plausible bounds, or minimise shock severity subject to capital falling to a trigger |
| Bounds | Default probability between 0% and 100%, non-negative volatility, stated rate and price ranges |
| Economic constraints | Couple credit, collateral and funding changes so the scenario remains coherent |
| Output review | Reprice the candidate, inspect which limits bind and challenge plausibility |
Excel Solver is an optimisation tool. Use changing cells for risk factors, a calculated loss or capital cell as the objective, and explicit bounds. A worst-loss result under arbitrary bounds is not automatically a reverse-failure scenario.
For the frontier above, fix the default probability at 10%, set a target loss of ₹650 crore and use the yield change as the changing cell. Solver or direct algebra gives 2.35%, or 235 basis points.
For nonlinear option books, try several initial points, inspect a coarse grid and check the candidate by full repricing. A local optimum can miss a worse combination. Principal Component Analysis (PCA) can reduce the number of search dimensions, but omitted factors and residual shocks still require testing.
Scaling a historical shock vector by 1.5 magnifies its moves. It does not, by itself, create a new correlation structure or capture a liquidity feedback loop.
EXTENDED LEARNING
Expected loss, unexpected loss and concentration
Stress losses complement statistical credit measures. With fixed Exposure at Default (EAD) and Loss Given Default (LGD), let D equal 1 on default and 0 otherwise, with Probability of Default (PD) equal to p.
For two such loan-loss variables with correlation ρ:
Assume loan X has exposure ₹100 crore, default probability 1% and loss fraction 50%. Loan Y has exposure ₹60 crore, default probability 3% and loss fraction 40%. Expected losses are ₹0.50 crore and ₹0.72 crore. Individual unexpected losses are approximately ₹4.975 crore and ₹4.094 crore.
| Loan-loss correlation | Portfolio UL | Normal approximation: 3.090 × UL |
|---|---|---|
| 0.30 | ₹7.330 crore | ₹22.650 crore |
| 1.00 | ₹9.069 crore | ₹28.023 crore |
At 99.9% confidence, a common economic-capital definition is loss quantile minus expected loss. Multiplying standard deviation by a normal quantile is only a shortcut and can misrepresent skewed credit tails. Some sources use “Credit Value at Risk” for the total loss quantile, so state the convention.
The correlation here is between default indicators or resulting fixed-severity losses. It is not interchangeable with the latent asset correlation used in a one-factor credit model. Concentration also includes common sectors, collateral, guarantors and funding sources.
EXTENDED LEARNING
Scenario probabilities and integration with tail measures
Most stress tests ask “what happens if this scenario occurs?” without estimating its probability. An optional modelling extension assigns explicit probabilities and combines stress outcomes with a historical or simulated loss distribution.
For example, assign a combined 2% probability to two mutually exclusive stress outcomes, 1% each. Allocate the remaining 98% to 100 equally weighted ordinary scenarios, so each ordinary scenario receives 0.98% probability.
For a fully specified teaching distribution, suppose every ordinary scenario has a ₹2 crore loss and the stress outcomes have losses of ₹10 crore and ₹20 crore. Using the smallest loss whose cumulative probability reaches the confidence level:
| Measure | Result | Reason |
|---|---|---|
| 99% Value at Risk (VaR) | ₹10 crore | Cumulative probability reaches 99% at 10 |
| 99% Expected Shortfall (ES) | ₹20 crore | The worst 1% is entirely the loss of 20 |
| Expected loss | ₹2.26 crore | 0.98 × 2 + 0.01 × 10 + 0.01 × 20 |
For discrete data, include only the required fraction of any probability mass at a tail boundary when calculating Expected Shortfall. Avoid double counting stress events already represented in the ordinary scenarios.
Empirical probabilities come from observed frequencies under modelling assumptions. Subjective probabilities reflect judgement. Rare-event weights are especially uncertain. Recalculate results over alternative weights and avoid presenting a judgemental probability as an established crisis frequency.
A joint scenario can use conditional probabilities: P(A and B) = P(A) × P(B given A). Multiplying two unconditional probabilities requires independence, which may be a poor crisis assumption. Probability-weighted integration is an optional risk-model technique, not a requirement that every regulatory stress scenario receive an occurrence probability.
EXTENDED LEARNING
Stress Capital Buffer: worked calculation and current context
The US Stress Capital Buffer (SCB) connects supervisory stress results with capital requirements. A familiar single-exercise teaching representation is:
The dividend add-on uses specified projected common dividends and the prescribed Risk-Weighted Assets (RWA) denominator. This shorthand omits detailed regulatory calculation and transition provisions.
| Hypothetical input | Bank A | Bank B |
|---|---|---|
| Starting Common Equity Tier 1 ratio | 12.0% | 11.0% |
| Lowest stressed ratio | 8.8% | 10.2% |
| Ratio decline | 3.2 percentage points | 0.8 percentage points |
| Dividend add-on | 0.6 percentage points | 0.4 percentage points |
| Illustrative buffer after 2.5% floor | 3.8% | 2.5% |
For Bank A, a simplified capital stack of a 4.5% Common Equity Tier 1 minimum plus a 3.8% buffer is 8.3%, before any applicable systemic surcharge or other requirements. Bank B’s raw 1.2% calculation is below the 2.5% floor.
Sources: Federal Reserve capital-planning rule and 30 September 2026 final-rule announcement. Exercise horizons, effective dates and institution categories should be checked in the applicable year’s official documents.
EXTENDED LEARNING
India: macro stress tests and bank-level capital assessment
The Reserve Bank of India (RBI) assesses system resilience through macro-financial stress analysis, including its Financial Stability Report (FSR). System-level results do not replace a bank’s own Internal Capital Adequacy Assessment Process (ICAAP), the forward-looking assessment of capital needed for its material risks.
| Macro exercise | Bank-level ICAAP |
|---|---|
| Common macroeconomic conditions support a system-wide view. | Institution-specific concentrations, business plans and off-balance-sheet risks require tailored scenarios. |
| Aggregates show the broad distribution of resilience. | A system average can conceal an individual bank, currency or legal-entity weakness. |
| Scenario outcomes are conditional projections. | Board-approved limits, capital planning and credible management actions should follow from results. |
An ICAAP should connect to risk appetite, capital allocation and the Supervisory Review and Evaluation Process (SREP). The RBI’s commercial-bank capital directions contain stress-testing and scenario-analysis requirements. The applicable requirements depend on bank type and current directions.
In the Bank Kaveri case, 5.5% and 8% remain explicitly stated teaching comparison levels. A real assessment must also consider Tier 1 and total capital, how Common Equity Tier 1 is allocated to meet those minima, conservation and systemic buffers, and supervisory requirements. A breach of a buffer is not the same as immediate insolvency.
For the Gross Non-Performing Asset (GNPA) ratio, use the report’s observation date, scenario horizon and institution coverage. This guide does not copy headline ratios from an older slide or a textbook as if they were current data.
Source: RBI Commercial Banks: Prudential Norms on Capital Adequacy Directions, 2025, updated 7 October 2026. Consult the official directions and latest Financial Stability Report for numerical requirements and projections.
EXTENDED LEARNING
A complete stress programme: additional exposures and decisions
| Exposure or control | A question that can reveal a missing risk |
|---|---|
| Wrong-way risk | Does exposure or loss severity increase when the counterparty becomes less creditworthy? |
| Pipeline and warehousing | What happens to assets awaiting sale or securitisation if the intended distribution market closes? |
| Off-balance-sheet and reputation risk | Will commitments draw down or will management support an affiliated vehicle despite no contractual duty? |
| Concentrated collateral or guarantors | Do nominally different borrowers rely on the same security or protection provider? |
| Hedge effectiveness | Can a hedge counterparty fail, a basis widen or a market become impossible to trade? |
| Operational and cyber events | Can payments, access to collateral or customer confidence fail during a market shock? |
| Scenario gaming | Does the mitigation protect a broad family of adverse outcomes or only the exact prescribed test points? |
| Decision and ownership | Who acts, by when, at what cost, and which warning indicator triggers escalation? |
A useful board summary identifies the scenario, pre-action capital and liquidity results, failure boundaries, proposed actions, execution lead times and remaining vulnerabilities. Present the result after action separately so that planned mitigation does not conceal the underlying exposure.
Reading and teaching references
John C. Hull, Risk Management and Financial Institutions, fifth edition, Chapter 22, printed pages 497–511, provides the conceptual background on conditional scenarios, feedback effects, reverse searches and probability integration. Regulatory thresholds described in that 2018 edition require current-source verification.
The integrated Kaveri, combined-shock and refinancing examples align with the Session 12 teaching material, with quotation conventions and allowance assumptions stated explicitly here. The figures are hypothetical, and the extensions use original explanatory text.
LEARNING SECTION 19
Sources and further learning
- Basel Committee: stress testing principles and reverse testing
- Basel Framework: Liquidity Coverage Ratio
- Basel Framework: Net Stable Funding Ratio
- Basel Framework: leverage ratio
- Federal Reserve: 2026 stress-test materials
- Federal Reserve: capital planning and stress-test questions
- European Banking Authority: EU-wide stress testing
- Cboe: Volatility Index methodology
- New York Fed: Secured Overnight Financing Rate
- European Central Bank: Composite Indicator of Systemic Stress
- IFRS Foundation: IFRS 9 Financial Instruments
- Basel market-risk standards
Updated 1 November 2026. All bank examples and internal thresholds are hypothetical teaching assumptions. The guide summarises concepts and does not specify the applicable regulatory requirement for a particular institution.