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LEARNING SECTION 01
What is market risk, and why does it require capital?
Market risk is the possibility of losses as interest rates, equity prices, exchange rates, credit spreads, commodity prices or implied volatilities change. Both securities and derivatives can generate it. A position can carry several risks at once: a corporate bond responds to the risk-free yield curve, its issuer’s credit spread and possible default.
Market risk
A bond loses value when yields or spreads rise.
Credit risk
A borrower or derivatives counterparty fails to pay.
Liquidity risk
Selling quickly requires a discount or becomes impossible.
Capital absorbs losses; risk limits constrain exposures; hedges change sensitivities; liquidity resources fund cash needs. These controls serve different purposes. A market-risk capital charge is neither a forecast of the next loss nor cash set aside in a segregated account.
LEARNING SECTION 02
How did Basel market-risk regulation evolve?
| Milestone | Change | Teaching significance |
|---|---|---|
| 1974 · BCBS established | International supervisory cooperation | The Committee sets standards; domestic authorities implement them. |
| 1988 · Basel I | 8% total capital standard focused on credit RWA | The original Accord did not contain today’s market-risk architecture. |
| 1993 / 1995 · consultations | Development of market-risk proposals | Standardised and internal-model alternatives were developed. |
| January 1996 · Market Risk Amendment | Standardised charges and approved VaR models; effective end-1997 | Trading-book price risk entered the capital framework. |
| 2004 / 2005 / 2006 · Basel II | Three pillars; trading-book refinements integrated in the comprehensive version | Model governance, specific risk and disclosure mattered alongside measurement. |
| 2007–09 · crisis and Basel 2.5 | 2009 revisions added stressed VaR and incremental risk; implementation by end-2011 | Recent benign data and a 10-day horizon missed stressed credit and liquidity risks. |
| 2010–11 · Basel III | Stronger capital quality, buffers and leverage/liquidity reforms | These changed bank resilience; ES-based FRTB came later. |
| 2012 / 2013 / 2014 · FRTB consultations | Fundamental redesign of the trading-book framework | Reconsidered the boundary, models, standardised charges and illiquidity. |
| January 2016 · first final FRTB standard | ES, liquidity horizons and revised SA / IMA | Initial final text; subsequently revised. |
| December 2017 · Basel III finalisation | Broader reforms and revised implementation timetable | Added the aggregate output-floor context. |
| March 2018 / January 2019 | Targeted consultation followed by revised final market-risk standard | 2019 replaced the 2016 version; corrections published February 2019. |
| March 2020 / January 2023 | BCBS deferred the Basel III implementation target by one year | 1 January 2023 is the Basel target, not a universal domestic go-live date. |
| India · September 2026 / April 2027 | RBI final SSA directions issued 21 September 2026; effective 1 April 2027 | Domestic SSA must be distinguished from full FRTB SA and IMA. |
Source: BCBS history · BCBS 2009 trading-book revisions · BCBS January 2016 market-risk standard · BCBS January 2019 revised standard · BCBS implementation deferral, March 2020 · RBI market-risk directions, 21 September 2026
LEARNING SECTION 03
Which approaches belong to Basel II, Basel 2.5 and Basel III / FRTB?
VaR framework
99% one-tailed VaR, 10-day regulatory horizon; standardised alternative.
VaR + stressed VaR
Current and stressed measures, plus credit-related trading-book charges.
Tail loss + liquidity
97.5% ES under IMA; granular SA; desk eligibility and risk-factor data tests.
| Feature | Legacy IMA / Basel 2.5 | FRTB |
|---|---|---|
| Core model metric | 99% VaR; stressed VaR under Basel 2.5 | 97.5% stressed, liquidity-adjusted ES |
| Credit in trading book | Specific risk, IRC and applicable securitisation / correlation-trading treatment | Credit spread risk plus separate default risk treatment |
| Market illiquidity | Limited recognition under a common 10-day measure | Risk-factor liquidity horizons: 10, 20, 40, 60, 120 days |
| Approval | Supervisory model approval | Bank and trading-desk requirements; backtesting and PLA |
| Data gaps | Model validation and specific-risk controls | Modellable factors versus NMRFs with stress-scenario capital |
| Regime | Standardised route | Approved model route | Calculation to learn |
|---|---|---|---|
| Basel II | Legacy standardised measurement: general + specific risk; FX, commodity and option rules | 99% ten-day VaR with multiplier and average / latest comparison | Sections on legacy SA and VaR capital |
| Basel 2.5 | Legacy SA with strengthened credit / securitisation treatments | VaR + stressed VaR + applicable IRC / other charges | Separate current and stressed maxima |
| Early Basel III | Applicable Basel 2.5 trading-book rules continue until local replacement | Same applicable trading-book model regime, with stronger capital quality and buffers | Apply capital ratios to total RWA |
| Final Basel III market-risk reform / FRTB | Full SA = SBM + DRC + RRAO; SSA where permitted | Stressed liquidity-adjusted ES + NMRF + DRC, subject to desk tests | Three distinct FRTB routes below |
First learn the loss measures in the next sections. Then follow the regulatory sequence: legacy standardised charges → legacy IMA → Basel 2.5 → Basel III capital → FRTB routes. Each capital illustration identifies its own portfolio and assumptions; different example totals are not a like-for-like impact estimate.
Source: BCBS 2009 trading-book revisions · BCBS January 2019 revised standard
LEARNING SECTION 04
Which positions belong in the trading book?
The regulatory boundary determines the capital treatment. FRTB tightens designation and restrictions on moving positions between the trading and banking books. Accounting fair value alone does not establish that every instrument belongs in the regulatory trading book. Trading intent, instrument restrictions and supervisory rules matter.
| Position / risk | Typical Basel treatment | Keep separate |
|---|---|---|
| Trading securities and derivatives | Trading-book interest rate, spread and equity risks enter market risk | Derivatives also have counterparty credit risk. |
| FX and commodity exposures | Market-risk coverage can extend across both books | A banking-book label does not remove FX risk. |
| Banking-book interest-rate exposure | IRRBB framework, principally Pillar 2 | Do not apply the trading-book VaR charge to the entire loan book. |
| Counterparty CVA movements | Separate CVA risk framework | CVA is not CVaR / expected shortfall. |
A book transfer cannot create free capital
Assume a permitted transfer would reduce a position’s capital requirement from ₹6 crore to ₹4 crore. The regulatory boundary rules can require a ₹2 crore capital surcharge, preventing a reduction purely through reclassification. Approval and permitted-transfer conditions still apply.
LEARNING SECTION 05
How do sensitivities connect positions to losses?
| Metric | Meaning | Illustration |
|---|---|---|
| Modified duration / DV01 | Yield sensitivity; DV01 is the value change for 1 basis point | ₹100 crore bond × duration 4 × 0.0001 = ₹0.04 crore per bp. |
| CS01 | Value sensitivity to a 1 bp credit-spread move | Keep risk-free yield and credit-spread changes distinct. |
| Delta (Δ) | First-order price sensitivity | Approximate change: Δ × change in underlying. |
| Gamma (Γ) | Change in delta / second-order price effect | Approximate addition: ½Γ × (price change)². |
| Vega | Sensitivity to implied volatility | State whether quoted per 1 volatility point or per unit volatility. |
| Basis / correlation risk | Mismatch between supposedly hedged factors | Two related curves need not move together. |
Duration-based loss
A ₹100 crore fixed-rate bond has modified duration 4. If its yield rises 50 bp, ΔV ≈ −4 × 100 × 0.005 = −₹2.00 crore, ignoring convexity and spread changes. This is a scenario loss, not a complete Basel capital calculation.
LEARNING SECTION 06
What does Value at Risk actually tell us?
Let L be portfolio loss over a stated horizon; positive values mean losses. VaR at confidence α is a quantile of that loss distribution. A 99% one-day VaR of ₹3.49 crore means the model assigns approximately 1% probability to a larger one-day loss. It says nothing about how severe those exceedances may be.
VaR may fail subadditivity for some loss distributions: the measured risk of a combined portfolio can exceed the sum of individual VaRs. This is one reason to study expected shortfall.
LEARNING SECTION 07
Which methods estimate VaR?
| Method | Mechanics | Strength | Limitation |
|---|---|---|---|
| Variance–covariance / delta-normal | Map sensitivities to normally distributed factor changes and a covariance matrix | Fast and transparent for linear portfolios | Normal tails and linearisation can understate option and jump risks. |
| Historical simulation | Apply past joint factor changes to today’s positions; revalue and rank losses | Preserves observed joint scenarios | Future crises may differ; results depend on window and weighting. |
| Monte Carlo simulation | Simulate a specified joint factor model, revalue and rank losses | Flexible for nonlinear portfolios | Depends on distributions, dependence, calibration and simulation accuracy. |
Full revaluation is especially useful for options and structured positions. It does not remove model risk: a sophisticated valuation engine can still receive unrealistic scenarios.
LEARNING SECTION 08
Case 1 · Calculate normal VaR and portfolio diversification
₹100 crore equity portfolio
Assume one-day return volatility 1.50%, zero mean loss and a linear position. Loss standard deviation = 100 × 1.50% = ₹1.50 crore. With z0.99 = 2.326348:
Under independent, identically distributed normal daily changes, ten-day VaR ≈ ₹3.4895 × √10 = ₹11.0348 crore. Drift, serial dependence, volatility clustering and nonlinear payoffs can invalidate this shortcut. FRTB’s ES base observations are ten-day changes, not one-day ES multiplied by √10.
Two positions, one portfolio
Let currency loss standard deviations be ₹1.00 and ₹0.80 crore, with correlation 0.25. Then σp = √(1 + 0.64 + 0.40) = ₹1.4283 crore. Portfolio 99% normal VaR = ₹3.3227 crore. The sum of standalone VaRs is ₹4.1874 crore. Diversification benefit depends on the assumed dependence and may shrink in stress.
LEARNING SECTION 09
What are CVaR and expected shortfall?
Expected shortfall (ES), often called Conditional VaR (CVaR) or Average VaR, averages losses in the worst tail. For continuous distributions ES equals the conditional mean beyond VaR. At a probability mass on the VaR threshold, use the quantile-integral definition so that exactly the required tail probability is included; simply averaging all losses greater than or equal to VaR can be wrong.
Compare like with like
| Measure | Same one-day normal loss model: μ = 0, σ = ₹1.50 crore |
|---|---|
| 97.5% VaR | ₹2.9399 crore |
| 97.5% ES / CVaR | ₹3.5067 crore |
| 99% VaR | ₹3.4895 crore |
| 99% ES / CVaR | ₹3.9978 crore |
At the same confidence and horizon, ES is at least VaR. The closeness of normal 97.5% ES and 99% VaR explains the FRTB confidence calibration, but the two are not interchangeable under fat tails.
Figure 1 · A threshold versus an average tail loss
LEARNING SECTION 10
Case 2 · Why does the tail beyond VaR matter?
Consider 100 equally likely, ordered one-day losses. The first 94 are at or below ₹1 crore; the 95th loss is ₹2 crore. Use the empirical quantile infimum convention, so 95% VaR is the 95th order statistic. The top five scenarios form the 5% ES tail.
| Portfolio | Worst five losses (₹ crore) | 95% VaR | 95% ES |
|---|---|---|---|
| A | 3, 4, 5, 6, 7 | 2.00 | 5.00 |
| B | 3, 4, 5, 6, 32 | 2.00 | 10.00 |
The VaRs match, but B’s average tail loss is double. A quantile alone does not describe tail severity. With finite observations, define ranking, interpolation and fractional-tail treatment explicitly.
Same threshold. Different tail.
Lengths show the relative risk measures for the discrete teaching example.
LEARNING SECTION 11
Basel II · Approach A: the legacy standardised method
The legacy standardised method adds prescribed charges across the applicable risk types. Debt and equity treatment separates general market movements from issuer-specific risk. Debt general risk uses maturity or duration ladders with offsetting disallowances. FX uses an overall net open position; commodities and options have their own methods. A single risk weight on the entire trading-book notional is not this method.
Equity plus FX, with no debt, commodities or options
Assume long equity positions of ₹80 crore and short equity positions of ₹20 crore in different issuers, in the same national market. Use the baseline 8% specific and 8% general equity charges, without discretionary concessions. Gross equity exposure = 80 + 20 = ₹100 crore; net exposure = 80 − 20 = ₹60 crore.
| Component | Calculation | ₹ crore |
|---|---|---|
| Equity specific risk | 8% × gross 100 | 8.00 |
| Equity general risk | 8% × absolute net 60 | 4.80 |
| FX charge | 8% × overall net open position of 40 | 3.20 |
| Total market-risk charge | 8 + 4.8 + 3.2 | 16.00 |
| Market RWA | 12.5 × 16 | 200.00 |
The FX position of ₹40 crore is assumed already determined under the relevant currency and gold aggregation rules. The example excludes options and all other risk classes.
LEARNING SECTION 12
Basel II · Approach B: the approved VaR internal model
The legacy model used daily 99% one-tailed VaR with a ten-trading-day holding period for regulatory capital. Subject to approval, one-day results could be scaled. Capital used the larger of the latest VaR and a multiplier times the preceding 60-business-day average. The multiplier had a minimum of 3, with possible additions. Specific-risk treatment and other requirements had to be addressed separately.
VaR is not itself the capital charge
Latest ten-day VaR = ₹12 crore; 60-day average = ₹10 crore; mc = 3. Then KVaR = max(12, 30) = ₹30 crore, before any separately applicable charges.
LEARNING SECTION 13
Basel 2.5 · Add stressed VaR and incremental risk
Basel 2.5 supplemented current VaR with stressed VaR calibrated to a continuous twelve-month period of significant stress for the current portfolio. The incremental risk charge (IRC) addressed default and migration risk in relevant non-securitisation credit positions, at 99.9% confidence over a one-year capital horizon with liquidity-horizon assumptions. Securitisations and correlation trading had distinct treatments.
+ max(sVaRlatest, ms × sVaR̄60) + applicable additional charges
A Basel 2.5 bridge
Use current VaR inputs 12 and 10, stressed VaR inputs 20 and 18, both multipliers 3, and an already determined applicable IRC of ₹8 crore. Capital = 30 + 54 + 8 = ₹92 crore. Market RWA = 12.5 × 92 = ₹1,150 crore. This illustration assumes no further applicable securitisation or specific-risk charges.
Source: BCBS 2009 trading-book revisions
LEARNING SECTION 14
Basel III · What changed before FRTB?
The initial Basel III package strengthened the numerator—especially CET1 quality and loss absorption—and introduced buffers and leverage / liquidity safeguards. The older Tier 3 category, which had been permitted for eligible market-risk capital, was abolished under Basel III. It did not instantly replace every bank’s VaR framework with ES. Basel 2.5 market-risk rules could continue while jurisdictions prepared the later FRTB replacement.
Same market RWA, stronger capital structure
Take the ₹92 crore Basel 2.5 market charge above: market RWA = ₹1,150 crore. Add credit RWA ₹2,000 crore and operational RWA ₹350 crore, for total RWA ₹3,500 crore. Under Basel III baseline minima plus the full 2.5% CCB, the required capital stack is:
| Requirement | Ratio × ₹3,500 crore | Amount · ₹ crore |
|---|---|---|
| CET1 including full CCB | 7.0% × 3500 | 245.00 |
| Tier 1 including full CCB | 8.5% × 3500 | 297.50 |
| Total including full CCB | 10.5% × 3500 | 367.50 |
One mix exactly meeting these thresholds is CET1 ₹245 crore, AT1 ₹52.50 crore and Tier 2 ₹70 crore. Higher CET1 can substitute for lower-tier capital. These are bank-wide Basel baselines, not RBI thresholds and not an additional market charge on top of the RWA calculation.
Source: BCBS Basel III overview · RBI capital-adequacy directions
LEARNING SECTION 15
What is the FRTB architecture?
FRTB—the Fundamental Review of the Trading Book—is the Basel redesign of market-risk capital. It combines a firmer book boundary with a revised standardised approach and an internal-model approach. Supervisory approval governs model use; model-ineligible desks revert to standardised capital.
Sensitivities + default + residual risk
SBM captures delta, vega and curvature. Add DRC and RRAO where applicable.
ES + NMRF + default risk
Stress and liquidity calibration; desk backtesting / PLA; add standardised capital for ineligible desks.
A simplified standardised approach is available at supervisory discretion for qualifying banks with smaller or less complex trading activities. It is a separate route, not a simplified ES model.
Source: BCBS January 2019 revised standard · Basel MAR20: standardised structure · Basel MAR40: simplified standardised approach
LEARNING SECTION 16
FRTB · Route 1: simplified standardised approach (SSA)
SSA recalibrates the legacy risk-class charges and sums them. It retains a simpler structure for eligible banks subject to supervisory permission. It is distinct from the full sensitivities-based SA and from ES-based IMA.
Four global Basel SSA risk classes
| Risk class | Unscaled charge | Scalar | Scaled charge |
|---|---|---|---|
| Interest rate | 10.00 | 1.3 | 13.00 |
| Equity | 2.00 | 3.5 | 7.00 |
| Commodity | 1.00 | 1.9 | 1.90 |
| FX | 3.00 | 1.2 | 3.60 |
| Total | — | — | 25.50 |
Market RWA = 12.5 × ₹25.50 = ₹318.75 crore. These are illustrative completed base charges, not risk-weight percentages applied to notionals. The RBI three-class formula is presented separately in the India section.
LEARNING SECTION 17
FRTB · Route 2: full standardised approach (SA)
| SBM risk class | Examples of underlying factors |
|---|---|
| General interest rate risk (GIRR) | Currency yield curves, tenors, inflation and cross-currency basis |
| Credit spread: non-securitisations | Issuer credit-spread curves |
| Credit spread: securitisations outside correlation trading | Securitisation spread risk buckets |
| Credit spread: correlation trading portfolio (CTP) | Eligible correlation-trading spread risks |
| Equity | Equity prices and repo rates |
| Commodity | Commodity prices, grades, locations and maturities |
| Foreign exchange | Exchange rates |
Delta measures first-order changes; vega captures implied-volatility sensitivity; curvature captures nonlinear price changes under prescribed upward and downward shocks after removing the delta component. Apply regulatory weights, buckets and aggregation rules. Calculate the overall SBM charge in low, medium and high correlation scenarios and select the largest total; do not choose each component’s maximum independently and then add them.
Source: Basel MAR20: standardised structure · Basel MAR21: sensitivities-based method
LEARNING SECTION 18
Case 3 · Build a sensitivities-based charge
The following uses hypothetical weighted sensitivities to isolate aggregation. These are capital inputs already multiplied by compatible risk weights—not raw DV01 values and not a prescribed risk-weight table.
Kb = √max(0, Σk WSk² + Σk≠ℓ ρkℓWSkWSℓ)This is the within-bucket delta / vega form; cross-bucket aggregation and curvature use their own rules.
A long–short hedge remains exposed to basis risk
Two weighted delta sensitivities are +₹4 crore and −₹3 crore in one bucket, with medium correlation 0.50. The medium charge is √(16 + 9 − 12) = ₹3.6056 crore. Using low correlation max(2ρ − 1, 0.75ρ) = 0.375 gives ₹4.0000 crore; high correlation min(1.25ρ, 1) = 0.625 gives ₹3.1623 crore. Lower correlation weakens this hedge.
| Scenario | Delta total | Vega total | Curvature total | SBM total |
|---|---|---|---|---|
| Low | 4.00 | 1.00 | 0.50 | 5.50 |
| Medium | 3.6056 | 1.20 | 0.60 | 5.4056 |
| High | 3.1623 | 1.50 | 0.80 | 5.4623 |
The vega and curvature entries are hypothetical completed aggregates for the same respective scenarios. SBM = max(5.50, 5.4056, 5.4623) = ₹5.50 crore. If DRC = ₹2.00 crore and RRAO = ₹0.20 crore, KSA = ₹7.70 crore and market RWA = ₹96.25 crore.
Source: Basel MAR21: sensitivities-based method
Figure 2 · Three correlation scenarios
LEARNING SECTION 19
How do default risk and residual risk enter SA?
The default risk charge (DRC) covers jump-to-default risk. Spread sensitivity is not a substitute for default capital. For non-securitisations, determine gross jump-to-default (JTD), apply permitted issuer netting and maturity adjustments, then calculate bucket charges using rating weights and hedge-benefit rules. Securitisation and CTP calculations are separate.
| Non-securitisation rating | AAA | AA | A | BBB | BB | B | CCC | Unrated | Defaulted |
|---|---|---|---|---|---|---|---|---|---|
| DRC risk weight | 0.5% | 2% | 3% | 6% | 15% | 30% | 50% | 15% | 100% |
One unhedged senior unsecured corporate bond
Assume a long BBB bond at par, notional ₹100 crore, remaining maturity over one year and no accrued P&L adjustment. Using the SA supervisory LGD of 75% for senior debt: gross JTD = ₹75 crore. With no short hedge or other positions, DRC = 6% × 75 = ₹4.50 crore. The 6% is a DRC weight, not the credit-risk SA RWA weight.
RRAO captures specified exotic-underlying or other residual risks that SBM and DRC may not sufficiently capture. Applicable gross notionals are multiplied by 1.0% for exotic underlyings or 0.1% for other residual risks. Scope and exclusions must be checked; it is not a charge on every option.
A residual-risk add-on
An eligible other-residual-risk instrument with gross notional ₹200 crore attracts ₹0.20 crore RRAO at 0.1%, in addition to its applicable SBM and DRC. An exotic-underlying instrument of the same notional would attract ₹2.00 crore at 1%.
Source: Basel MAR22: default risk charge · Basel MAR23: residual risk add-on
LEARNING SECTION 20
FRTB · Route 3: internal models and stressed ES
The IMA uses daily, one-tailed 97.5% ES. Build liquidity-adjusted ES from ten-day factor changes. Stress calibration uses a reduced set of factors with adequate history, scaled to reflect current full-factor coverage. The reduced set must explain at least 75% of full ES on average over the preceding twelve weeks.
Current coverage meets stressed calibration
ESF,C = ₹5 crore; ESR,C = ₹4 crore; ESR,S = ₹8 crore. The coverage ratio is 1.25, so stressed ES = 8 × 1.25 = ₹10 crore. The current reduced/full ratio is 80%; that single observation alone does not prove the twelve-week eligibility test.
LEARNING SECTION 21
Case 4 · How are liquidity horizons incorporated?
FRTB assigns risk factors to 10, 20, 40, 60 or 120-day horizons. Typical examples include ten days for large-cap equity price risk, forty days for investment-grade corporate spreads and sixty days for high-yield corporate spreads. Maturity caps and detailed mappings apply. Nested factor subsets avoid treating each position as a separate standalone loss.
| Ten-day ES input (₹ crore) | Factor shocks retained | Incremental weight | Contribution to ES² |
|---|---|---|---|
| 3.00 | All factors | 1 | 9.0000 |
| 2.00 | LH ≥ 20 days | (20−10)/10 = 1 | 4.0000 |
| 1.00 | LH ≥ 40 days | (40−20)/10 = 2 | 2.0000 |
| 0.50 | LH ≥ 60 days | (60−40)/10 = 2 | 0.5000 |
| 0.25 | LH ≥ 120 days | (120−60)/10 = 6 | 0.3750 |
These are hypothetical nested ten-day ES outputs. They are not individual-asset ES values to be added. A flat √12 multiplier on the whole portfolio would incorrectly treat all risks as 120-day risks.
Source: Basel MAR33: internal-model capital
Figure 3 · Liquidity horizons add to squared ES
LEARNING SECTION 22
What makes a risk factor modellable?
The risk-factor eligibility test (RFET) asks whether enough representative real prices exist. Under the Basel test, a factor needs either at least 24 observations over the relevant year with at least four in every ninety-day period, or at least 100 observations over twelve months. Count at most one observation per day; data quality, representativeness and bucketing also matter.
Modellable factor
Eligible factors enter ES, subject to model and data requirements.
Non-modellable factor
Apply stress-scenario capital rather than silently dropping the risk.
For example, 30 observations all concentrated in one month do not satisfy the 24-observation route’s spacing test. A pricing model’s ability to interpolate a price is different from evidence of real market observations. NMRF stress-scenario calibration and liquidity-horizon floors are governed by MAR33.
Source: Basel MAR31: model requirements
LEARNING SECTION 23
Why do backtesting and P&L attribution both matter?
| Control | Question answered | Main comparison |
|---|---|---|
| Backtesting | Did actual or hypothetical losses exceed predicted quantiles too often? | One-day VaR against APL and HPL |
| P&L attribution (PLA) | Does the risk model explain the desk’s valuation changes? | Risk-theoretical P&L (RTPL) against hypothetical P&L (HPL) |
| Stress testing | What if conditions move beyond the calibration sample? | Historical and hypothetical severe scenarios |
Desk backtesting uses 99% and 97.5% one-day VaR. More than twelve 99% exceptions or thirty 97.5% exceptions over the most recent twelve months makes the desk model-ineligible. PLA green requires Spearman correlation above 0.80 and KS statistic below 0.09; red results from correlation below 0.70 or KS above 0.12; other outcomes are amber. Red means SA; amber attracts a surcharge. Re-entry conditions apply.
LEARNING SECTION 24
Case 5 · From ES to the complete IMA capital bridge
FRTB limits diversification across the five broad IMA risk classes. The modellable-risk charge combines the diversified stressed ES measure and the sum of separately calculated risk-class measures, with equal weights. NMRF stress-scenario capital is added through the non-default charge; DRC is separate.
A model-approved portfolio plus SA desks
| Step | Inputs and calculation | ₹ crore |
|---|---|---|
| Diversification constraint | 0.5 × 10 + 0.5 × 14 | 12.00 |
| Latest non-default measure | Latest IMCC 12 + latest SES 2 | 14.00 |
| Average-based non-default measure | 1.5 × average IMCC 11 + average SES 1.8 | 18.30 |
| C_A | max(14, 18.30) | 18.30 |
| IMA DRC | Assume latest 3; twelve-week average 2.8 → max | 3.00 |
| Model-ineligible desks | Completed SA charge C_U | 4.00 |
| Total market capital | 18.30 + 3.00 + 4.00; no amber surcharge assumed | 25.30 |
| Market RWA | 12.5 × 25.30 | 316.25 |
The IMA default model uses a 99.9% one-year default-risk measure, with its own modelling, hedging and capital rules. It is not the SA rating-weight calculation, and it is not the legacy IRC default-and-migration charge. If an eligible desk is amber, the prescribed additional surcharge must also be included.
LEARNING SECTION 25
How does market-risk capital become bank-wide capital adequacy?
Total RWA = credit RWA + market RWA + operational RWA
CET1 ratio = CET1 / Total RWA
Tier 1 ratio = (CET1 + AT1) / Total RWA
Total capital ratio = (CET1 + AT1 + Tier 2) / Total RWA
The factor 12.5 is 1 ÷ 8% = 12.5, the Basel conversion from a capital charge to RWA. Do not replace it with 1 ÷ 9% ≈ 11.11 because RBI has a higher minimum total capital ratio. Apply the applicable capital percentages to the resulting total RWA. Additional CVA RWA and other components, where required, must also be included in the appropriate regulatory totals.
All three ratios must pass
Credit RWA ₹800 crore, operational RWA ₹100 crore and market capital ₹8 crore give market RWA ₹100 crore and total RWA ₹1,000 crore. CET1 ₹80 crore, AT1 ₹15 crore and Tier 2 ₹20 crore produce 8.00%, 9.50% and 11.50%. These exactly meet RBI baseline ratios including the full 2.5% CCB, before D-SIB, countercyclical, Pillar 2 or other requirements.
If market capital rises to ₹12 crore with regulatory capital unchanged, total RWA becomes ₹1,050 crore. Ratios fall to 7.62%, 9.05% and 10.95%. Meeting all three combined thresholds needs +₹4.00 crore CET1, +₹0.75 crore AT1 (or more CET1) and +₹1.00 crore Tier 2: total ₹5.75 crore. Alternatively, ₹5.75 crore of CET1 alone meets all three. This isolates the RWA effect; an actual trading loss can also reduce CET1.
Source: Basel MAR40: simplified standardised approach · RBI capital-adequacy directions
LEARNING SECTION 26
How do buffers and the output floor interact with market risk?
| Baseline ratios | CET1 | Tier 1 | Total |
|---|---|---|---|
| Basel minima | 4.5% | 6.0% | 8.0% |
| Basel minima + full 2.5% CCB | 7.0% | 8.5% | 10.5% |
| RBI minima | 5.5% | 7.0% | 9.0% |
| RBI minima + full 2.5% CCB | 8.0% | 9.5% | 11.5% |
The CCB is met with CET1. Capital conservation restrictions can arise when buffers are used; distinguish minimum-ratio breaches from buffer depletion. Bank-specific buffers and supervisory requirements may increase these figures.
The floor operates at aggregate level
If model-based total RWA is ₹1,000 crore and the relevant standardised total is ₹1,500 crore, the floor is ₹1,087.50 crore. At 10.5%, baseline total capital including the full CCB is ₹114.19 crore. Do not apply a standalone 72.5% floor separately to each trading desk. Domestic adoption, scope and transition schedules must be checked.
Source: BCBS Basel III overview · BCBS Basel III finalisation, December 2017 · RBI capital-adequacy directions
For the complete credit-risk and output-floor background, read Basel Capital Adequacy for Credit Risk.
LEARNING SECTION 27
Which approach applies in India?
RBI’s final Commercial Banks – Minimum Capital Requirements for Market Risk Directions, 2026, issued 21 September 2026, take effect on 1 April 2027. They prescribe SSA for covered commercial banks; their defined scope excludes Small Finance Banks, Payments Banks and Local Area Banks. Their issuance does not mean all Indian banks must adopt ES-based FRTB internal models.
| Point | RBI final directions · effective 1 April 2027 |
|---|---|
| Regulatory trading book | HFT under the applicable investment directions; HTM, AFS and FVTPL non-HFT remain in the banking book, subject to stated exceptions. |
| Scope of risk | Interest rate and equity risk for trading-book instruments; FX including gold and precious metals across trading and banking books. |
| SSA capital | 1.3 × CR_IR + 3.5 × CR_EQ + 1.2 × CR_FX |
| RWA conversion | 12.5 × the resulting market-risk capital charge |
| Compliance | At consolidated and standalone levels; continuous compliance at each business-day close. |
| Boundary discipline | No reclassification for capital arbitrage; capital-reducing transfers may require a disclosed Pillar 1 surcharge. |
RBI final SSA scalars
Assume already calculated unscaled interest rate, equity and FX capital requirements of ₹10, ₹2 and ₹3 crore, including applicable option components. Final SSA charge = 1.3 × 10 + 3.5 × 2 + 1.2 × 3 = ₹23.60 crore. Market RWA = ₹295.00 crore.
Source: RBI market-risk directions, 21 September 2026 · RBI capital-adequacy directions · Basel MAR40: simplified standardised approach
Three bonds: from duration to RBI market RWA
Assume distinct plain fixed-rate INR HFT issues, no options, and no other exposures. Market values and modified durations are inputs. A and C are different Central Government issues.
| Bond / issuer | Signed value | Rating / residual maturity | Modified duration | Specific charge |
|---|---|---|---|---|
| A · Central Government | +100 | Domestic government / 2.7 years | 2.20 | 0.00 |
| B · Corporate | +50 | AA / 3.0 years | 2.40 | 50 × 1.60% = 0.80 |
| C · Central Government | −40 | Domestic government / 2.6 years | 2.10 | 0.00 |
1 · Specific risk. Domestic Central Government securities attract zero specific risk. The AA corporate with more than 24 months remaining attracts 1.60%. Total = ₹0.80 crore. Residual maturity determines this charge.
2 · General risk. Modified durations fall in the >1.9–2.8 year band, with a 0.80% yield shock. Slot these plain bonds by modified duration, rather than residual maturity.
| Bond | Signed sensitivity: value × modified duration × shock | ₹ crore |
|---|---|---|
| A | 100 × 2.20 × 0.80% | +1.7600 |
| B | 50 × 2.40 × 0.80% | +0.9600 |
| C | −40 × 2.10 × 0.80% | −0.6720 |
3 · Ladder aggregation. Long = 2.7200; short magnitude = 0.6720; net long = 2.0480. Matched amount = min(2.7200, 0.6720) = 0.6720. Vertical disallowance = 5% × 0.6720 = 0.0336. General charge = 2.0480 + 0.0336 = ₹2.0816 crore. One occupied band means zero horizontal matching.
Scaled capital = 1.3 × 2.8816 = ₹3.74608 crore
Market RWA = 12.5 × 3.74608 = ₹46.8260 crore
Display capital ₹3.75 crore and RWA ₹46.83 crore; retain precision. Additional bands need horizontal disallowances; currencies need separate ladders. Different government issues cannot use identical-position offsets.
RBI Directions, 21 September 2026: paragraphs 40, 43, 47–49; Tables 1, 3, 4; effective 1 April 2027. Compare Basel MAR40.29.
LEARNING SECTION 28
What do VaR, ES and capital still leave to risk management?
Every metric depends on positions, valuations, scenarios and data. A calm sample can miss regime change; a liquid quote may disappear when many institutions sell simultaneously. Stress tests should examine basis widening, volatility jumps, concentration, correlation breakdown, hedge gaps and funding / margin needs together.
| Control | Practical use |
|---|---|
| Risk appetite and limits | Set desk limits for sensitivities, VaR / ES, concentration and losses. |
| Independent valuation | Validate prices, reserves, curves and model assumptions. |
| Scenario analysis | Combine rate, spread, equity, FX and volatility shocks with liquidity effects. |
| Model governance | Independent validation, change control, backtesting, PLA and data lineage. |
| Pillar 2 / ICAAP | Assess risks inadequately captured in Pillar 1 and the bank’s own capital needs. |
| Pillar 3 | Disclose approaches, exposures and capital with transparent scope. |
The 2007–09 crisis motivated the shift towards stressed calibration and illiquidity treatment. The lesson is broader than changing a confidence level: capital measurement must reflect risks that become difficult to hedge or exit when markets are disrupted.
LEARNING SECTION 29
Interactive laboratories · reproduce the examples
Lab 1 · Normal VaR versus ES
Linear portfolio; zero mean loss; independent normal daily changes. This is a statistical teaching model, not the FRTB regulatory ES engine.
Lab 2 · Nested liquidity-horizon ES
Enter consistent ten-day ES outputs for nested factor sets. The laboratory reproduces Case 4 before stress scaling, the diversification constraint and other capital components.
Incremental weights: 1, 1, 2, 2, 6. Nested-subset ES need not decrease monotonically when hedges are removed; non-negative finite inputs are required.
Lab 3 · Market capital, RWA and all three ratios
Excludes additional buffers, Pillar 2, the leverage ratio and any further output-floor increase. Inputs assume unchanged RWA after capital issuance.
LEARNING SECTION 30
How can the calculations be reproduced in Excel?
Market Risk Excel Companion
Follow the article through 19 calculation and practice tabs, plus Contents. The Normal, LH and Capital tabs use the exact cell layout in the formula table below.
Start here: Normal and VaR_vs_ES → Tail_Case2 → VaR_Capital → SSA and IR_SSA_3Bonds → SBM_Case3 → Stressed_ES and LH → IMA_Bridge → Capital and Output_Floor.
Other tabs cover Sensitivities, Diversification, Legacy_SA, Basel3_Stack, DRC_RRAO, RFET and Backtest_PLA. The three-bond interest-rate example in Section 27 is reproduced step by step in the IR_SSA_3Bonds tab.
Open in Excel with automatic calculation enabled. Currency amounts are ₹ crore unless stated otherwise.
Use separate input and result cells. The layout below is a compact recipe; percentages must be stored as Excel percentages, not whole numbers. Each panel is a separate worksheet. Currency values are ₹ crore.
| Sheet / cell | Input or formula | Meaning |
|---|---|---|
| Normal!B2 / B3 / B4 / B5 | 100 / 1.5% / 99% / 1 | Value / daily volatility / confidence / days |
| Normal!B7 | =B2*B3*SQRT(B5) | Horizon loss standard deviation; zero mean |
| Normal!B8 | =NORM.S.INV(B4)*B7 | Normal VaR |
| Normal!B9 | =B7*NORM.S.DIST(NORM.S.INV(B4),FALSE)/(1-B4) | Normal ES |
| LH!B2:B6 | 3; 2; 1; 0.5; 0.25 | Nested ten-day ES outputs |
| LH!C2:C6 | 1; 1; 2; 2; 6 | Incremental horizon weights |
| LH!B8 | =SQRT(SUMPRODUCT(B2:B6,B2:B6,C2:C6)) | Liquidity-adjusted ES |
| Capital!B2:B7 | 8; 800; 100; 80; 15; 20 | Market charge / credit RWA / op RWA / CET1 / AT1 / Tier2 |
| Capital!B9 | =12.5*B2 | Market RWA |
| Capital!B10 | =B3+B4+B9 | Total RWA |
| Capital!B11 | =B5/B10 | CET1 ratio |
| Capital!B12 | =(B5+B6)/B10 | Tier 1 ratio |
| Capital!B13 | =SUM(B5:B7)/B10 | Total capital ratio |
| Capital!B15:B17 | 8%; 9.5%; 11.5% | RBI combined baseline targets |
| Capital!B19 | =MAX(0,B15*B10-B5,B16*B10-SUM(B5:B6),B17*B10-SUM(B5:B7)) | Additional CET1 alone satisfying all three |