Basel Capital Adequacy
for Market Risk

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.

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?

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?

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.

Source: Basel RBC25: regulatory-book boundary

LEARNING SECTION 05

How do sensitivities connect positions to losses?

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?

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

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.

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.

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.

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.

Source: Basel II comprehensive framework, 2006

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.

Source: Basel II comprehensive framework, 2006

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.

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.

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.

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.

Source: Basel MAR40: simplified standardised approach

LEARNING SECTION 17

FRTB · Route 2: full standardised approach (SA)

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.

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, K_SA = ₹7.70 crore and market RWA = ₹96.25 crore.

Source: Basel MAR21: sensitivities-based method

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.

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.

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.

Source: Basel MAR33: internal-model capital

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.

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

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.

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?

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.

Source: Basel MAR32: backtesting and P&L attribution

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.

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.

Source: Basel MAR33: internal-model capital

LEARNING SECTION 25

How does market-risk capital become bank-wide capital adequacy?

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.

Source: Basel MAR40: simplified standardised approach · RBI capital-adequacy directions

LEARNING SECTION 26

How do buffers and the output floor interact with market risk?

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.

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.

Source: RBI market-risk directions, 21 September 2026 · RBI capital-adequacy directions · Basel MAR40: simplified standardised approach

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.

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.

Source: BCBS January 2016 market-risk standard

LEARNING SECTION 29

Interactive laboratories · reproduce the examples

LEARNING SECTION 30

How can the calculations be reproduced in Excel?

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.