Basel Accords and Capital Requirements

Basel Accords (Basel I, II, III, III “Final”) are an international regulatory standard for bank capital, developed by the Basel Committee on Banking Supervision (BCBS) under the Bank for International Settlements (BIS). Their goal is to ensure that banks have sufficient capital to absorb losses and reduce systemic risk. The evolution of these accords reflects the lessons of financial crises: Basel I (after the debt crisis of the 1980s), Basel II (after the development of financial innovations), Basel III (after the 2008 crisis). Every bank employee, regulator, and investor is required to understand this system.

Basel I (1988): Simple Framework

Principle. Minimum bank capital ≥ 8% of Risk-Weighted Assets (RWA).

Risk weights. Assets are weighted by category:

• 0%: cash, OECD government debt.
• 20%: interbank claims (OECD banks).
• 50%: mortgage loans.
• 100%: corporate loans, equities.

Capital tiers.

• Tier 1: equity capital, retained earnings.
• Tier 2: subordinated debt, hybrid instruments.

Critique. The crude weighting categories ignore quality within each category (a AAA-rated corporation and a BB startup both receive 100%). No account taken of correlations. Regulatory arbitrage: banks securitized high-quality assets, leaving high-risk assets on the balance sheet with the same weight.

Basel II (2004–2007): Three Pillars

Pillar 1 — Minimum capital requirements.

Credit risk can be assessed in two ways:

Standardized Approach (SA): external ratings (S&P, Moody’s) → risk weights. AAA-AA: 20%, A: 50%, BBB: 100%, below BB: 150%.

IRB (Internal Ratings-Based). Banks use internal models to assess PD, LGD, EAD. Regulator assigns a formula for RWA:

RWA = K(PD, LGD, M, ρ) × EAD × 12.5, where K is the capital function from the Vasicek model (Asymptotic Single Risk Factor, ASRF):

K = LGD · [N((N^{−1}(PD) + √ρ·N^{−1}(0.999))/√(1−ρ)) − PD] · maturity adjustment.

The parameter ρ (asset correlation) is set by the regulator: 12% for retail, 12–24% for corporates (depends on PD), 24% for large banks.

Foundation IRB: bank estimates only PD, LGD = 45% (standard). Advanced IRB: bank estimates PD, LGD, EAD internally.

Market risk. VaR-model (10-day, 99%) or standardized approach.

Operational risk. Basic Indicator (15% of gross income), Standardized, Advanced Measurement Approach (AMA — internal models).

Pillar 2 — Supervisory review. Regulator assesses internal models and may set individual capital add-ons (Pillar 2 capital).

Pillar 3 — Market discipline. Mandatory disclosure of information about capital, RWA, and models.

Basel III (2010–2019): Response to the 2008 Crisis

The fiasco of 2008 showed: banks had 8% RWA capital, but the real share of “true” capital (CET1) was about ~2%. Basel III solutions:

Capital requirements (CET1 — Common Equity Tier 1):

• CET1 ≥ 4.5% RWA (minimum).
• Capital Conservation Buffer: 2.5% CET1 (available in stress, but restricts dividend payments).
• Countercyclical Buffer: 0–2.5% CET1 (activated during credit growth phase).
• G-SIB Surcharge: 1–3.5% for globally systemically important banks (G-SIBs).
• Total CET1 for a large bank: 4.5 + 2.5 + 1.5 = 8.5%.

Leverage Ratio: Tier 1 / Total Exposure (without weighting) ≥ 3% (5% for G-SIBs). Protects against downward RWA modeling.

Liquidity Coverage Ratio (LCR): HQLA (High-Quality Liquid Assets) / 30-day stressed outflows ≥ 100%. Ensures survival for 30 days of deposit outflow.

Net Stable Funding Ratio (NSFR): Available Stable Funding / Required Stable Funding ≥ 100%. Long-term liquidity.

Basel III “Final” / Basel IV (2017–2023, Implementation up to 2028)

• SA-CCR (Standardized Approach for Counterparty Credit Risk). Replaces the Current Exposure Method for derivatives.
• FRTB (Fundamental Review of the Trading Book). Replaces VaR with Expected Shortfall (97.5%) for market risk. Liquidity horizons 10–120 days by asset type.
• Output Floor. RWA calculated by internal models ≥ 72.5% of RWA calculated by the standardized approach. Limits “model arbitrage.”
• Operational Risk SMA (Standardised Measurement Approach). Replaces AMA. Capital = function of bank size × Internal Loss Multiplier.

Numerical Example

A bank with a portfolio:

• €500 million corporate loans (PD = 2%, LGD = 45%, M = 3 years).
• €200 million interbank (PD = 0.5%, LGD = 40%).
• €100 million retail mortgages (PD = 1%, LGD = 25%).

RWA by IRB (simplified, ρ corporates ≈ 0.20, interbank ≈ 0.20, retail ≈ 0.15).

Corporates: K_corp ≈ 0.45·[N((N^{−1}(0.02) + √0.20·2.33)/√0.80) − 0.02] · 1.0 (M-adjustment) ≈ 0.45·[N((−2.054 + 1.042)/0.894) − 0.02] = 0.45·[N(−1.13) − 0.02] = 0.45·[0.129 − 0.02] = 0.049. RWA_corp = 500·0.049·12.5 = 306 million.

Interbank (M = 1): K ≈ 0.4·[N(...)] ≈ 0.015. RWA_mb = 200·0.015·12.5 = 38 million.

Retail: K ≈ 0.025·0.25 = 0.006. RWA_ret = 100·0.006·12.5 = 8 million.

RWA total ≈ 352 million.

Minimum CET1 (Basel III): 8.5% × 352 = 30 million. With Output Floor (72.5%): check standardized RWA. For corporates (BBB) — 100% × 500 = 500. For interbank (AA) — 20% × 200 = 40. Retail — 35% × 100 = 35. SA-RWA = 575. Floor: max(IRB, 0.725·SA) = max(352, 416.9) = 417 million.

CET1 requirement: 8.5% × 417 = 35.4 million. With actual CET1 = 40 million — buffer +4.6 million.

If CET1 = 25 million — deficit of 10.4 million, the bank must either raise capital (rights issue) or reduce assets.

Real Applications

• G-SIBs (JPMorgan, HSBC, ICBC, Sber). The toughest requirements, careful prudential supervision. CET1 14–17%.
• EBA Stress Tests (Europe). Every 2 years. 70 largest EU banks are simulated under adverse scenarios. 2023: average CET1 in severely adverse — 10.4% (vs. 15.0% baseline).
• DFAST/CCAR (USA). Fed stress tests for banks > $250 billion in assets. Ban on dividends/buybacks if failed.
• Basel in Russia. The Bank of Russia adapted Basel III since 2014. Standard H1.0 ≥ 8%, H1.1 ≥ 4.5%, H1.2 ≥ 6%.
• Failures of Basel. Credit Suisse (2023): formally complied with Basel III (CET1 14%), but AT1 wipe-out (CHF 16 billion) cast doubt on the whole system. Silicon Valley Bank (2023): not a G-SIB, simplified requirements — loss of the entire deposit base in 24 hours.

Assignment. A bank with a portfolio: €500 million corporate loans (PD = 2%, LGD = 45%, M = 3), €200 million interbank (PD = 0.5%, LGD = 40%), €100 million retail (PD = 3%, LGD = 35%). (a) Implement the function K(PD, LGD, M, asset_class) according to the IRB formula. (b) Calculate RWA for each segment. (c) Find the minimum CET1 according to Basel III (8.5% — without G-SIB add-on). (d) If actual CET1 = €40 million — what is the deficit? What actions can the bank take (raise capital / reduce loans)? (e) Compare with the calculation by Basel IV Output Floor (need to calculate SA-RWA, e.g., corporates = 100% or by rating).