詳細ガイド 近日公開
Expected Loss Calculatorの包括的な教育ガイドを準備中です。ステップバイステップの解説、数式、実例、専門家のヒントをお届けしますので、もうしばらくお待ちください。
Expected Loss (EL) is the mean (average) credit loss that a lender expects to experience from a loan or portfolio of loans over a given time horizon, typically one year. It is the statistical central tendency of the credit loss distribution — the amount a bank should provision for (as a cost of doing business in credit), rather than the unexpected tail loss for which capital is held. The fundamental Basel credit risk formula is: EL = PD × LGD × EAD, where PD is the probability of default, LGD is the loss given default (as a fraction), and EAD is the exposure at default (the outstanding balance at the time of default). PD (Probability of Default) represents the likelihood the borrower will fail to pay within the horizon. LGD (Loss Given Default) is the fraction of the outstanding amount that is ultimately lost after recovery efforts, collateral liquidation, and bankruptcy proceedings — typically 20–80% depending on collateral and loan seniority. EAD (Exposure at Default) is the expected outstanding balance at the time of default, which for revolving facilities may differ from the current drawn balance. Expected loss has a critical role in two related but distinct frameworks: (1) Banking book provisioning under IFRS 9 / US GAAP CECL, where provisions must reflect lifetime or 12-month EL depending on credit stage; and (2) Basel regulatory capital, where EL is compared to provisions — if provisions exceed EL, the surplus reduces required capital; if provisions fall short, the deficit is deducted from capital. This alignment ensures banks' accounting provisions are consistent with their regulatory capital requirements. Unexpected Loss (UL) is the volatility around EL — the standard deviation of the credit loss distribution. Regulatory capital (under Basel IRB) is held against UL (specifically, the 99.9th percentile loss minus EL), not against EL itself, because EL should be covered by pricing and provisions. Economic capital covers losses at even higher confidence levels (99.97%) for internal risk management. For portfolio EL, individual loan ELs sum linearly (EL is additive), but Unexpected Loss is not additive — it benefits from diversification. This is why portfolio credit risk modeling requires correlation assumptions to compute portfolio UL and economic capital, even though EL itself is straightforward.
EL = PD × LGD × EAD UL (single loan) = EAD × LGD × √(PD × (1 − PD)) EL (portfolio) = Σ EL_i = Σ PD_i × LGD_i × EAD_i
- 1Estimate PD for each borrower using internal credit models, external ratings, or Basel IRB estimates.
- 2Determine LGD: for secured loans, LGD depends on collateral value, liquidation costs, and recovery time. Senior unsecured: 40–60%. Senior secured: 20–40%.
- 3Calculate EAD: for term loans, EAD = current outstanding balance. For revolving credit, EAD = drawn balance + credit conversion factor × undrawn commitment.
- 4Compute individual EL: EL = PD × LGD × EAD for each exposure.
- 5Sum ELs across the portfolio for total portfolio expected loss.
- 6Compare total EL to actual provisions: if provisions exceed EL, surplus reduces capital requirement. If provisions fall short, shortfall is deducted from capital.
- 7Use EL for loan pricing: minimum spread = EL / (1 − PD) plus cost of capital on unexpected loss.
Very low EL — investment grade; UL is 13× EL
EL = 0.0015 × 0.40 × $10,000,000 = $6,000. The expected credit loss on a $10M investment-grade loan is only $6,000 per year — 0.06% of the balance. This should be recovered in the loan's credit spread. UL = $10M × 0.40 × √(0.0015 × 0.9985) = $10M × 0.40 × 0.03873 = $154,920. Unexpected loss is approximately 25× EL, reflecting that while defaults are rare, when they happen the loss is significant. Regulatory capital under Basel IRB would be approximately 1.5–3% of EAD for this rating, covering the unexpected loss at 99.9% confidence.
EL/EAD=2.2% — must be recovered in loan pricing
EL = 0.04 × 0.55 × $2,000,000 = $44,000. UL = $2M × 0.55 × √(0.04 × 0.96) = $2M × 0.55 × 0.196 = $215,600. The 220 bps spread floor (just for EL) means the loan must be priced at SOFR + 220 bps minimum to break even on expected losses. Adding cost of capital on the UL (assume 15% ROE on 8% capital): capital = 8% × $2M = $160K; capital cost = 15% × $160K = $24K/yr; adds another 120 bps. Minimum loan spread = approximately 340 bps — consistent with typical BB corporate lending spreads.
Low LGD from real estate collateral reduces EL despite moderate PD
Per-loan EL = 0.012 × 0.25 × $250,000 = $750. Portfolio EL = 1,000 × $750 = $750,000. EL as % of portfolio = $750K / $250M = 0.30%. The low LGD of 25% (reflecting the security of a mortgage — even defaulted mortgages recover 75% through property sale) keeps portfolio EL relatively low. For IFRS 9 provisioning: Stage 1 loans (no significant credit deterioration) use 12-month EL = 0.30% = $750K provision needed. If economic conditions deteriorate and loans move to Stage 2, lifetime EL (5+ years) would be required.
Revolving facilities draw down heavily before default — CCF adjusts for this
EAD = Drawn + (CCF × Undrawn) = $2,000,000 + (0.75 × $3,000,000) = $2,000,000 + $2,250,000 = $4,250,000. EL = 0.03 × 0.60 × $4,250,000 = $76,500. The credit conversion factor (CCF) of 75% reflects the empirical observation that troubled borrowers draw heavily on revolving facilities before defaulting — turning undrawn commitments into outstanding debt. Basel prescribes CCFs of 75% for revolving commitments under the standardized approach, and allows internal estimates under AIRB.
IFRS 9 / CECL loan loss provisioning for banks
Basel IRB credit risk capital calculation
Loan pricing and RAROC analysis for credit decisions
CLO and credit portfolio structured product risk analysis
Internal credit risk reporting and portfolio monitoring dashboards
In practice, this edge case requires careful consideration because standard assumptions may not hold. When encountering this scenario in expected loss calculator calculations, practitioners should verify boundary conditions, check for division-by-zero risks, and consider whether the model's assumptions remain valid under these extreme conditions.
In practice, this edge case requires careful consideration because standard assumptions may not hold. When encountering this scenario in expected loss calculator calculations, practitioners should verify boundary conditions, check for division-by-zero risks, and consider whether the model's assumptions remain valid under these extreme conditions.
In practice, this edge case requires careful consideration because standard assumptions may not hold. When encountering this scenario in expected loss calculator calculations, practitioners should verify boundary conditions, check for division-by-zero risks, and consider whether the model's assumptions remain valid under these extreme conditions.
| Asset Class | Typical PD Range | Typical LGD | Typical EL/EAD | Capital Intensity |
|---|---|---|---|---|
| Investment Grade Corporate | 0.05–0.50% | 35–45% | 0.02–0.23% | Low |
| Sub-Investment Grade Corporate | 1–10% | 45–65% | 0.45–6.5% | High |
| Senior Secured Commercial RE | 0.50–2.0% | 20–35% | 0.10–0.70% | Moderate |
| Residential Mortgage | 0.50–3.0% | 15–30% | 0.08–0.90% | Low-Moderate |
| SME (Senior Secured) | 2–8% | 30–50% | 0.60–4.0% | Moderate-High |
| Consumer Credit Card | 2–8% | 70–90% | 1.40–7.20% | High |
| Leveraged Loan (B-rated) | 4–8% | 40–60% | 1.60–4.80% | High |
What is the difference between expected loss and unexpected loss?
Expected loss (EL) is the average credit loss anticipated over time — the mean of the credit loss distribution. It should be covered by loan pricing (credit spread) and loan loss provisions. Unexpected loss (UL) is the variability of credit losses around the mean — the standard deviation and tail of the loss distribution that occurs due to random default clustering and systemic factors. Capital is held against unexpected loss, specifically the difference between the 99.9th percentile loss and EL under Basel IRB. The fundamental principle: EL is a cost of lending (recovered through pricing), UL is the risk (covered by capital).
How does IFRS 9 use expected loss?
IFRS 9 (effective 2018) replaced the IAS 39 incurred loss model with an expected credit loss (ECL) model. Under IFRS 9: Stage 1 assets (no significant credit deterioration since origination) require a 12-month ECL provision (the EL from default events possible in the next 12 months). Stage 2 assets (significant credit deterioration) require lifetime ECL provisions (the EL over the remaining life of the instrument). Stage 3 assets (already in default) require full lifetime ECL with interest recognized only on net carrying value. The forward-looking nature of IFRS 9 requires incorporating macro-economic forecasts (GDP, unemployment, house prices) into PD and LGD estimates.
What is the CECL model and how does it differ from IFRS 9?
The Current Expected Credit Loss (CECL) standard (ASU 2016-13, effective for large U.S. banks from 2020) requires U.S. GAAP entities to recognize lifetime expected losses upon origination for most financial assets — more conservative than IFRS 9's two-bucket approach. Under CECL, all loans are provisioned for expected losses over their full contractual life from day 1, incorporating current and forecasted economic conditions. This produces significantly higher provisions than the old incurred loss model, particularly for longer-term assets like mortgages. CECL eliminates the dual-bucket structure of IFRS 9, applying a single lifetime ECL across all loans.
How is LGD determined in practice?
LGD depends primarily on: (1) Collateral quality and coverage — secured loans with high-quality collateral (commercial real estate, equipment) have LGD of 20–40%; unsecured loans have LGD of 50–75%; (2) Seniority in the capital structure — senior secured > senior unsecured > subordinated > equity; (3) Industry — industries with more tangible assets (real estate, utilities) have higher recovery than software or professional services; (4) Macroeconomic conditions — LGD rises in recessions when collateral values decline and competition for buyer is reduced; (5) Legal jurisdiction — recovery rates vary significantly by country based on insolvency law and enforcement efficiency.
What is the credit conversion factor for off-balance-sheet items?
The credit conversion factor (CCF) converts off-balance-sheet exposures to credit-equivalent on-balance-sheet amounts. Under Basel standardized approach: committed but undrawn revolving credit facilities with maturity > 1 year: 75% CCF; commitments with maturity ≤ 1 year: 25% CCF; unconditionally cancellable commitments: 10% CCF; letters of credit: 100% CCF; performance bonds: 50% CCF. Under AIRB, banks estimate CCFs internally. The high CCF for revolving facilities (75%) reflects that borrowers systematically draw down credit lines as their financial condition deteriorates — the commitment becomes fully drawn precisely when default probability is highest.
How is EL used in loan pricing and RAROC?
Loan pricing uses a risk-adjusted return framework: the all-in credit spread must recover: (1) Expected loss (EL = PD × LGD) — the provision cost; (2) Return on regulatory capital — regulatory capital (approximately 8–12% of EAD for corporate loans under Basel IRB) must earn the bank's hurdle rate (typically 12–15% ROE); (3) Funding cost (SOFR/LIBOR plus bank-specific funding spread); (4) Operating costs and overheads. Risk-adjusted return on capital (RAROC) = (Revenue − EL − Operating Costs) / Economic Capital. Loans should only be originated if RAROC exceeds the bank's hurdle rate, ensuring risk-adjusted profitability.
Why does portfolio EL sum linearly but portfolio UL does not?
EL is a linear expectation: E[L_portfolio] = Σ E[L_i] = Σ EL_i. This additivity holds regardless of correlations between individual loan defaults. Unexpected loss (standard deviation) is not additive because: Var[L_portfolio] = Σ_i Var[L_i] + 2 Σ_{i<j} Cov[L_i, L_j]. The covariance terms reflect default correlation — when borrowers are correlated, portfolio variance exceeds the sum of individual variances. Diversification (low correlations) reduces portfolio UL below the sum of individual ULs, which is why diversified loan portfolios require less capital per dollar of EAD than concentrated single-name portfolios. This mathematical property drives the capital benefit of loan diversification.
プロのヒント
Build an EL heat map across your loan portfolio by PD band and LGD bucket. The cells with the highest concentration of EL (high PD × high LGD) deserve the greatest scrutiny and tightest credit oversight, regardless of their individual loan sizes.
ご存知でしたか？
The Basel I Accord (1988), which first introduced internationally coordinated bank capital requirements, used flat risk weights without any explicit PD × LGD framework. The breakthrough came with Basel II (2004), which introduced the Internal Ratings-Based approach using EL = PD × LGD × EAD. This allowed banks to finally align capital allocation with actual borrower risk — a transformation that took over a decade of academic research and international regulatory negotiation to implement.