RAROC (Risk-Adjusted Return on Capital) measures the risk-adjusted profitability of a banking product. It answers: "Does this deal generate enough return to justify the capital the bank must hold against it?"
Banks use RAROC as their primary pricing and credit decision metric. A deal that earns a 15% RAROC is more attractive than one earning 8%, and both are measured against the bank's hurdle rate (typically 10-15%).
For a corporate treasurer, understanding RAROC means understanding how your bank evaluates your facilities -- and why different banks offer different pricing for the same deal.
Revenue - Cost - Funding Cost - Expected Loss
RAROC = (1 - Tax) × [ ──────────────────────────────────────────────── + Risk-Free Rate ]
Economic Capital (FPE)
The rest of this document explains each component in detail.
Revenue is the total annual income the bank earns from the facility:
Revenue = Spread × Average Drawn
+ Commitment Fee × (Average Volume - Average Drawn)
+ Flat Fee + Participation Fee + Upfront Fee
| Component | Description |
|---|---|
| Spread | Annual margin over reference rate (e.g., 150bp over EURIBOR) |
| Commitment fee | Annual fee on the undrawn portion of committed facilities |
| Flat fee | Fixed annual fee |
| Participation fee | One-time participation fee |
| Upfront fee | One-time upfront fee |
The bank's operating cost to manage the facility. Calculated as a percentage of revenue:
| Product Category | Cost/Income Ratio |
|---|---|
| Credit facilities (loans, revolvers, guarantees) | 40% |
| Capital markets | 60% |
| Derivatives (swaps, options, forwards) | 75% |
| Cash management | 80% |
When comparing across banks, each bank's actual cost-to-income ratio (from their annual report) is used instead.
EAD is the bank's expected credit exposure if the borrower defaults. It accounts for the fact that committed but undrawn facilities may be drawn down before default.
EAD = CAD × Average Drawn + CA × Average Volume + CG × Collateral Value
The coefficients depend on the product type and whether the facility is committed:
| Product | CAD | CA | CG |
|---|---|---|---|
| Term loans / revolving credit | 0.25 | 0.75 | -1 |
| Financial guarantees | 0.25 | 0.75 | -1 |
| Technical guarantees | 0.125 | 0.375 | -1 |
| Import documentary credits | 0.125 | 0.375 | -1 |
| Cautions (sureties) | 0.05 | 0.15 | -1 |
| Product | CAD | CA | CG |
|---|---|---|---|
| Term loans / revolving credit | 1.0 | 0 | -1 |
| Financial guarantees | 1.0 | 0 | -1 |
| Technical guarantees | 0.5 | 0 | -1 |
| Cautions (sureties) | 0.2 | 0 | -1 |
Example: EUR 30M committed term loan, EUR 25M average drawn, no collateral: - EAD = 0.25 × 25,000,000 + 0.75 × 30,000,000 = EUR 28,750,000
PD is the likelihood that the borrower defaults within one year. It is derived from the borrower's credit rating using S&P Global long-run average corporate default rates.
| Moody's | S&P / Fitch | PD |
|---|---|---|
| Aaa | AAA | 0.01% |
| Aa1 | AA+ | 0.01% |
| Aa2 | AA | 0.01% |
| Aa3 | AA- | 0.03% |
| A1 | A+ | 0.04% |
| A2 | A | 0.05% |
| A3 | A- | 0.07% |
| Baa1 | BBB+ | 0.10% |
| Baa2 | BBB | 0.16% |
| Baa3 | BBB- | 0.24% |
| Ba1 | BB+ | 0.38% |
| Ba2 | BB | 0.63% |
| Ba3 | BB- | 1.11% |
| B1 | B+ | 2.14% |
| B2 | B | 3.82% |
| B3 | B- | 7.12% |
| Caa1 | CCC+ | 15.00% |
Under Basel III, PD is floored at 5 basis points (0.05%). Even a AAA-rated borrower cannot have a PD below this floor.
When the facility is partially guaranteed (GRR > 0), the effective PD used in the capital formula is reduced:
PD (adjusted) = PD × (1 - GRR)
A 50% guarantee recovery rate halves the effective PD.
LGD is the percentage of exposure the bank expects to lose if the borrower defaults:
LGD = 1 - GRR
Where GRR (Global Guarantee Recovery Rate) represents the percentage of the exposure covered by guarantees or collateral.
Basel III imposes minimum LGD values that cannot be breached regardless of collateral:
| Collateral Type | LGD Floor |
|---|---|
| Unsecured (no collateral) | 25% |
| Receivables / Real estate | 10% |
| Financial instruments | 0% |
This is the core of the Basel IRB framework. The capital requirement K determines how much equity the bank must hold against the exposure.
Asset correlation measures how much the borrower's default risk depends on the overall economy:
R = 0.12 × [1 + exp(-50 × PD) - 2 × exp(-50)] / [1 - exp(-50)]
Higher-rated borrowers have higher correlation (their defaults are more systemic). Lower-rated borrowers default more idiosyncratically.
Longer maturities create more risk because there is more time for the borrower's credit quality to deteriorate:
b = (0.11852 - 0.05478 × ln(PD))²
The IRB formula calculates the capital charge at the 99.9th percentile of the loss distribution:
z = √(1/(1-R)) × N⁻¹(PD) + √(R/(1-R)) × N⁻¹(0.999)K = LGD × [N(z) - PD] × [1 + (M - 2.5) × b] / (1 - 1.5 × b)
Where: - N⁻¹ = inverse cumulative normal distribution - N = cumulative normal distribution - M = maturity in years - 0.999 = Basel 99.9% confidence level
Maturity effect: The formula is calibrated to M = 2.5 years. Shorter maturities reduce K; longer maturities increase it.
Under Basel III (CRR3), the IRB capital requirement cannot fall below a percentage of the Standardised Approach risk weight:
K = max(K, Output Floor % × SA Risk Weight / 12.5)
Standardised risk weights for corporates:
| PD Range | SA Risk Weight |
|---|---|
| PD ≤ 0.05% | 20% |
| 0.05% < PD ≤ 0.15% | 50% |
| 0.15% < PD ≤ 0.75% | 75% |
| 0.75% < PD ≤ 3.0% | 100% |
| PD > 3.0% | 150% |
| Year | Floor |
|---|---|
| 2025 | 50.0% |
| 2026 | 55.0% |
| 2027 | 60.0% |
| 2028 | 65.0% |
| 2029 | 70.0% |
| 2030+ | 72.5% |
Economic capital is the equity the bank must allocate against the facility:
FPE = EAD × K
This is the denominator of the RAROC calculation -- the "capital at risk" that must earn its return.
Example: EAD of EUR 28.75M, K = 8% → FPE = 28,750,000 × 0.08 = EUR 2,300,000
The average annual loss the bank anticipates:
Expected Loss = EAD × PD (adjusted)
Expected loss is a cost of doing business, not a risk. It is deducted from revenue before calculating the return on risk capital.
The bank's cost of borrowing the funds it lends:
Funding Cost = Funding Spread × EAD
The funding spread varies by bank (typically 10-25bp above the interbank rate) and reflects the bank's own credit quality and funding structure.
Putting it all together:
Revenue - Cost - Funding Cost - Expected Loss
RAROC = (1 - Tax) × [ ──────────────────────────────────────────────── + Risk-Free Rate ]
FPE
The risk-free rate is added because the bank earns a return on the equity capital it holds (currently 3.25%, EUR mid-swap rate).
Full worked example:
| Component | Value |
|---|---|
| Facility | EUR 30M committed term loan, EUR 25M drawn |
| Rating | BBB+ (PD = 0.10%) |
| Spread | 150bp |
| Commitment fee | 25bp on undrawn |
| Maturity | 5 years |
| GRR | 40% |
| Revenue | EUR 387,500 |
| Cost (40%) | EUR 155,000 |
| EAD | EUR 28,750,000 |
| PD (adjusted) | 0.10% × (1 - 0.40) = 0.06% |
| LGD | max(1 - 0.40, 0.25) = 0.60 |
| K (risk weight) | ~4.8% |
| FPE | EUR 1,380,000 |
| Expected loss | EUR 17,250 |
| Funding cost (15bp) | EUR 43,125 |
| Numerator | 387,500 - 155,000 - 43,125 - 17,250 = EUR 172,125 |
| Return on capital | 172,125 / 1,380,000 = 12.47% |
| + Risk-free rate | 12.47% + 3.25% = 15.72% |
| After tax (25%) | 15.72% × (1 - 0.25) = 11.79% |
The engine can solve backwards:
Given a target RAROC (e.g., 12%), the solver finds the exact spread that achieves it. Uses Brent's root-finding method.
Given a target RAROC, the solver finds the minimum guarantee recovery rate needed.
Different banks have different: - Cost-to-income ratios (40-76%) -- operational efficiency - Tax rates (22-34%) -- jurisdiction and structure - Funding costs (10-25bp) -- credit quality and deposit base - LGD estimates (14-46%) -- internal model calibration (A-IRB banks)
This means the same deal yields different RAROC values at different banks. A EUR 25M BBB+ loan might show RAROC of 12.3% at HSBC but only 8.5% at Deutsche Bank -- explaining the 55bp spread difference.
The engine uses actual parameters from each bank's Pillar 3 CR6 regulatory disclosures to make these comparisons real, not theoretical.
Banks use different regulatory approaches for their corporate portfolios:
| Approach | PD Source | LGD Source | Banks |
|---|---|---|---|
| A-IRB (Advanced) | Bank's internal model | Bank's internal model | Most large European & US banks |
| F-IRB (Foundation) | Bank's internal model | Regulatory fixed (45% unsecured) | Some banks, Chinese banks |
| Mixed | Varies by portfolio segment | Varies | Banks transitioning or with multiple portfolios |
The formulas implemented follow:
- BIS CRE31 -- IRB approach: risk weight functions (asset correlation, capital requirement) - BIS CRE32 -- IRB approach: risk quantification (PD, LGD, EAD requirements) - BIS d424 -- Basel III standardised approach (output floor risk weights) - CRR3 (EU 2024/1623) -- European implementation of Basel III finalization - S&P Global -- Long-run average corporate default rates (PD calibration)
| Parameter | Default | Description |
|---|---|---|
| Risk-free rate | 3.25% | EUR mid-swap rate |
| Bank tax rate | 25% | Effective corporate tax rate |
| Funding cost | 0bp | Bank's marginal funding spread |
| Output floor | 55% | Basel III floor (2026 phase-in) |
| PD floor | 5bp | Minimum PD (Basel III) |
| LGD floor (unsecured) | 25% | Minimum LGD without collateral |
| LGD floor (secured) | 10% | Minimum LGD with receivables/RE |
| Target RAROC | 12% | Bank's hurdle rate |