How does the RAROC framework work for lending decisions, and what determines the hurdle rate?

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AcadiFi · Accepted Answer

**RAROC (Risk-Adjusted Return on Capital)** measures the risk-adjusted profitability of a transaction, business line, or entire bank. It is the primary tool for ensuring that every dollar of risk capital earns an adequate return. **RAROC Formula** **RAROC = (Revenue - Costs - Expected Loss + Return on EC) / Economic Capital** | Component | Definition | |---|---| | Revenue | Interest income + fees | | Costs | Funding cost + operating expenses | | Expected Loss | PD x LGD x EAD (provisioned, not a surprise) | | Return on EC | Interest earned on the capital set aside (invested in safe assets) | | Economic Capital | Capital allocated based on unexpected loss at target confidence | **Worked Example — Loan Pricing** Clarendon National Bank is evaluating a $25 million 5-year term loan to Bridgewell Industries (BB-rated). | Component | Value | |---|---| | Loan rate | 6.50% | | Funding cost (FTP) | 4.10% | | Net interest income | 2.40% x $25M = $600,000 | | Origination fee | 0.50% x $25M = $125,000 (amortized over 5 years = $25,000/yr) | | Operating cost allocation | $45,000/year | | PD (1-year) | 2.8% | | LGD | 40% | | Expected Loss | 0.028 x 0.40 x $25M = $280,000 | | Economic Capital (from internal model) | $3,125,000 | | Return on EC (invested at 4.0%) | $125,000 | **RAROC = ($600,000 + $25,000 - $45,000 - $280,000 + $125,000) / $3,125,000** **RAROC = $425,000 / $3,125,000 = 13.6%** ```mermaid flowchart TD A["Revenue: $625K"] --> E["Risk-Adjusted Income: $425K"] B["Operating Cost: -$45K"] --> E C["Expected Loss: -$280K"] --> E D["Return on EC: +$125K"] --> E E --> F{"RAROC 13.6% vs Hurdle?"} F -->|"> 12% hurdle"| G["Approve: Value-creating"] F -->|"< 12% hurdle"| H["Decline or reprice"] ``` **Setting the Hurdle Rate** The hurdle rate is typically the bank's **cost of equity** — the return shareholders require for bearing the risk: - Common approach: CAPM-based cost of equity = Risk-free rate + Beta x Equity risk premium - Example: 4.5% + 1.1 x 7.0% = **12.2%** - Some banks use a single bank-wide hurdle; others differentiate by business line **When RAROC < Hurdle** If the loan's RAROC (13.6%) exceeds the 12.2% hurdle, it creates **economic value added (EVA)**. If it falls below, the bank has options: 1. **Reprice** — increase the loan rate until RAROC exceeds the hurdle 2. **Restructure** — add collateral (reduces LGD), shorten tenor (reduces EC) 3. **Decline** — walk away from the transaction 4. **Syndicate** — retain only a portion, distribute the rest **Pitfalls:** - RAROC is backward-looking if based on historical PDs — need to use through-the-cycle estimates - Ignores client relationship value (cross-selling deposits, treasury management) - EC allocation methodology can be gamed by business units For more on credit risk capital allocation, explore our FRM Part II materials.

How does the RAROC framework work for lending decisions, and what determines the hurdle rate?

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