What is RAROC and how do banks use it for performance measurement and capital allocation?

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AcadiFi · Accepted Answer

RAROC (Risk-Adjusted Return on Capital) is a performance metric that evaluates the return a business line generates relative to the economic capital it consumes. Unlike simple ROE (which uses accounting equity), RAROC uses **economic capital** — a risk-based measure of how much capital is needed to absorb unexpected losses. **The RAROC Formula** RAROC = (Revenue − Costs − Expected Losses + Return on Economic Capital) / Economic Capital Or in simplified form: RAROC = (Risk-Adjusted Net Income) / Economic Capital **Worked Example** Clearwater National Bank evaluates two business lines: **Corporate Lending Division:** - Net interest income: $45 million - Fee income: $8 million - Operating costs: $18 million - Expected credit losses: $12 million - Economic capital allocated: $200 million - Return on EC (invested at risk-free rate 4%): $8 million RAROC = ($45M + $8M − $18M − $12M + $8M) / $200M = $31M / $200M = **15.5%** **Trading Division:** - Net trading revenue: $65 million - Operating costs: $30 million - Expected losses: $5 million - Economic capital allocated: $400 million - Return on EC: $16 million RAROC = ($65M − $30M − $5M + $16M) / $400M = $46M / $400M = **11.5%** **Interpretation:** Even though the trading division generates more absolute profit ($46M vs. $31M), corporate lending creates more value per unit of risk capital (15.5% vs. 11.5%). **Value Creation: RAROC vs. Hurdle Rate** A business line creates shareholder value only if: RAROC > Hurdle Rate (typically the cost of equity capital) If Clearwater's cost of equity is 12%: - Corporate Lending: 15.5% > 12% — **creates value** - Trading: 11.5% < 12% — **destroys value** (should be shrunk or restructured) ```mermaid flowchart TD A[Compute RAROC for each business line] --> B{RAROC > Hurdle Rate?} B -->|Yes| C[Business creates value
Allocate more capital] B -->|No| D[Business destroys value
Restructure or exit] E[Hurdle Rate = Cost of Equity
Typically 10-15%] --> B ``` **RAROC vs. ROE:** | Feature | ROE | RAROC | |---------|-----|-------| | Denominator | Book equity | Economic capital | | Risk sensitivity | None — ignores risk differences | High — based on actual risk | | Loss treatment | Uses provisions (backward-looking) | Uses expected loss (forward-looking) | | Comparability | Misleading across business lines | Apples-to-apples comparison | **Exam Tip:** The FRM may ask you to rank business lines by RAROC and identify which ones should receive more capital vs. less. Also know that **ARAROC** (Adjusted RAROC) subtracts the hurdle rate to show pure value creation: ARAROC = RAROC − Hurdle Rate. For more on capital allocation and risk-adjusted metrics, visit our FRM practice section.

What is RAROC and how do banks use it for performance measurement and capital allocation?

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