Risk-Adjusted Return On Capital (RAROC)

Key takeaways
* RAROC (risk-adjusted return on capital) measures return per unit of capital after accounting for expected losses and the opportunity cost of capital.
* It helps compare investments or business lines with different risk profiles and allocate capital efficiently.
* RAROC = (Revenue − Expenses − Expected Loss + Income from Capital) / Capital.
* Calculating expected loss accurately (probability × loss) is critical; RAROC can be data- and model-intensive and should not be the sole decision metric.

What is RAROC?

Risk-adjusted return on capital (RAROC) is a profitability metric that adjusts returns for expected risk. By incorporating expected losses and the income associated with holding capital, RAROC provides a normalized rate of return that lets analysts compare projects, business lines, or investments with differing risk profiles.

RAROC is widely used in banking and financial services for capital allocation, pricing, and performance measurement.

Formula

RAROC = (r − e − EL + IFC) / C

Where:
* r = Revenue
* e = Expenses
* EL = Expected loss (average loss expected over a specified period)
* IFC = Income from capital (often estimated as capital charges × risk-free rate)
* C = Capital (amount allocated or at risk)

Income from capital (IFC) represents the opportunity cost or income generated by holding regulatory/allocated capital, typically proxied by the risk-free rate applied to the capital charge.

Interpreting RAROC

• A higher RAROC indicates more return per unit of capital after accounting for risk.
• Use RAROC to compare alternatives that differ in risk: a higher raw ROI may be less attractive once expected losses are included.
• RAROC supports decisions on pricing, capital allocation, and whether an investment meets a firm’s required return threshold.

Origins

RAROC was developed at Bankers Trust in the late 1970s as a refinement of simple return-on-capital measures to better reflect credit, market, and operational risks in wholesale banking activities. Variants and similarly named metrics (e.g., RORAC, RARORAC) were later adopted across financial institutions and nonbank firms.

RAROC versus RORAC and other variants

• RORAC (return on risk-adjusted capital) and RAROC are closely related; the distinction often lies in how capital or returns are adjusted for risk. In practice, institutions may use slightly different definitions or adjustments, but the goal is similar: compare returns on a risk-consistent basis.
• RARORAC is another variant emphasizing risk-adjusted returns on risk-adjusted capital.
• Terminology and exact calculation conventions vary across firms—always check local definitions when comparing reported metrics.

Calculating expected loss

Expected loss (EL) is typically estimated as:
EL = Probability of default (PD) × Loss given default (LGD) × Exposure at default (EAD)
For noncredit risks, EL can be estimated as the probability of an adverse event times the average loss if that event occurs. Accurate EL estimation requires historical data, scenario analysis, or model-based forecasts.

Other risk–return measures

Common complementary measures include:
* Sharpe ratio — compares excess return to return volatility (standard deviation).
* Risk-adjusted return metrics specific to credit or market risk (e.g., economic capital models).
These measures emphasize different dimensions of risk (volatility vs. expected loss vs. capital consumption) and are often used together.

Limitations and practical cautions

• Data and modeling demands: EL and capital charges require sound inputs; poor estimates produce misleading RAROC results.
• Overreliance risk: A high RAROC does not guarantee a desirable investment if model assumptions understate tail risk or correlated exposures.
• Comparability issues: Different definitions of capital, IFC, or EL across firms make cross-company comparisons difficult.
• Time horizon and granularity: RAROC is sensitive to the measurement period and the way capital is allocated across activities.

Simple example

Suppose an investment yields revenue = 120, expenses = 10, expected loss = 20, capital allocated = 50, and the risk-free rate is 2% (IFC ≈ 50 × 2% = 1).
RAROC = (120 − 10 − 20 + 1) / 50 = 91 / 50 = 1.82 → 182% (annualized rate per unit of capital)

When to use RAROC

Use RAROC for internal performance measurement, pricing, acquisition assessment, and capital-allocation decisions where risk-adjusted comparability matters. Combine RAROC with stress testing, scenario analysis, and other risk measures to form a robust decision framework.

Conclusion

RAROC offers a disciplined way to evaluate returns after accounting for expected losses and the cost of capital. It improves decision-making by aligning profitability with the risks taken, but it depends on the quality of loss and capital estimates and should be used alongside other risk measures and judgment.