RAROC: Risk-Adjusted Return on Capital

Key Takeaways

• The risk adjusted return on capital RAROC measure divides risk-adjusted profit by economic capital.
• Economic capital is the buffer held against unexpected, tail losses, not the expected losses covered by provisions.
• It was developed at Bankers Trust in the late 1970s to price loans and allocate capital by risk.
• A higher RAROC means more profit per unit of capital at risk, which guides where to deploy capital.

What Risk Adjusted Return on Capital RAROC Means

RAROC is a profitability measure built for businesses where risk consumes capital, above all banks. It was developed at Bankers Trust in the late 1970s, with Dan Borge often credited as principal designer, in response to growing regulatory focus on capital adequacy.

The idea is to compare returns on a like-for-like basis after accounting for risk. A loan book that looks profitable on raw interest income may be a poor use of capital once you subtract expected losses and charge for the capital held against worst-case losses. RAROC makes that comparison explicit by dividing risk-adjusted profit by economic capital.

The Intuition

Two business units can report the same accounting profit while consuming very different amounts of risk capital. A unit making safe, secured loans needs a small buffer against surprises. A unit making volatile, unsecured loans needs a large one. Judging both on raw profit rewards the riskier unit unfairly.

RAROC corrects that by putting capital at risk in the denominator. The riskier unit must hold more economic capital, so it needs more profit to post the same RAROC. This lets management compare units, price new deals, and decide where an extra dollar of capital earns the best risk-adjusted return. It is, in spirit, the banking cousin of the Sharpe ratio, return divided by a risk-based quantity.

How It Works

The general form divides risk-adjusted net income by economic capital:

RAROC = (revenue - costs - expected loss + return on capital) / economic capital

Where:

expected loss (EL) = PD * LGD * EAD
PD  = probability of default
LGD = loss given default (fraction not recovered)
EAD = exposure at default (amount owed when default hits)
economic capital (EC) = capital held against unexpected (tail) losses
return on capital = income from investing the capital buffer at a safe rate

Expected loss is a predictable cost, so it is subtracted in the numerator like any other expense. Economic capital, by contrast, covers the unexpected losses beyond the average. It is usually sized to a high confidence level, often near 99.9%, so the firm survives a severe but plausible shock. The return on the invested capital buffer is added back because that capital earns something while it sits there.

A higher RAROC signals capital is working harder. Firms compare a deal's RAROC against a hurdle rate, often the cost of equity, and accept deals that clear it.

Worked Example

Suppose a loan generates 8 million in revenue and carries 3 million in costs. The expected loss is computed from a 2% probability of default, a 40% loss given default, and 100 million of exposure at default.

Expected loss = 0.02 times 0.40 times 100,000,000 = 800,000.

Economic capital held against unexpected loss = 10,000,000. Suppose the buffer earns 2%, adding 200,000 of return on capital.

Risk-adjusted profit = 8,000,000 - 3,000,000 - 800,000 + 200,000 = 4,400,000.

RAROC = 4,400,000 / 10,000,000 = 0.44, or 44%.

If the firm's hurdle rate is 12%, this loan clears it comfortably and creates value. A second loan with the same profit but double the economic capital would post a 22% RAROC, still acceptable but a weaker use of capital.

Common Mistakes

1. Confusing economic capital with regulatory capital. Economic capital is the firm's own estimate of the buffer needed for tail losses. Regulatory capital is a rule-based minimum. RAROC uses the economic figure.

2. Double-counting expected loss. Expected loss belongs in the numerator as a cost. Putting it in the capital denominator as well understates RAROC and distorts pricing.

3. Ignoring the confidence level. Economic capital depends on the chosen confidence level. A 99% and a 99.97% standard produce different capital figures and different RAROCs.

4. Treating a high RAROC as risk-free. A high ratio reflects modeled risk. If the default and loss models are wrong, the apparent return on capital is illusory.

5. Comparing RAROC across firms with different models. Economic capital methods vary. Two banks can compute RAROC differently, so cross-firm comparisons need care.

Frequently Asked Questions

What is risk adjusted return on capital RAROC in simple terms? Risk adjusted return on capital RAROC is profit after risk costs divided by the capital a firm holds against worst-case losses. A higher number means capital is earning more per unit of risk.

How does RAROC affect investment decisions? Banks use RAROC to price loans and allocate capital. A deal that clears the firm's hurdle rate, often the cost of equity, creates value, while one below it destroys value even if it looks profitable.

What is a real-world example of RAROC? A 100 million loan with 4.4 million of risk-adjusted profit and 10 million of economic capital posts a 44% RAROC. Doubling the capital required for the same profit halves the ratio to 22%.

How can investors and managers use RAROC effectively? Set a hurdle rate equal to the cost of equity, separate expected loss from economic capital, and state the confidence level used so the capital figure is interpretable and comparable.

How is RAROC different from the Sharpe ratio? RAROC divides risk-adjusted profit by economic capital tied to tail losses, used inside banks. The Sharpe ratio divides excess return by standard deviation, used for market portfolios. Different risk denominators, similar spirit.

Sources

1. Treasury Today. "RAROC/RARORAC." https://treasurytoday.com/treasury-practice/raroc-rarorac/
2. Ryan O'Connell, CFA. "RAROC: Risk-Adjusted Return on Capital Explained." https://ryanoconnellfinance.com/raroc-risk-adjusted-performance/
3. Diversification.com. "Risk adjusted return on capital (RAROC): Meaning, Criticisms and Real-World Uses." https://diversification.com/term/risk-adjusted-return-on-capital-raroc
4. Umbrex. "Risk-Adjusted Return on Capital (RAROC)." https://umbrex.com/resources/frameworks/strategy-frameworks/risk-adjusted-return-on-capital/

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.