RAROC and Risk-Adjusted Capital
RAROC divides a business line's profit by the risk capital it consumes rather than the raw capital it was allocated, so a bank can compare a safe, low-margin loan book against a risky, high-margin trading desk on a level playing field.
Prerequisites: Economic Capital
Comparing a mortgage-lending division to a proprietary trading desk by raw profit alone is misleading — the trading desk might post a bigger number simply because it took vastly more risk to get there. RAROC, risk-adjusted return on capital, exists to answer a more useful question: for every dollar of capital a business line puts genuinely at risk, how much return does it produce?
RAROC divides a risk-adjusted profit figure by economic capital (the capital actually consumed by the business's risk), producing a percentage that lets a bank compare wildly different business lines — a loan book, a trading desk, an insurance unit — on the same basis.
The formula
In words: start with profit, but subtract the loss you'd expect to take on average (not just realized losses this year), then divide by the economic capital that risk requires the business to hold. The result is a rate of return, directly comparable to a bank's cost of capital — the minimum return shareholders demand for supplying that capital in the first place.
Worked example
A loan book earns $30 million in revenue, has $5 million in expenses, an expected credit loss of $5 million, and requires $150 million of economic capital. A trading desk earns $90 million in revenue, has $20 million in expenses, an expected loss of $10 million, and requires $500 million of economic capital.
The trading desk produces triple the raw dollar profit, but because it consumes more than three times the risk capital, its risk-adjusted return is actually lower. If the bank's cost of capital is 10%, both clear the hurdle, but the loan book is the more capital-efficient business — the one that should get incremental capital first if the bank is deciding where to grow.
What this means in practice
Banks use RAROC to set capital allocation, bonus pools, and even pricing: a loan or trade that doesn't clear the bank's hurdle rate on a RAROC basis is, by this framework, destroying shareholder value even if it's nominally "profitable." It reframes internal competition for capital away from "who made the most money" toward "who made the most money per unit of risk actually taken."
RAROC is highly sensitive to how economic capital is estimated for each business line, and different risk models can assign very different capital charges to the same exposure. A business line unhappy with its RAROC has a strong incentive to lobby for a friendlier capital model rather than to actually reduce its risk — a well-known internal-politics failure mode of the framework.
Related concepts
Practice in interviews
Further reading
- Crouhy, Galai & Mark, The Essentials of Risk Management (ch. 17)