Why the Measure Depends on the Decision
Two projects can produce different amounts of earnings and require different amounts of capital. A project may earn more per dollar of capital but create fewer total dollars of value. Choosing a performance measure therefore begins with the decision: are you comparing capital efficiency, measuring value created, or deciding how to allocate scarce capital?
The comparison is meaningful only if earnings, capital, and the hurdle rate use consistent bases. The definitions below assume a single measurement period, the same currency and tax basis for all earnings, and capital measured for that same period. Treat earnings as risk-adjusted earnings after expected losses and relevant expenses; do not compare one project’s pretax earnings with another’s after-tax earnings.
Economic profit compares earnings with the capital charge required by the hurdle rate. Positive economic profit means earnings exceed that charge; negative economic profit means they do not. A hurdle rate must be applied consistently: for example, do not use an annual earnings estimate with a multi-year capital charge unless both are first brought to a common period and basis.
What Each Measure Answers
| Decision question | Measure to examine | Reason |
|---|---|---|
| Which project earns more per dollar of capital? | RAROC | It expresses earnings relative to capital used. |
| Which project creates more dollars above the required return? | Economic profit | It subtracts the capital charge from earnings. |
| Should a project be accepted as a standalone use of capital? | Economic profit, with a no-project baseline | It shows whether the project clears the hurdle and by how much. |
| How should a fixed capital budget be allocated? | Depends on the objective and constraints | Maximizing earnings and maximizing economic profit are not always the same problem. |
When every project requires the same amount of capital, RAROC and economic profit give the same ranking: a higher RAROC means higher earnings and, at a common hurdle rate and capital amount, higher economic profit. When project capital differs, the rankings can diverge. A higher RAROC signals better use of each capital dollar, but not necessarily a larger total contribution.
Worked Example: Higher Capital Efficiency, Lower Total Value
A hypothetical insurer compares two one-year projects. Project North requires $8 million of economic capital and produces $1.36 million of risk-adjusted earnings. Project South requires $20 million and produces $3.00 million. The annual hurdle rate is 12%. Which project has the higher RAROC, and which creates more economic profit?
Method. Calculate each project’s earnings-to-capital ratio and subtract the capital charge from its earnings. Both projects use the same one-year earnings and capital basis.
For North, the RAROC is \(1.36/8=0.17\), or 17%. Its capital charge is \(0.12(8)=$0.96\) million, so its economic profit is \(1.36-0.96=$0.40\) million.
For South, the RAROC is \(3.00/20=0.15\), or 15%. Its capital charge is \(0.12(20)=$2.40\) million, so its economic profit is \(3.00-2.40=$0.60\) million.
North ranks higher on RAROC, while South creates more economic profit. If the decision is to select the project with the greatest dollar contribution above the hurdle, South is preferred. If the decision is to compare earnings per dollar of capital, North is preferred. Check: both projects exceed the 12% hurdle, and their calculated economic profits equal their earnings less their stated capital charges. The common mistake is to treat the higher RAROC as proof of greater total value.
The Relationship Between RAROC and Economic Profit
For positive capital, economic profit can be written directly in terms of RAROC. This identity explains when the measures agree and why their rankings sometimes differ.
The second line follows by distributing \(C\): \(C(E/C)=E\), since \(C>0\). Thus, for a standalone project with positive capital, economic profit is positive exactly when its RAROC exceeds the hurdle rate. This is a test of value creation relative to the hurdle, not a guarantee that the project is the best choice among all possible projects.
For two projects with different capital amounts, the spread \(\text{RAROC}-h\) is multiplied by each project’s capital. A smaller spread on a much larger capital base can produce greater economic profit. If the capital amounts are equal, the multiplication is by the same positive amount, so the RAROC ranking and economic-profit ranking agree.
Worked Example: Allocating a Capital Budget for Different Objectives
A hypothetical portfolio manager has a capital budget of at most $12 million. Project A can use up to $8 million at a fixed RAROC of 14%; Project B can use up to $10 million at 9%; and Project C can use up to $4 million at −2%. Assume the projects are divisible, returns per dollar are fixed over these ranges, and there are no interactions or other constraints. Compare the allocation that maximizes earnings with the allocation that maximizes economic profit when the annual hurdle is 10%.
Method. With fixed RAROCs, each additional dollar allocated to a project produces the same amount of earnings. For maximum earnings with a budget that may be left unspent, use available capital on positive RAROCs in descending order, respecting project limits; do not allocate to negative RAROCs. For maximum economic profit, compare each project’s RAROC with the hurdle.
For maximum earnings, A ranks first at 14%, followed by B at 9%. Allocate $8 million to A and then $4 million to B, using the $12 million budget. Earnings are \(0.14($8\text{ million})=$1.12\) million from A and \(0.09($4\text{ million})=$0.36\) million from B, for total earnings of $1.48 million. Do not use C: its −2% RAROC would reduce earnings.
For economic profit, A’s contribution is \((0.14-0.10)($8\text{ million})=$0.32\) million. B’s contribution for each dollar allocated is below the hurdle; at $4 million its economic profit would be \((0.09-0.10)($4\text{ million})=-$0.04\) million. C is further below the hurdle. The economic-profit-maximizing allocation is therefore $8 million to A and no capital to B or C, leaving $4 million unallocated. Total economic profit is $0.32 million.
The two allocations answer different questions. Spending $4 million on B increases raw earnings by $0.36 million but reduces economic profit by $0.04 million relative to leaving that capital unallocated. Check: at the earnings-maximizing allocation, the capital charge is \(0.10($12\text{ million})=$1.20\) million, and $1.48 million minus $1.20 million is $0.28 million of economic profit—$0.04 million less than the $0.32 million achieved by allocating only to A. The assumption that capital is available does not mean it must be spent.
Assessing Growth and Performance
A project’s average RAROC can differ substantially from the return on an additional tranche of business. When considering growth, calculate incremental earnings divided by incremental capital, and calculate incremental economic profit using that same tranche. Comparing an incremental proposal with an existing portfolio’s average RAROC can hide a decline in value.
Worked Example: A Profitable Business With Value-Destroying Growth
A hypothetical business line currently produces $1.80 million of annual risk-adjusted earnings and uses $15 million of capital. A proposed expansion is expected to add $0.30 million of annual earnings and require $4 million of additional capital. The annual hurdle rate is 10%. Should the expansion be accepted based on its incremental contribution, and what does the expanded line’s average RAROC show?
Method. First calculate the existing line’s average RAROC and economic profit. Then assess the proposal on its incremental earnings and capital before calculating the expanded line’s average.
The existing line’s RAROC is \(1.80/15=12\%\). Its economic profit is \(1.80-0.10(15)=$0.30\) million.
The expansion’s incremental RAROC is \(0.30/4=7.5\%\). Its incremental capital charge is \(0.10(4)=$0.40\) million, so its incremental economic profit is \(0.30-0.40=-$0.10\) million. On these assumptions, the expansion does not meet the hurdle and reduces economic profit by $0.10 million.
After expansion, total earnings are \(1.80+0.30=$2.10\) million and total capital is \(15+4=$19\) million. The expanded line’s average RAROC is \(2.10/19=11.0526\%\), or 11.05% to two decimal places. Its total economic profit is \(2.10-0.10(19)=$0.20\) million, down from $0.30 million.
The expanded line still has an average RAROC above the hurdle, but the proposed tranche has an incremental RAROC below it. Check: the decline in total economic profit, from $0.30 million to $0.20 million, matches the proposal’s −$0.10 million incremental economic profit. The trap is to accept the expansion because the combined average RAROC remains above 10%.
Choosing a Measure for Incentives
RAROC can support comparisons of capital efficiency, while economic profit expresses a dollar amount above or below a capital hurdle. Neither measure is automatically fair or complete for every incentive decision. A RAROC target can encourage efficient capital use but may favor a small, high-rate activity over a larger activity that creates more total value. Economic profit can make the scale of value creation visible, but may favor larger units and depends on a well-calibrated capital charge.
For performance assessment, use a measure aligned with what the manager is being asked to achieve. If the objective is value creation relative to a specified cost of capital, economic profit directly measures that contribution. If the objective is capital efficiency, RAROC provides the ratio. In either case, ensure that earnings and capital reflect the relevant period and that the capital measure is applied consistently. For growth decisions, focus on the incremental effect rather than relying only on an existing business’s average result.
Common Mistakes and Exam Traps
- Confusing a rate with a dollar amount. The project with the highest RAROC does not necessarily have the highest economic profit when capital amounts differ.
- Accepting every project above zero RAROC. A positive RAROC can still be below the hurdle and produce negative economic profit.
- Assuming a capital budget must be fully used. If the objective is to maximize earnings subject to a budget of at most a stated amount, allocate first to the highest positive RAROCs and leave capital unallocated if all remaining eligible RAROCs are negative. If the objective is to maximize economic profit, do not allocate to opportunities with negative economic profit merely to exhaust the budget.
- Using average returns to judge an addition. A business can have average RAROC above the hurdle while its proposed incremental tranche falls below it.
- Mixing bases. A RAROC comparison or capital charge is unreliable if earnings, capital, tax treatment, or measurement periods are inconsistent.
For example, suppose a project uses $1 million and has a RAROC of −1%, while the capital budget is $1 million or less. The wrong calculation allocates the full $1 million because it is the highest-ranked available project, producing \(-0.01($1\text{ million})=-$10,000\) of earnings. The correction is to allocate nothing if no other eligible positive-return project is available: the budget is a maximum, not a requirement to invest, and zero earnings exceed a $10,000 loss.
Check Your Understanding
For each problem, use consistent annual earnings, capital, and hurdle assumptions.
- A hypothetical project requires $6 million of capital and earns $840,000; a second requires $10 million and earns $1.30 million. At a 10% hurdle, calculate each RAROC and economic profit. Which has the higher RAROC, and which has greater economic profit? (Answer: First project: 14% RAROC and $240,000 economic profit; second: 13% and $300,000. The first has higher RAROC; the second has greater economic profit.)
- A manager has a budget of at most $9 million. Project A can use $4 million at a fixed 16% RAROC; project B can use $8 million at 8%. Assume divisibility, no interactions, and a 10% hurdle. State the earnings-maximizing and economic-profit-maximizing allocations. (Answer: Maximize earnings with $4 million to A and $5 million to B, producing $1.04 million of earnings. Maximize economic profit with $4 million to A only, producing $240,000 of economic profit.)
- A standalone project produces annual risk-adjusted earnings of $720,000 and requires $6.5 million of capital. At an 11% hurdle, find its RAROC and economic profit, and state whether it clears the hurdle. (Answer: RAROC is approximately 11.08%; economic profit is $5,000, so it clears the hurdle.)
- An existing line earns $2.40 million on $20 million of capital. A proposed tranche adds $350,000 of earnings and $4 million of capital. At a 10% hurdle, calculate the tranche’s RAROC and economic profit, and the expanded line’s average RAROC and economic profit. (Answer: Tranche RAROC is 8.75% and tranche economic profit is −$50,000. Expanded average RAROC is approximately 11.46%, and expanded economic profit is $350,000.)
- Two divisible projects each have a $5 million maximum capital requirement. Project P earns $600,000 at full use; project Q earns $550,000 at full use. Both have fixed returns per dollar, and a $5 million total capital budget is available. If the objective is maximum earnings, which project receives capital? If the objective is maximum economic profit at a 9% hurdle, which receives capital, and what is that profit? (Answer: Both objectives allocate the $5 million to P. Its RAROC is 12%, so economic profit is $600,000 − $450,000 = $150,000.)