Integrated Business-Line Capital Decision Workshop

Putting the Decision Together

A business-line proposal can look attractive on one measure and still be unsuitable to accept. Its expected contribution may exceed the return required on its capital, for example, while the amount of capital it consumes exceeds the organization’s available capacity. A defensible decision therefore combines the proposed price, expected losses, expenses, allocated capital, a return hurdle, and any binding capital limit.

The calculations below use a consistent one-year, pre-tax basis. Premiums, expected losses, expenses, contributions, and capital are stated in dollars or thousands of dollars as indicated. Unless stated otherwise, investment income and other revenue are excluded; if they are relevant, they must be included consistently in the contribution measure. All products and figures are hypothetical.

Definition: Let $P$ be annual premium, $E[L]$ expected annual losses, and $e$ annual expenses. Define the expected annual contribution as $N=P-E[L]-e$. Let $K>0$ be the economic capital allocated to the business, $h$ the required annual return on capital, and $K_{\max}$ the capital available for the decision. Then $\operatorname{RAROC}=N/K$, economic profit is $\operatorname{EP}=N-hK$, and the proposal satisfies the capital constraint if $K\leq K_{\max}$.

RAROC is a return ratio; economic profit is a dollar amount. Both use the same contribution and capital basis here. A proposal meets the return hurdle when its RAROC is at least $h$, or, equivalently, when its economic profit is nonnegative. That comparison alone does not establish that the proposal is feasible under a separate capital limit.

Why the Return Test and Capacity Test Are Separate

For positive allocated capital, the relationship between RAROC and economic profit follows directly from their definitions:

\operatorname{EP}=N-hK =K\left(\frac{N}{K}-h\right) =K(\operatorname{RAROC}-h).

Since $K>0$, economic profit is nonnegative exactly when $\operatorname{RAROC}\geq h$. This establishes equivalence between the two return-hurdle tests, not between either test and capital feasibility. Feasibility is a distinct inequality, $K\leq K_{\max}$. A proposal can pass the return test and fail the capacity test.

Decision rule: First calculate contribution and allocated capital on a consistent basis. Then test both the return hurdle and the capital limit. A proposal that fails either required condition is not an acceptable use of capacity unless the decision-maker explicitly changes the hurdle, the available capacity, or the proposal.

Worked Decision Process

Calculate contribution.
Subtract expected losses and expenses from the proposed premium, ensuring that all amounts cover the same period and business scope.

Assess return.
Divide contribution by allocated capital for RAROC, or subtract the hurdle charge $hK$ for economic profit.

Assess feasibility.
Compare required capital with the capital limit. Do not infer feasibility from a passing RAROC.

Recommend an action.
State whether to accept, reject, defer, or reprice, and identify the calculation or constraint that drives the recommendation.

Worked Example: Evaluating One Proposed Book

A hypothetical insurer considers a one-year book with premium of $1,200,000, expected losses of $720,000, and expenses of $180,000. The allocated capital is $2,500,000, the RAROC hurdle is 10%, and up to $2,600,000 of capital is available. Calculate the contribution, RAROC, and economic profit, and recommend whether the proposal meets both tests.

Method. Calculate the annual contribution first, then use the same contribution for both return measures.

Contribution is $N=\$1{,}200{,}000-\$720{,}000-\$180{,}000=\$300{,}000$. The RAROC is $\$300{,}000/\$2{,}500{,}000=0.12=12\%$.

The hurdle charge is $0.10\times \$2{,}500{,}000=\$250{,}000$. Therefore, economic profit is $\$300{,}000-\$250{,}000=\$50{,}000$. The capital test is also satisfied because $\$2{,}500{,}000\leq \$2{,}600{,}000$.

Recommendation. The book passes the 10% return hurdle and fits within available capital. The calculation checks: $12\%-10\%=2\%$, and $2\%\times \$2{,}500{,}000=\$50{,}000$, equal to the economic profit found directly.

Common mistake avoided. A RAROC above the hurdle does not, by itself, prove feasibility. Here both tests pass, but the capacity comparison is a separate calculation that must be shown.

Comparing Proposals Under a Capital Limit

When proposals compete for scarce capacity, compare their economics without overlooking feasibility. The return hurdle indicates whether expected contribution compensates for allocated capital at the required rate. The capacity limit determines whether the organization can undertake the proposal now. If only one proposal may be chosen, the decision should also recognize that accepting one may use capacity that could support another.

Worked Example: Two Proposals and a Binding Capital Limit

A hypothetical insurer must choose between two mutually exclusive one-year proposals. Proposal A has premium of $1,500,000, expected losses of $950,000, expenses of $190,000, and allocated capital of $3,000,000. Proposal B has premium of $1,280,000, expected losses of $800,000, expenses of $170,000, and allocated capital of $2,400,000. The hurdle is 10%, and only $2,500,000 of capital is available. Calculate each proposal’s contribution, RAROC, economic profit, and feasibility.

Method. Calculate each proposal independently, then apply the hurdle and capacity tests separately.

For A, contribution is $\$1{,}500{,}000-\$950{,}000-\$190{,}000=\$360{,}000$. Its RAROC is $\$360{,}000/\$3{,}000{,}000=12\%$. Its hurdle charge is $0.10\times \$3{,}000{,}000=\$300{,}000$, so its economic profit is $\$360{,}000-\$300{,}000=\$60{,}000$. A passes the return hurdle, but it is not feasible: $\$3{,}000{,}000>\$2{,}500{,}000$.

For B, contribution is $\$1{,}280{,}000-\$800{,}000-\$170{,}000=\$310{,}000$. Its RAROC is $\$310{,}000/\$2{,}400{,}000=0.1291667$, or 12.92% to two decimal places. Its hurdle charge is $0.10\times \$2{,}400{,}000=\$240{,}000$, so its economic profit is $\$310{,}000-\$240{,}000=\$70{,}000$. B passes the return hurdle and is feasible because $\$2{,}400{,}000\leq \$2{,}500{,}000$.

Recommendation. Both proposals meet the hurdle, but only B satisfies the capital limit. B is the defensible choice among these alternatives, and it also has the higher economic profit: $70,000 versus A’s $60,000.

Common mistake and correction. The incorrect conclusion is “both are feasible because both have RAROC above 10%.” That calculation confuses the return test with the capacity test. A requires $3,000,000, which exceeds the $2,500,000 limit; only B is feasible.

Pricing to Meet a Return Hurdle

The same decision framework can identify a minimum premium consistent with a required return. With expected losses, expenses, capital, and hurdle fixed, the proposal meets the hurdle when $P-E[L]-e\geq hK$. Rearranging gives the minimum premium:

P_{\min}=E[L]+e+hK.

This is a one-period expected-value calculation under the stated assumptions. It does not guarantee that actual losses will equal expected losses, and it does not replace any separate capital-capacity test. If the inputs change, the price threshold must be recalculated.

Worked Example: Repricing a Quote That Misses the Hurdle

A hypothetical insurer quotes $920,000 for a one-year book. Expected losses are $600,000, expenses are $160,000, allocated capital is $1,500,000, the hurdle is 12%, and the capital limit is $1,600,000. Determine whether the quote meets the hurdle, calculate the minimum premium, and assess a revised quote of $960,000.

Method. First calculate contribution and return at the original quote. Then solve the hurdle inequality for premium and check the revised quote and capital limit.

At $920,000, contribution is $\$920{,}000-\$600{,}000-\$160{,}000=\$160{,}000$. RAROC is $\$160{,}000/\$1{,}500{,}000=10.6667\%$, or 10.67% to two decimal places. The hurdle charge is $0.12\times \$1{,}500{,}000=\$180{,}000$. Thus, economic profit is $\$160{,}000-\$180{,}000=-\$20{,}000$, so the original quote fails the hurdle.

The minimum premium is $\$600{,}000+\$160{,}000+\$180{,}000=\$940{,}000$. At the revised $960,000 quote, contribution is $\$960{,}000-\$600{,}000-\$160{,}000=\$200{,}000$. RAROC is $\$200{,}000/\$1{,}500{,}000=13.3333\%$, or 13.33% to two decimal places, and economic profit is $\$200{,}000-\$180{,}000=\$20{,}000$. The capital test passes because $\$1{,}500{,}000\leq \$1{,}600{,}000$.

Recommendation. The original quote should not be accepted on the stated assumptions. A premium of at least $940,000 meets the hurdle; the revised $960,000 quote meets both the return and capital tests. As a check, its contribution exceeds the hurdle charge by exactly $20,000.

Common mistake avoided. Comparing the $920,000 premium directly with the hurdle charge would mix revenue with required profit. The required contribution is $180,000, so expected losses and expenses must also be covered: the minimum premium is $600,000+$160,000+$180,000, not merely $180,000.

Interpreting the Recommendation

These calculations support a decision only to the extent that their inputs and scope match the business being considered. In particular:

Keep the time basis consistent. Annual premium, expected losses, expenses, hurdle rate, and capital-return interpretation must refer to compatible periods.
Use the contribution actually intended by the decision rule. If the organization’s measure includes additional revenue or costs, include them consistently rather than silently omitting them.
Use the relevant capital amount. A business line’s allocated capital is not automatically the same as the organization’s remaining capital capacity.
State feasibility explicitly. Passing the hurdle does not remove a binding capital constraint. A proposal that exceeds the limit may need to be reduced, restructured, deferred, or declined.
Describe uncertainty honestly. Expected losses and allocated capital are estimates. A positive expected economic profit is not a guarantee of a positive realized result.

If assumptions change, the conclusion may change. For instance, higher expected losses reduce contribution dollar for dollar unless price or another component changes. Higher allocated capital increases the hurdle charge $hK$, and may also cause the proposal to breach the capital limit. A sound recommendation therefore reports the decisive calculations and the assumptions on which they depend, rather than presenting a RAROC figure in isolation.

Key takeaway: A complete business-line capital decision combines three distinct questions: What is expected contribution after losses and expenses? Does that contribution meet the required return on allocated capital? Does the capital requirement fit within available capacity? Answer all three before recommending acceptance.

Check Your Understanding

For each hypothetical one-year proposal, calculate the requested measures and apply both the return hurdle and capital limit. Amounts are in dollars unless stated otherwise.

A proposal has premium $780,000, expected losses $510,000, expenses $120,000, allocated capital $1,100,000, hurdle 11%, and available capital $1,200,000. What are its contribution, RAROC, and economic profit, and does it pass both tests? (Answer: Contribution $150,000; RAROC 13.6364%; economic profit $29,000; it passes the hurdle and capital limit.)
Two mutually exclusive proposals have the following figures: A has contribution $270,000 and capital $2,400,000; B has contribution $250,000 and capital $2,000,000. The hurdle is 10%, and available capital is $2,100,000. Which proposal is feasible, and what is the economic profit of each? (Answer: A has economic profit $30,000 but is infeasible because $2,400,000 exceeds the limit; B has economic profit $50,000 and is feasible.)
A hypothetical quote has expected losses $430,000, expenses $90,000, allocated capital $800,000, hurdle 9.5%, and proposed premium $590,000. Calculate the minimum premium and the economic profit at the proposed premium. (Answer: Minimum premium $596,000; proposed contribution $70,000; economic profit $-\$6,000$, so the quote misses the hurdle by $6,000.)
A business has contribution $240,000, allocated capital $2,200,000, hurdle 10.5%, and available capital $2,000,000. Calculate RAROC and economic profit, then state whether it is acceptable under both tests. (Answer: RAROC 10.9091%; economic profit $9,000; it passes the hurdle but is infeasible because $2,200,000 exceeds the $2,000,000 limit.)
A proposal has premium $1,050,000, expected losses $640,000, expenses $170,000, allocated capital $2,000,000, hurdle 12%, and available capital $2,100,000. Calculate the minimum premium, RAROC, and economic profit at the proposed price. (Answer: Minimum premium $1,050,000; contribution $240,000; RAROC 12%; economic profit $0; it exactly meets the hurdle and passes the capital limit.)

What You'll Learn