Evaluating Incremental Business With Marginal RAROC

Why Evaluate Business at the Margin?

A business unit can have an acceptable overall risk-adjusted return while a proposed policy or account fails to meet the return required for the capital it uses. Conversely, a proposal can improve the portfolio even when its return, calculated as a ratio, is difficult to interpret because it reduces required capital. The decision therefore concerns what the business adds or changes, not only the portfolio’s current or resulting average.

Marginal RAROC compares the change in risk-adjusted profit with the change in economic capital caused by a proposed decision. It is useful only when both changes are measured consistently and the capital change is positive. A hurdle comparison then provides a decision rule: does the added profit adequately compensate for the added capital?

Definition: Let $P_0$ and $K_0$ be the risk-adjusted profit and economic capital before a proposed change, and let $P_1$ and $K_1$ be the corresponding amounts after it. Define $\Delta P=P_1-P_0$ and $\Delta K=K_1-K_0$. When $\Delta K>0$, marginal RAROC is $\Delta P/\Delta K$. The profit and capital must use the same scope, measurement date, and decision horizon.

In this tutorial, $P$ is annual risk-adjusted profit before any capital charge: it is after expected losses and relevant expenses, and is measured on the same tax basis throughout a comparison. $K$ is economic capital on the matching basis. The hurdle rate $h$ is the required return on that capital. The examples use annual amounts in thousands of dollars unless stated otherwise.

The Incremental Decision Rule

If a proposal requires additional capital, its marginal RAROC should be compared with the hurdle rate—not merely with the existing portfolio’s RAROC. The equivalent test is whether the proposal increases economic profit, where economic profit is risk-adjusted profit less the required return on economic capital.

\operatorname{EP}=P-hK

The change in economic profit follows directly by subtracting the pre-decision amount from the post-decision amount:

\Delta\operatorname{EP} =(P_1-hK_1)-(P_0-hK_0) =(P_1-P_0)-h(K_1-K_0) =\Delta P-h\Delta K

When $\Delta K>0$, divide the economic-profit test by the positive quantity $\Delta K$. This gives $\Delta\operatorname{EP}>0$ exactly when $\Delta P/\Delta K>h$. Thus the marginal RAROC test and the incremental economic-profit test give the same accept-or-reject result under these conditions. Equality means the proposal exactly meets the hurdle; it creates no incremental economic profit.

Decision rule: If $\Delta K>0$, accept on this financial criterion when $\Delta P/\Delta K>h$, equivalently when $\Delta P-h\Delta K>0$. If $\Delta K=0$, the ratio is undefined and the change in economic profit is $\Delta P$. If $\Delta K<0$, use the economic-profit change directly; dividing by negative capital change reverses the inequality and does not produce the usual marginal return interpretation.

This result is an algebraic justification, not an assumption that every risk or strategic consideration is captured by a single rate. A decision-maker still needs a consistent profit measure, an appropriate capital estimate, and a hurdle suited to the decision. Marginal RAROC is a decision aid, not a substitute for those judgments.

Set the comparison basis.
Specify the decision horizon, profit definition, capital measure, and hurdle. Keep them consistent before and after the proposal.

Calculate the changes.
Find $\Delta P=P_1-P_0$ and $\Delta K=K_1-K_0$, including any effects the proposal has on the existing portfolio.

Apply the right test.
For positive $\Delta K$, compare $\Delta P/\Delta K$ with $h$. Otherwise, calculate $\Delta\operatorname{EP}=\Delta P-h\Delta K$ directly.

Check the interpretation.
Report whether incremental economic profit rises or falls, and do not use the combined portfolio’s average return as a substitute for the incremental test.

Worked Applications

Worked Example: A Policy That Clears the Hurdle

A hypothetical insurer has annual risk-adjusted profit of $120,000 and economic capital of $1,000,000. A proposed policy is expected to add $210,000 of premium, $130,000 of expected losses, and $44,000 of expenses. The policy requires $240,000 of additional capital. The annual hurdle rate is 12%. Should the insurer accept the policy on this criterion?

Method. Calculate incremental profit from the expected premium, losses, and expenses, then compare marginal RAROC with the hurdle. All figures are annual and on the same basis.

Incremental profit: $210-130-44=36$, so $\Delta P=\$36,000$. The incremental capital is $\Delta K=\$240,000$, or 240 in thousands.

Marginal RAROC: $36/240=0.15$, or 15.00%. Since $15.00\%>12.00\%$, the policy clears the hurdle.

Economic-profit check: The required return on the added capital is $0.12(240)=28.8$, or $28,800. Therefore, $\Delta\operatorname{EP}=36-28.8=7.2$, or $7,200. The proposal increases economic profit by $7,200.

After acceptance, profit is $120+36=156$, or $156,000, and capital is $1,000+240=1,240$, or $1,240,000. The combined portfolio RAROC is $156/1,240=0.125806$, or 12.58% to two decimal places. This is a check on the resulting portfolio, not the decision statistic: the proposal’s own marginal return is 15.00%.

Common mistake avoided: Comparing only the resulting 12.58% portfolio RAROC with the 12% hurdle would obscure how the policy itself performs. The incremental calculation identifies that the policy adds $7,200 of economic profit.

Worked Example: An Acceptable Portfolio With a Weak Addition

A hypothetical account portfolio currently has annual risk-adjusted profit of $200,000 and economic capital of $1,600,000. A new account is expected to add $160,000 of premium, $102,000 of expected losses, and $28,000 of expenses; it also requires $300,000 of additional capital. The hurdle is 11%. Evaluate the account and explain why the combined portfolio return is not the correct substitute.

Method. Compute the account’s incremental profit and capital, apply the marginal hurdle, and then compare with the combined result to identify the distinction.

Incremental profit: $160-102-28=30$, so $\Delta P=\$30,000$. Incremental capital is $\Delta K=\$300,000$.

Marginal RAROC: $30/300=0.10$, or 10.00%. This is below the 11.00% hurdle, so the account fails the criterion.

Economic-profit check: The capital charge at the hurdle is $0.11(300)=33$, or $33,000. Thus, $\Delta\operatorname{EP}=30-33=-3$, or negative $3,000.

The combined portfolio would have profit $200+30=230$, or $230,000, and capital $1,600+300=1,900$, or $1,900,000. Its RAROC is $230/1,900=0.1210526$, or 12.11% to two decimal places. Although 12.11% exceeds the 11% hurdle, the new account reduces economic profit by $3,000 relative to the hurdle. The existing portfolio’s strong return raises the combined average; it does not make the account’s incremental return acceptable.

Common mistake shown: The wrong decision is to accept because $230/1,900=12.11\%>11\%$. That calculation evaluates the whole portfolio, not the added account. The correction is $30/300=10.00\%<11.00\%$, so reject under the stated criterion.

Worked Example: A Proposal That Releases Capital

A hypothetical portfolio has annual risk-adjusted profit of $90,000 and economic capital of $800,000. A proposed change is expected to add $58,000 of revenue, $25,000 of expected losses, and $15,000 of expenses. The capital model indicates that total economic capital after the change will be $700,000. The hurdle is 12%. Evaluate the proposal.

Method. Calculate the change in profit and capital, then use incremental economic profit because the capital change is negative.

The change in profit is $58-25-15=18$, so $\Delta P=\$18,000$. The change in capital is $700-800=-100$, so $\Delta K=-\$100,000$.

The usual marginal RAROC ratio would be $18/(-100)=-18\%$. This negative ratio is not a meaningful return-on-additional-capital measure: the proposal releases capital rather than requiring it. The correct hurdle test is the change in economic profit:

\Delta\operatorname{EP} =18-0.12(-100) =18+12 =30

The proposal increases economic profit by $30,000. As a check, before the change, economic profit is $90-0.12(800)=90-96=-6$, or negative $6,000. After the change, it is $108-0.12(700)=108-84=24$, or $24,000. The increase is $24-(-6)=30$, or $30,000. The proposal therefore passes the stated criterion.

Common mistake avoided: Interpreting $-18\%$ as a return that must clear 12% would lead to rejection. The denominator is negative, so use $\Delta P-h\Delta K$ directly and verify it against the before-and-after economic-profit amounts.

Practical Checks and Common Traps

The calculations are short, but the decision can change if profit, capital, or timing is defined inconsistently. In practice, document the components used to determine the incremental amounts and make sure the capital estimate reflects the proposed business in the relevant portfolio, rather than assuming that standalone capital is automatically the capital change.

Using total instead of incremental amounts. The ratio $P_1/K_1$ is the combined portfolio’s RAROC. For a proposal requiring positive additional capital, the relevant ratio is $(P_1-P_0)/(K_1-K_0)$.
Charging capital twice. If $P$ is defined before the capital charge, use $P-hK$ to calculate economic profit. Do not first subtract the hurdle charge from profit and then subtract it again.
Mixing profit definitions. For example, comparing pretax incremental profit with an after-tax hurdle is not a like-for-like test. State and consistently apply the tax, expense, and expected-loss basis.
Mixing horizons. An annual profit change cannot be compared directly with a capital amount or hurdle defined for a different period without an appropriate conversion.
Treating a negative capital change as an ordinary denominator. If $\Delta K<0$, a negative ratio does not by itself mean the proposal destroys value. Assess $\Delta\operatorname{EP}$ directly.
Assuming a hurdle test captures every consideration. The test answers whether a proposal adds economic profit at the specified hurdle. It does not, by itself, resolve strategic, operational, or other constraints.

Key takeaway: For positive incremental capital, compare incremental profit per unit of incremental capital with the hurdle. For any sign of capital change, the general decision quantity is $\Delta P-h\Delta K$. This incremental economic-profit test keeps the decision focused on what the proposal changes.

The approach is aligned with the CAS Exam 9 (Risk Management for Actuaries) syllabus: identify a decision’s incremental profit and capital, apply the hurdle on a consistent basis, and interpret the result without confusing marginal performance with a portfolio average.

Check Your Understanding

For each problem, state whether the proposal clears the stated hurdle under the incremental criterion. Amounts are annual and in thousands of dollars unless noted.

A portfolio has profit of 84 and capital of 700. A proposed account adds profit of 18 and capital of 120. The hurdle is 14%. Calculate marginal RAROC and incremental economic profit. (Answer: Marginal RAROC is 15.00%; incremental economic profit is 1.2, so accept.)
A portfolio has profit of 150 and capital of 1,200. A proposed investment adds profit of 24 and capital of 240. The hurdle is 9%. Calculate the marginal return and the change in economic profit. (Answer: Marginal RAROC is 10.00%; incremental economic profit is 2.4, so accept.)
A proposed policy adds revenue of 96, expected losses of 62, expenses of 21, and capital of 125. The hurdle is 10%. Find incremental profit, marginal RAROC, and incremental economic profit. (Answer: Incremental profit is 13; marginal RAROC is 10.40%; incremental economic profit is 0.5, so accept.)
A proposal adds profit of 28 and capital of 350. The hurdle is 9%. Calculate the marginal RAROC and incremental economic profit, and state the decision. (Answer: Marginal RAROC is 8.00%; incremental economic profit is $-3.5$, so reject.)
A portfolio has profit of 70 and capital of 500. A change adds profit of 12 but reduces total capital by 50. The hurdle is 11%. Calculate the change in economic profit and explain whether the usual marginal RAROC ratio is suitable. (Answer: Incremental economic profit is $12-0.11(-50)=17.5$, so accept; the usual ratio is not a meaningful return-on-additional-capital measure because incremental capital is negative.)

What You'll Learn