Skip to content

FRM Exam Part II · Integrated Risk Management

Economic Capital and Capital Allocation for FRM Part II

Updated 11 October 2026 · Fact-checked

Economic capital is the capital a bank needs to absorb unexpected losses at a chosen confidence level over a set horizon, found as loss quantile minus expected loss. You allocate it to business units by their risk contribution. RAROC = risk-adjusted return ÷ economic capital, compared with a hurdle rate.

Understand Economic Capital and Capital Allocation

Economic capital is the bank's own estimate of the capital it needs to stay solvent. It covers unexpected loss (UL) at a chosen confidence level and time horizon, usually one year. The confidence level is often tied to a target credit rating. For example, a 99.97% level is often linked to an AA-type rating.

Expected loss is not covered by capital. It is a cost of doing business, priced into loans and covered by provisions. Capital is the buffer for losses above that. So economic capital = loss quantile at the confidence level − expected loss. Some banks also add a view of the total loss distribution across market, credit, operational and other risks.

Regulatory capital is the minimum set by supervisors under Basel rules, using prescribed formulas or approved models. Economic capital is internal and risk-sensitive, and it can be higher or lower than the regulatory figure. Banks use it for pricing, limit setting and performance measurement. Regulators still require regulatory capital to be met.

Diversification means the sum of stand-alone capital for each unit is larger than the capital for the whole bank. Capital allocation (attribution) splits the bank-level figure back to units. Common methods are stand-alone, incremental and marginal/component contribution. Only component (covariance-based) contributions add up exactly to the total.

RAROC (risk-adjusted return on capital) measures return per unit of economic capital. Risk-adjusted return is revenue minus costs minus expected loss, often plus the return earned on the capital. A unit creates value if RAROC exceeds the hurdle rate, which is the shareholders' required return.

Key formulas to remember

Economic capital
EC = Loss quantile at confidence level − Expected loss (UL at that level)
Horizon is usually one year. Capital covers unexpected loss, not expected loss.
RAROC
RAROC = (Revenue − Costs − Expected loss + Return on capital) ÷ Economic capital
Use the version the question gives. Some versions omit the return on capital.
Value-creation test
Create value if RAROC > hurdle rate
Hurdle rate is the shareholders' required return on equity.
Portfolio standard deviation of two units
σp = √(σ1² + σ2² + 2ρσ1σ2)
Used when capital is approximated by a multiple of loss standard deviation.
Component (covariance) contribution
Contribution of unit i = wi × Cov(Li, Lp) ÷ σp, scaled by the capital multiple
Contributions sum to total capital. Stand-alone figures do not.
Diversification benefit
Benefit = Σ stand-alone EC − Bank-level EC
Positive when correlation between units is below 1.
Economic profit (EVA-style)
Economic profit = Risk-adjusted return − (Hurdle rate × Economic capital)
Positive economic profit matches RAROC above the hurdle.

How to solve Economic Capital and Capital Allocation questions

Use this order for most questions on economic capital, allocation and RAROC.

  1. 1Identify what is asked: economic capital, an allocation, RAROC, or a comparison with regulatory capital.
  2. 2Write down the confidence level, horizon and loss figures. Separate expected loss from the quantile.
  3. 3Compute economic capital as quantile minus expected loss, unless the question gives unexpected loss directly.
  4. 4For allocation, check which method is used. Stand-alone ignores diversification. Incremental measures the change from adding the unit. Component uses covariance and sums to the total.
  5. 5Build risk-adjusted return: revenue less costs less expected loss, plus capital benefit only if the formula includes it.
  6. 6Divide by economic capital to get RAROC, then compare it with the hurdle rate.
  7. 7Interpret the result in words: value created or destroyed, and what decision follows (price, grow, cut or reallocate).
  8. 8Check units, the horizon and whether the answer is a percentage or a currency amount.

Quickest way: Four-line shortcut for RAROC questions

When to use it: Use it when the question gives revenue, cost, expected loss and capital and asks for RAROC or a decision.

  1. Compute numerator: revenue − costs − expected loss (add capital return only if told).
  2. Divide by the capital figure given. If only quantile is given, subtract expected loss first.
  3. Compare with the hurdle rate: higher means value creation.
  4. Scan options for the trap: a figure using total loss instead of unexpected loss, or one ignoring expected loss.

Common mistakes in Economic Capital and Capital Allocation

  • Treating economic capital as the full loss quantile

    Students remember VaR as the capital figure and skip the expected loss step.

    Fix: Subtract expected loss from the quantile. Capital covers unexpected loss only.

  • Forgetting to deduct expected loss in RAROC

    Revenue minus cost looks like a complete return figure.

    Fix: Always deduct expected loss in the numerator. It is the cost of credit and other losses.

  • Assuming stand-alone capital sums to bank capital

    Adding unit figures is easy and looks natural.

    Fix: Remember diversification. The sum of stand-alone capital is above bank-level capital when correlation is below 1. Only component contributions add up exactly.

  • Confusing economic and regulatory capital

    Both are called capital requirements and both rely on loss distributions.

    Fix: Regulatory capital is the supervisory minimum from Basel rules. Economic capital is an internal estimate used for management. They can differ in either direction.

  • Reading a high RAROC as automatically good

    Students compare RAROC across units without the hurdle rate or risk of mismeasured capital.

    Fix: Compare with the hurdle rate and check the capital estimate. A high RAROC may reflect understated capital.

  • Using a different confidence level or horizon from the question

    Students plug in familiar values such as 99% or ten days.

    Fix: Use the confidence level and horizon stated. Economic capital is usually one year and often at a much higher level than regulatory VaR.

Worked examples

Example 1

A bank's one-year credit loss distribution has a 99.9% quantile of ₹850 crore and an expected loss of ₹150 crore. The business earns revenue of ₹260 crore, has costs of ₹90 crore, and the expected loss above applies. The hurdle rate is 15%. Compute economic capital, RAROC (ignore return on capital) and say whether the unit creates value.

Show the solution
  1. Economic capital = 850 − 150 = ₹700 crore.
  2. Risk-adjusted return = 260 − 90 − 150 = ₹20 crore.
  3. RAROC = 20 ÷ 700 = 2.86%.
  4. Compare with the hurdle: 2.86% is below 15%.

Answer: Economic capital is ₹700 crore, RAROC is about 2.86%, below the 15% hurdle, so the unit destroys shareholder value on these figures.

Example 2

A bank has two units. Unit A has stand-alone economic capital of USD 60 million and Unit B has USD 80 million. Their losses are correlated at 0.5. Treating capital as proportional to loss standard deviation, what is bank-level capital and the diversification benefit?

Show the solution
  1. Capital scales with standard deviation, so use the portfolio formula on the capital figures.
  2. Bank EC = √(60² + 80² + 2 × 0.5 × 60 × 80).
  3. 60² = 3,600. 80² = 6,400. 2 × 0.5 × 60 × 80 = 4,800.
  4. Sum = 3,600 + 6,400 + 4,800 = 14,800. √14,800 ≈ 121.65.
  5. Sum of stand-alone = 60 + 80 = 140.
  6. Diversification benefit = 140 − 121.65 = 18.35.

Answer: Bank-level economic capital is about USD 121.65 million, giving a diversification benefit of about USD 18.35 million.

Exam tips

  • Read whether the question gives the loss quantile or the unexpected loss. This decides whether you subtract expected loss.
  • Check the RAROC definition in the question stem. Include return on capital only when stated.
  • For allocation questions, ask whether the answer must sum to the total. If yes, component contribution is the method.
  • Be ready to state two or three differences between economic and regulatory capital in words.
  • Always compare RAROC with the hurdle rate before choosing the answer about value creation.

Practice questions from Integrated Risk Management

Economic Capital and Capital Allocation in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Economic Capital and Capital Allocation: frequently asked questions

What is the difference between economic capital and regulatory capital?

Economic capital is the bank's internal estimate of capital needed to cover unexpected losses at its chosen confidence level. Regulatory capital is the minimum required by supervisors under Basel rules. The two can differ, and banks use economic capital for pricing and performance measurement.

What is the RAROC formula?

RAROC = risk-adjusted return ÷ economic capital. Risk-adjusted return is revenue minus costs minus expected loss, sometimes plus the return earned on the capital. Compare the result with the hurdle rate.

How do you allocate economic capital to business units?

Common methods are stand-alone, incremental and component (marginal) contribution. Stand-alone ignores diversification. Component contribution uses each unit's covariance with the total portfolio loss and sums exactly to bank-level capital.

Why is expected loss excluded from economic capital?

Expected loss is a predictable cost, covered by pricing and provisions. Capital is held to absorb losses above that level, which are the unexpected losses.