FRM Exam Part II · Capital Structure in Banks

Economic Capital and Capital Allocation Using RAROC

Updated 11 October 2026 · Fact-checked

Economic capital is the buffer a bank's own model says it needs to absorb unexpected losses at a chosen confidence level. Banks allocate it to business lines and compute RAROC = risk-adjusted return ÷ economic capital. Compare RAROC with the hurdle rate: above it, the unit adds value.

Understand Economic Capital and Capital Allocation

Economic capital is the amount of capital a bank needs to survive unexpected losses over a set horizon, usually one year, at a chosen confidence level. The bank sets that level from its target credit rating. A bank aiming for a strong rating may choose 99.97% or 99.99%.

For credit risk, you start with the loss distribution of the portfolio. Expected loss (EL) is the average loss. It is a cost of doing business and is covered by pricing and provisions. Economic capital covers the unexpected loss: the credit VaR at the confidence level minus EL. So economic capital = credit VaR − EL.

Regulatory capital is the minimum set by supervisors under Basel rules. It uses prescribed formulas and one set of rules for all banks. Economic capital is internal, risk-sensitive and reflects the bank's own portfolio, concentrations and diversification. The two often differ. Banks must hold at least the regulatory minimum, whatever the internal figure says.

Capital allocation spreads total economic capital across business lines, so each unit is judged on the risk it takes. Stand-alone capital for a unit ignores diversification. Because of diversification, the sum of stand-alone capitals exceeds the bank's total. Methods such as marginal or component (contribution) capital split the diversified total. Contributions add up to the total.

RAROC (risk-adjusted return on capital) then measures performance. Revenue is reduced by costs and by expected loss, so the return is risk-adjusted. Divide by economic capital. If RAROC exceeds the hurdle rate (the shareholders' required return, linked to the cost of equity), the unit creates value.

Key formulas to remember

Economic capital (credit): Economic capital = Credit VaR (at confidence level) − Expected loss; Covers unexpected loss only. Expected loss is covered by pricing and provisions.
Expected loss: EL = PD × LGD × EAD; Use the same horizon for PD, usually one year.
RAROC: RAROC = (Revenues − Costs − Expected loss + Return on economic capital) ÷ Economic capital; The return on capital term is optional. Many questions omit it. Use only the items the question gives.
Simple RAROC: RAROC = (Revenue − Costs − Expected loss) ÷ Economic capital; Compare the result with the hurdle rate.
Value-creation test: RAROC > hurdle rate → adds shareholder value; Equal to the hurdle rate means break-even.
Diversification effect: Σ stand-alone capital ≥ diversified total capital; Holds when correlations are below 1. The gap is the diversification benefit.

How to solve Economic Capital and Capital Allocation questions

Use this order for any economic capital or RAROC question. It keeps expected and unexpected loss apart.

1Read what is asked: economic capital, RAROC, allocation or comparison with regulatory capital.
2Compute expected loss as PD × LGD × EAD if it is not given.
3Find economic capital as credit VaR at the stated confidence level minus EL. If the capital figure is already given, use it directly.
4Build the numerator: revenue minus costs minus expected loss, adding any capital benefit only if the question includes it.
5Divide the numerator by economic capital to get RAROC.
6Compare RAROC with the hurdle rate and state whether the unit adds value.
7For allocation questions, use contributions that sum to the diversified total, not stand-alone figures.
8Check units, confidence level and horizon before choosing an option.

Quickest way: Three-line RAROC check

When to use it: Use when the question gives revenue, costs, EL and capital as numbers and asks for RAROC or a ranking of units.

Numerator = revenue − costs − EL. Do this first.
Divide by capital. Write it as a percentage.
Compare with the hurdle rate. Rank units by RAROC, but remember that the highest RAROC is not always the best use of capital if the hurdle is met by several units.

Common mistakes in Economic Capital and Capital Allocation

Using credit VaR as economic capital without subtracting expected loss.
Students treat the whole tail loss as the capital need.
Fix: Economic capital = credit VaR − EL, when the question defines it that way. Expected loss is handled through pricing and provisions.
Forgetting to deduct expected loss in the RAROC numerator.
Revenue minus costs looks like a complete profit figure.
Fix: RAROC is risk-adjusted, so expected loss always comes out of the return.
Treating economic capital and regulatory capital as the same.
Both are called capital and both cover credit losses.
Fix: Regulatory capital is a supervisory minimum from Basel rules. Economic capital is the bank's internal, risk-sensitive estimate. Keep them separate.
Allocating stand-alone capital and expecting it to sum to the bank total.
Students ignore diversification.
Fix: Stand-alone capitals sum to more than the diversified total. Use marginal or component contributions for a sum that matches.
Comparing RAROC with the wrong benchmark.
Students compare it with a risk-free rate or a market return.
Fix: Compare RAROC with the hurdle rate, which reflects the cost of equity.
Mixing confidence levels or horizons.
Options quote 99% and 99.97% figures close together.
Fix: Use the confidence level and horizon stated in the question. A higher confidence level gives higher capital.

Worked examples

Example 1

A bank's corporate loan portfolio has credit VaR of ₹950 crore at 99.9% over one year. PD = 2%, LGD = 40%, EAD = ₹5,000 crore. Find expected loss and economic capital.

Show the solution

EL = PD × LGD × EAD = 0.02 × 0.40 × 5,000.
0.02 × 0.40 = 0.008.
0.008 × 5,000 = ₹40 crore.
Economic capital = credit VaR − EL = 950 − 40 = ₹910 crore.

Answer: Expected loss is ₹40 crore and economic capital is ₹910 crore.

Example 2

A business unit earns revenue of $120 million, has costs of $70 million and expected loss of $20 million. Its economic capital is $200 million. The hurdle rate is 12%. Find RAROC and say whether the unit adds value.

Show the solution

Numerator = revenue − costs − EL = 120 − 70 − 20 = $30 million.
RAROC = 30 ÷ 200 = 0.15, or 15%.
Compare: 15% > 12% hurdle rate.

Answer: RAROC is 15%, above the 12% hurdle rate, so the unit adds shareholder value.

Exam tips

Look for whether the question gives credit VaR or unexpected loss. This decides if you subtract EL.
Always check that expected loss is deducted in the RAROC numerator.
When asked why a unit's allocated capital is lower than its stand-alone capital, answer diversification.
In definition questions, link economic capital to the bank's target rating and confidence level, and regulatory capital to supervisory minimums.
Do the arithmetic in the same units throughout. Mixed millions and crores cause lost marks.

Practice questions from Capital Structure in Banks

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?

Regulatory capital is the minimum set by supervisors under Basel rules using prescribed formulas. Economic capital is the bank's internal estimate of capital needed to absorb unexpected losses at a chosen confidence level. Banks must meet the regulatory minimum regardless of their internal figure.

How do I calculate RAROC for the FRM exam?

Take revenue, subtract costs and expected loss, then divide by economic capital. Compare the result with the hurdle rate. Use only the items the question provides.

Why is expected loss not part of economic capital?

Expected loss is predictable and is covered by pricing and provisions. Economic capital is held against unexpected loss, the deviation above the average. It is usually credit VaR minus expected loss.

Why does capital allocation need diversification?

Business lines do not all lose at once, so the bank's total capital is less than the sum of stand-alone capitals. Allocation methods such as marginal or component contributions split the diversified total so that the parts add up.