FRM Exam Part II · Risk Capital Attribution and Risk-Adjusted Performance Measurement

RAROC and Risk-Adjusted Performance Measures Explained

Updated 11 October 2026 · Fact-checked

RAROC (risk-adjusted return on capital) equals risk-adjusted income divided by economic capital. Risk-adjusted income is revenue minus costs minus expected loss. You compare RAROC with a hurdle rate, usually the cost of equity. If RAROC is above the hurdle, the unit creates value. RORAC adjusts the denominator instead.

Understand RAROC and Risk-Adjusted Performance Measures

A raw profit number ignores risk. A desk earning ₹50 crore with a huge tail risk is not better than a desk earning ₹40 crore with little risk. Risk-adjusted performance measures fix this by relating return to the risk taken.

RAROC is the main bank measure. The numerator is income after removing the average cost of risk: revenues, less operating costs, less expected loss (EL). EL is a normal cost of doing business, so it is deducted from income. The denominator is economic capital, the buffer held for unexpected loss at a chosen confidence level. Many versions also add the return earned on the capital (for example, a risk-free rate on the capital held) and subtract taxes. Read the question to see which items it includes.

RORAC (return on risk-adjusted capital) keeps the numerator as ordinary net income and puts the risk adjustment in the denominator, using risk capital. The key difference: RAROC adjusts the numerator for expected loss and divides by economic capital. RORAC does not adjust the return for risk and uses risk capital as the base. In practice the two names are often blurred, so follow the formula given in the question.

A RAROC number means little alone. You compare it with a hurdle rate, usually the shareholders' required return (cost of equity). RAROC above the hurdle means the unit earns more than the cost of the capital it uses. Below it, the unit destroys value. Economic value added follows the same idea in money terms: risk-adjusted income minus hurdle × capital.

Other measures use total or market risk in the denominator. The Sharpe ratio = (portfolio return − risk-free rate) ÷ standard deviation of return. It suits whole portfolios. The Treynor ratio uses beta instead, and Jensen's alpha measures return above CAPM. The information ratio uses active return over tracking error. Choose the measure that matches the risk the investor actually bears.

Key formulas to remember

RAROC: RAROC = (Revenue − Costs − Expected Loss) ÷ Economic Capital; Some versions add return on capital and subtract tax. Use the items the question lists.
RORAC: RORAC = Net Income ÷ Risk Capital; Risk adjustment is in the denominator only.
Hurdle test: RAROC > hurdle rate → creates value; Hurdle is usually the cost of equity.
Economic value added (risk-adjusted): EVA = Risk-adjusted income − hurdle rate × Economic Capital; Positive EVA is the same signal as RAROC above hurdle.
Sharpe ratio: Sharpe = (Rp − Rf) ÷ σp; Total risk. Best for a whole portfolio.
Treynor ratio: Treynor = (Rp − Rf) ÷ βp; Systematic risk only.
Jensen's alpha: α = Rp − [Rf + β(Rm − Rf)]; Return above the CAPM-required return.
Information ratio: IR = (Rp − Rb) ÷ Tracking error; Active return per unit of active risk.

How to solve RAROC and Risk-Adjusted Performance Measures questions

Use this order for any RAROC or performance-measure question.

1Identify which measure is asked: RAROC, RORAC, Sharpe, Treynor, alpha or information ratio.
2List the inputs given and note which are income items and which are capital or risk items.
3For RAROC, subtract costs and expected loss from revenue. Add capital benefit or subtract tax only if stated.
4Divide by economic capital (RAROC) or risk capital (RORAC). Check units and that rates are in the same period.
5For portfolio ratios, compute excess return over the risk-free rate first, then divide by the right risk measure.
6Compare the result with the hurdle rate or with the other options.
7State the interpretation: value creating or destroying, or which investment is better per unit of risk.
8Check that the answer is sensible, for example not mixing a 99.9% capital figure with a different confidence level.

Quickest way: Numerator first, then divide

When to use it: Numeric multiple-choice questions with all inputs given.

Write numerator = revenue − costs − EL on the page.
Divide by capital as a percentage.
Compare with the hurdle and eliminate options on the wrong side of it.
For ranking, compute each ratio and pick the highest.

Common mistakes in RAROC and Risk-Adjusted Performance Measures

Forgetting to subtract expected loss in RAROC.
Students treat EL as capital rather than a cost.
Fix: EL is a cost in the numerator. Capital covers unexpected loss.
Treating RORAC and RAROC as identical.
The names sound alike and textbooks blur them.
Fix: RAROC adjusts the numerator for EL and uses economic capital. RORAC uses unadjusted income over risk capital.
Using total standard deviation in the Treynor ratio or beta in the Sharpe ratio.
The formulas look similar.
Fix: Sharpe uses σ. Treynor uses β.
Comparing RAROC with the risk-free rate.
Confusing the Sharpe benchmark with the hurdle.
Fix: The RAROC benchmark is the hurdle rate, normally the cost of equity.
Forgetting to subtract the risk-free rate in excess return.
Rushing to use the headline return.
Fix: Always compute Rp − Rf before dividing.

Worked examples

Example 1

A corporate lending unit has revenue of $120 million, operating costs of $45 million and expected loss of $15 million. Economic capital is $300 million. The cost of equity (hurdle) is 12%. Compute RAROC and say whether the unit creates value.

Show the solution

Risk-adjusted income = 120 − 45 − 15 = $60 million.
RAROC = 60 ÷ 300 = 20%.
Compare with the 12% hurdle: 20% > 12%.
EVA = 60 − 0.12 × 300 = 60 − 36 = $24 million.

Answer: RAROC is 20%, above the 12% hurdle, so the unit creates value (EVA $24 million).

Example 2

Fund A returned 14% with volatility 20% and beta 1.2. Fund B returned 11% with volatility 10% and beta 0.8. The risk-free rate is 3%. Which fund has the higher Sharpe ratio, and what are the values?

Show the solution

Fund A: excess return = 14% − 3% = 11%. Sharpe = 11 ÷ 20 = 0.55.
Fund B: excess return = 11% − 3% = 8%. Sharpe = 8 ÷ 10 = 0.80.
0.80 > 0.55, so Fund B earns more excess return per unit of total risk.

Answer: Fund B is better: Sharpe 0.80 versus 0.55 for Fund A.

Exam tips

Read whether the question gives risk capital or economic capital and whether tax or capital return must be included.
Expect interpretation questions: RAROC above or below hurdle, and what to do with the business line.
When ranking funds, check whether the question implies total risk (Sharpe) or systematic risk (Treynor).
Do the numerator carefully. Most lost marks come from missing EL or costs.

Practice questions from Risk Capital Attribution and Risk-Adjusted Performance Measurement

RAROC and Risk-Adjusted Performance Measures: frequently asked questions

How do I calculate RAROC for FRM Part II?

Subtract operating costs and expected loss from revenue, then divide by economic capital. Add any capital benefit or subtract tax only if the question includes them. Compare the result with the hurdle rate.

What is the difference between RAROC and RORAC?

RAROC adjusts income for expected loss and divides by economic capital. RORAC uses unadjusted net income and divides by risk capital. Follow the definition in the question.

Why is expected loss deducted in RAROC?

Expected loss is an average, predictable cost of lending. Capital is held for unexpected loss, so EL is charged against income instead.

What hurdle rate do I use?

Usually the cost of equity, the return shareholders require. If the question gives a hurdle, use that.