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CFA Level II Exam · Measuring and Managing Market Risk

Risk Limits and Capital Allocation: Risk Budgeting, RAROC and Sharpe

Updated 7 October 2026 · Fact-checked

Risk limits and capital allocation is the process of setting how much risk each desk, manager or position may take, then assigning capital to the units that earn the best return per unit of risk. You solve questions by finding the risk measure, computing a ratio such as RAROC or Sharpe, and ranking the units.

Understand Risk Limits and Capital Allocation

Every firm has limited capital and limited ability to bear losses. Risk budgeting decides how total risk is split across business units, asset classes or managers. The budget is usually set with a risk measure such as VaR, tracking error or standard deviation. The sum of the parts rarely equals the total, because diversification lowers the combined risk.

Risk limits turn the budget into rules. Common limits include position limits (maximum size in one security or issuer), VaR limits, stop-loss limits (a loss level that forces a review or exit), scenario or stress limits, and leverage limits. Limits give early warning and stop one unit from taking an outsized bet. Too many tight limits can reduce returns and encourage gaming, so they must fit the strategy.

Capital allocation then asks which units earn enough for the risk they use. Raw profit is misleading, because a desk can make more simply by taking more risk. Risk-adjusted measures fix this by dividing return by a risk measure.

The Sharpe ratio divides excess return over the risk-free rate by total standard deviation. It suits a whole portfolio. RAROC (risk-adjusted return on capital) divides risk-adjusted expected return by economic capital, which is the capital held against unexpected loss, often tied to VaR. A unit is attractive if its RAROC exceeds the firm's hurdle rate, which is often the cost of equity.

In an item set, you are given a table of units with returns, costs, expected losses and capital or volatility. Your job is to pick the right numerator and denominator, compute them, and state what the result implies for limits or capital.

Key formulas to remember

RAROC
RAROC = (Revenue − Costs − Expected loss + Return on economic capital) ÷ Economic capital
Exact numerator varies by vignette. Always use what the vignette defines. Expected loss is deducted; unexpected loss is what capital covers.
Simple RAROC form
RAROC = Risk-adjusted expected return ÷ Economic capital
Compare with the hurdle rate. RAROC above hurdle means the unit adds value.
Sharpe ratio
Sharpe = (Rp − Rf) ÷ σp
Uses total risk. Best for a standalone portfolio, not for a small slice of a larger one.
Risk budget share
Share of risk = Unit risk contribution ÷ Total portfolio risk
Contributions use marginal or component risk, so they add up to the total. Standalone risks do not.
Capital allocation by ratio
Rank units by RAROC (or Sharpe) and shift capital to the highest ratio, subject to limits
Ranking assumes comparable risk measures and capital definitions.

How to solve Risk Limits and Capital Allocation questions

Use this order for any risk limit or capital allocation question in a vignette.

  1. 1Read the question first, then find the relevant exhibit: returns, costs, expected loss, capital, volatility or VaR.
  2. 2Identify the measure the vignette defines (RAROC, Sharpe, risk contribution) and its exact numerator and denominator.
  3. 3Check units and periods. Match annual returns with annual volatility and the same VaR horizon and confidence level.
  4. 4Compute the ratio for each unit, carefully deducting expected loss and costs where the definition says so.
  5. 5Compare with the hurdle rate or with the other units. Rank them.
  6. 6Decide the action: increase capital, reduce limits, or keep the allocation. Consider diversification and whether the unit's risk is standalone or marginal.
  7. 7Choose the option that matches your computed result, and rule out options that use the wrong risk measure.

Quickest way: Ratio-and-rank shortcut

When to use it: Use when the exhibit lists several units and the question asks which one deserves more capital or which meets the hurdle.

  1. Write numerator and denominator for each unit in one line.
  2. Divide once and round to two decimals.
  3. Compare with the hurdle. Anything below fails.
  4. If two options are close, check whether one uses expected loss or diversification the other ignores.

Common mistakes in Risk Limits and Capital Allocation

  • Using total profit instead of risk-adjusted return to judge a desk.

    Bigger profit looks better and the capital used is hidden in another exhibit.

    Fix: Always divide by capital or volatility before comparing.

  • Not deducting expected loss in RAROC.

    Students treat all credit losses as covered by capital.

    Fix: Expected loss is a cost of doing business and is deducted. Capital covers unexpected loss.

  • Using Sharpe ratio to rank units inside a larger diversified firm.

    Sharpe is the best-known measure, so it is used by default.

    Fix: Sharpe uses total risk. For a unit within a larger portfolio, marginal or contribution-based risk is more relevant.

  • Adding standalone VaRs to get the firm VaR.

    It seems logical that the parts sum to the whole.

    Fix: Only under perfect correlation do they sum. Otherwise firm VaR is lower, and risk budgets should use contributions.

  • Comparing RAROC with the risk-free rate instead of the hurdle rate.

    Confusion with the Sharpe ratio, which uses the risk-free rate.

    Fix: RAROC is judged against the firm's required return, usually the cost of equity.

Worked examples

Example 1

A bank reports for two units. Unit A: revenue ₹90 crore, costs ₹40 crore, expected loss ₹10 crore, economic capital ₹200 crore. Unit B: revenue ₹60 crore, costs ₹25 crore, expected loss ₹5 crore, economic capital ₹100 crore. Ignore return on capital. The hurdle rate is 18%. Q1: What is each RAROC? Q2: Which unit should receive more capital?

Show the solution
  1. Unit A risk-adjusted return = 90 − 40 − 10 = ₹40 crore.
  2. Unit A RAROC = 40 ÷ 200 = 20%.
  3. Unit B risk-adjusted return = 60 − 25 − 5 = ₹30 crore.
  4. Unit B RAROC = 30 ÷ 100 = 30%.
  5. Both exceed 18%, but B has the higher RAROC, so B earns more per rupee of capital.

Answer: Q1: A = 20%, B = 30%. Q2: Unit B, since it has the higher RAROC and both clear the hurdle (subject to limits and capacity).

Example 2

A fund has expected return 11%, volatility 14% and a risk-free rate of 3%. A second fund has expected return 9%, volatility 8%. Q1: Compute each Sharpe ratio. Q2: If the firm wants the better risk-adjusted fund, which is chosen?

Show the solution
  1. Fund 1: (11 − 3) ÷ 14 = 8 ÷ 14 = 0.571.
  2. Fund 2: (9 − 3) ÷ 8 = 6 ÷ 8 = 0.75.
  3. Higher Sharpe means more excess return per unit of total risk.
  4. Fund 2 ranks higher even though its return is lower.

Answer: Q1: Fund 1 = 0.57, Fund 2 = 0.75. Q2: Fund 2.

Exam tips

  • Read how the vignette defines RAROC. The numerator can differ, so do not rely on memory alone.
  • Remember the logic: Sharpe uses the risk-free rate and total risk; RAROC uses capital and a hurdle rate.
  • If a question asks about limits, think about what each limit controls: position size, loss, leverage or VaR.
  • Watch for diversification: contribution-based budgets sum to the total, standalone risks do not.
  • There is no penalty for wrong answers, so never leave a question blank.

Risk Limits 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.

Risk Limits and Capital Allocation: frequently asked questions

What is RAROC in simple terms?

RAROC is the risk-adjusted profit of a unit divided by the economic capital it uses. It shows return per rupee of capital at risk. If it is above the firm's hurdle rate, the unit is creating value.

What is the difference between RAROC and the Sharpe ratio?

Sharpe divides excess return over the risk-free rate by standard deviation. RAROC divides risk-adjusted return by economic capital and is compared with a hurdle rate. RAROC is common for business-unit capital allocation in banks.

What is risk budgeting?

Risk budgeting splits the total amount of risk a firm or portfolio is willing to take across units, managers or asset classes. It is usually expressed in VaR, tracking error or volatility. The aim is to spend risk where expected reward is highest.

How are risk limits set?

Limits are set from the risk budget, the firm's risk appetite and regulatory needs. Typical limits cover position size, VaR, stop-loss levels, stress scenarios and leverage. They should be monitored and reviewed regularly.