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FRM Part II · FRM Exam Part II

VaR and Risk Budgeting in Investment Management for FRM Part II

Risk budgeting splits a portfolio's total risk limit across assets, strategies or managers. You measure risk with absolute, relative (tracking error) VaR, then use marginal, incremental and component VaR to see who uses the budget. Component VaRs add up to total VaR. You then check that risk earns return.

What this chapter covers

This chapter is about how an investment organisation decides how much risk to take, where to take it and who takes it. Risk budgeting sets a total risk limit, usually in VaR or tracking error terms, and spreads it across asset classes, strategies or external managers. VaR here is a tool for allocation and control, not only for reporting a loss number.

You will meet three families of ideas. First, VaR measured against different benchmarks: absolute VaR (loss in value), relative VaR (loss against a benchmark) and tracking error VaR. Second, VaR decomposition: marginal VaR, incremental VaR and component VaR. Third, the link between risk and return: optimal allocation, Sharpe ratio and information ratio, and the fundamental law of active management, which ties the information ratio to skill and breadth.

The chapter builds on the VaR, correlation and portfolio theory you learned in Part I. It connects to the market risk topic in Part II, where VaR methods and limits appear again, and to the rest of the investment management topic: performance measurement, factor models and hedge fund risk. Questions are usually applied: a short case, some volatilities and weights, and a request for a risk figure or an interpretation.

The investment management topic is one of the six in the Part II exam, and this chapter supplies many of its calculation questions. The ideas are compact, the formulas are few and the questions are predictable in shape: compute a tracking error, a component VaR or an information ratio, then say what it means for the allocation. Candidates who learn the decomposition logic and the interpretation can earn these marks reliably, and the same logic helps you in market risk and performance questions.

VaR and Risk Budgeting in Investment Management: topics in the order to study them

  1. 1Risk Budgeting Framework and Asset Manager RiskStart with the purpose: who sets risk limits, what risks an asset manager faces and how a budget is organised. Everything else plugs into this.
  2. 2Absolute, Relative and Tracking Error VaRYou need to know which benchmark a VaR number is measured against before you can decompose or allocate it.
  3. 3Marginal, Incremental and Component VaRThis is the core calculation set. It shows how each position contributes to total risk and builds on the VaR measures above.
  4. 4Optimal Portfolio Allocation and Risk-Adjusted PerformanceOnce you can measure risk contributions, you compare them with expected returns. Optimal allocation equates return per unit of marginal risk.
  5. 5Fundamental Law of Active ManagementIt extends the information ratio idea from the previous topic into skill and breadth, so it comes after risk-adjusted performance.
  6. 6Risk Budgeting Across Managers and Decentralised Risk ManagementThis is the organisation-level application. It uses every earlier tool, so study it last.

How to prepare VaR and Risk Budgeting in Investment Management

Aim to be quick at a small set of calculations and clear on what each number says. Practise with short numerical cases, as the exam does.

  1. Read the framework topic once for structure: risk limits, who owns them, how budgets flow down. Note the vocabulary and do not memorise lists.
  2. Write down the three VaR types (absolute, relative, tracking error) and what each uses as its reference. Compute each from a given volatility and confidence multiplier until it is routine.
  3. Learn the decomposition logic: marginal VaR is the change in VaR for a small change in a position, component VaR is position × marginal VaR, and component VaRs sum to total VaR. Incremental VaR is the change from adding or removing a whole position. Solve at least ten problems of each kind.
  4. Practise the allocation rule: at the optimum, expected excess return divided by marginal VaR is equal across assets. Practise Sharpe ratio and information ratio, and say which one fits absolute and which fits relative mandates.
  5. Learn the fundamental law in its simple form, IR ≈ IC × √breadth, and work out what happens when skill or the number of independent bets changes. Remember its assumptions.
  6. Finish with manager-level cases: how to allocate a tracking error budget, why diversification across managers lowers total risk, and the trade-offs of decentralised risk management. Then do a timed set of mixed questions and review every miss.

Common mistakes in VaR and Risk Budgeting in Investment Management

  • Using total volatility when the question asks for relative VaR or tracking error VaR.

    Fix: Underline the reference in the question first. If a benchmark is mentioned, use the volatility of active return, not of the portfolio.

  • Treating incremental VaR and component VaR as the same thing.

    Fix: Remember that component VaR is a split of existing VaR that sums to the total. Incremental VaR is a full before-and-after change and generally does not sum.

  • Forgetting to multiply marginal VaR by the position size to get component VaR.

    Fix: Check that your component VaRs add up to the total VaR. If they do not, you missed a step.

  • Applying the fundamental law as an exact result in every case.

    Fix: Treat it as an approximation that assumes independent bets and a consistent skill measure. Be ready to explain what breaks if bets are correlated.

  • Choosing the asset with the highest return or lowest risk instead of the best return per unit of marginal risk.

    Fix: Compare excess return divided by marginal VaR. Shift risk toward the higher ratio until the ratios are equal.

  • Mixing time horizons and confidence levels, such as annual volatility with a daily VaR.

    Fix: Convert everything to one horizon before calculating, usually by multiplying by √time, and check the z-value for the stated confidence level.

Last-day revision: VaR and Risk Budgeting in Investment Management

  • Absolute VaR measures loss in value; relative VaR measures loss against a benchmark.
  • Tracking error is the standard deviation of active return (portfolio minus benchmark).
  • Tracking error VaR = z × tracking error × portfolio value, for a chosen confidence level.
  • Marginal VaR is the change in portfolio VaR for a small change in one position.
  • Component VaR = position × marginal VaR, and component VaRs sum to total portfolio VaR.
  • Incremental VaR is the change in VaR from adding or removing a whole position, so it is not the same as component VaR.
  • A negative marginal VaR means the position acts as a hedge to the portfolio.
  • At the optimal allocation, excess return ÷ marginal VaR is the same for every asset.
  • Sharpe ratio = (Rp − Rf) ÷ σp; information ratio = active return ÷ tracking error.
  • Fundamental law: IR ≈ IC × √breadth, where breadth means independent bets per year.
  • More skill or more independent bets raises the information ratio; correlated bets do not add breadth.
  • Diversifying across managers lowers total tracking error unless active bets are positively correlated.

VaR and Risk Budgeting in Investment Management practice questions

VaR and Risk Budgeting in Investment Management in other exams

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

VaR and Risk Budgeting in Investment Management: frequently asked questions

What is risk budgeting in FRM Part II?

It is the process of dividing an overall risk limit, such as VaR or tracking error, across asset classes, strategies or managers. The aim is to take risk where expected return per unit of risk is highest. You need both the calculations and the reasoning behind them.

How do I tell marginal, incremental and component VaR apart?

Marginal VaR is the effect of a very small change in a position. Incremental VaR is the effect of adding or removing the whole position. Component VaR is the position's share of current total VaR, and these shares sum to the total.

Do I need to memorise the fundamental law of active management?

Yes, in its simple form: the information ratio is approximately the information coefficient times the square root of breadth. You should also understand what raises or lowers each input. Questions often ask what happens when skill or the number of independent bets changes.

How should I practise this chapter?

Do short numerical problems on each VaR type until the steps are automatic. Then do mixed timed sets so you learn to spot which measure a question wants. Always finish by stating in words what your answer means for the portfolio.