Measuring and Managing Market Risk for CFA Level II

What this chapter covers

Measuring and Managing Market Risk: topics in the order to study them

1. 1Market Risk Management OverviewIt sets the vocabulary of risk factors, exposures and the purpose of measurement, which every later topic assumes.
2. 2Value at Risk (VaR) ConceptsYou need the definition, confidence level, horizon and scaling rules before you can estimate or extend VaR.
3. 3VaR Estimation MethodsOnce you know what VaR means, you learn how to compute it and compare the strengths and weaknesses of each method.
4. 4VaR Extensions: CVaR, Incremental and Marginal VaRThese build directly on VaR and answer its main flaws: tail losses and the contribution of single positions.
5. 5Sensitivity and Scenario Risk MeasuresThey complement VaR, so study them after you see where VaR falls short.
6. 6Risk Limits and Capital AllocationLimits and capital use the measures you have just learned, so they make sense only after those are clear.
7. 7Managing Market Risk and HedgingThis is the action step that ties measurement to decisions, and it draws on the whole chapter and on derivatives.

How to prepare Measuring and Managing Market Risk

1. Read the overview topic once and write a one-line definition of each risk term in your own words.
2. Master VaR first. Practise reading confidence level, horizon and inputs from a vignette, and converting between horizons using the square root of time rule where the conditions allow it.
3. Build a comparison grid for parametric, historical simulation and Monte Carlo VaR: assumptions, data needs, handling of non-normal returns and options, and cost.
4. Do the extensions and scenario topics as concept-plus-calculation: know what CVaR, incremental VaR and marginal VaR each tell you, and when a stress test beats VaR.
5. Study limits, capital allocation and hedging by asking what decision a manager would take and why, then link it to duration, delta and futures from other chapters.
6. Finish with timed item sets. For every wrong answer, note whether the cause was a data-reading slip, a formula error or a concept gap, and revise that cause.

Common mistakes in Measuring and Managing Market Risk

• Confusing one-tailed and two-tailed z-scores, such as using 1.96 (5% total across two tails) for a one-tailed 95% VaR, which should use 1.65. The reverse error is using 1.65 when the 5% was split across two tails (2.5% in each), which needs 1.96.

  Fix: Decide first how many tails the question uses. One-tailed 5% (95% confidence) uses z = 1.65. Two-tailed 5% in total (2.5% per tail) uses z = 1.96. VaR is normally a one-tailed loss measure. Pick the matching z-score and report VaR as a positive loss.

• Scaling VaR to a new horizon wrongly, for example multiplying by the number of days instead of its square root.

  Fix: Convert the standard deviation to the new horizon first, and note the conditions behind the square root rule before applying it.

• Treating VaR as the maximum possible loss.

  Fix: Say it as 'the loss that is exceeded with the stated probability'. Link this to CVaR and stress tests for losses beyond it.

• Assigning the wrong strength to each estimation method, such as saying historical simulation needs a normality assumption.

  Fix: Keep a one-page comparison grid and test yourself on assumptions, data needs, treatment of options and weaknesses.

• Confusing marginal VaR with incremental VaR.

  Fix: Remember marginal is for a tiny change in position size, while incremental is for a full addition or removal. Say it before you read the options.

• Treating hedging as removing all risk, and ignoring costs, basis risk or model risk in the answer.

  Fix: In any hedging question, ask what risk remains after the hedge and what the hedge costs, then choose the option that reflects both.

Last-day revision: Measuring and Managing Market Risk

• ✓VaR is the minimum loss that would be expected to be exceeded with a given probability (for example 5%) over a set horizon, so it is the loss cutoff at the chosen tail probability.
• ✓Parametric VaR under normality uses a z-score times standard deviation, adjusted for the expected return and horizon.
• ✓Scaling VaR to a longer horizon with the square root of time assumes returns are independent and identically distributed.
• ✓Historical simulation uses actual past changes and needs no distribution assumption, but depends on the chosen window being representative.
• ✓Monte Carlo VaR is the most flexible, handles options and non-linear exposures, but is slow and depends on model assumptions.
• ✓CVaR is the expected loss given that the loss is at or beyond the VaR cutoff, so it is at least as large as VaR.
• ✓Marginal VaR is the change in portfolio VaR for a very small change in a position; incremental VaR is the change from adding or removing a whole position.
• ✓VaR does not say how large losses can be beyond the cutoff, and it can understate tail risk when returns are fat-tailed.
• ✓Stress tests and scenario analysis cover extreme events VaR may miss, and can be historical or hypothetical.
• ✓Sensitivity measures such as duration, delta and beta give the change in value for a small change in one risk factor.
• ✓Risk limits, such as VaR limits, position limits and stop-loss rules, tie risk taking to a budget and to allocated capital.
• ✓Hedging reduces exposure but costs money and can create basis risk and leave residual risk.

Measuring and Managing Market Risk in other exams

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

• CMA FinalMarket Risk Management
• FRM Part IMeasures of Financial Risk
• CA FinalRisk Management
• FRM Part IIPortfolio Risk: Analytical Methods