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FRM Exam Part II · Market-Driven Scenarios: An Approach for Plausible Scenario Construction

Plausibility and Construction of Market-Driven Scenarios

Updated 11 October 2026 · Fact-checked

A market-driven scenario shocks a few key market factors, then uses their statistical relationships to infer moves in all other factors. The result is internally consistent and plausible. To solve questions, pick the shocked factors, estimate the implied moves from correlations and volatilities, then check the plausibility of the whole set.

Understand Plausibility and Construction of Market-Driven Scenarios

A stress scenario is a set of assumed moves in risk factors, such as equity indices, interest rates, credit spreads and FX rates. The hard part is not the size of the shock. It is deciding what all the other factors do at the same time.

A market-driven scenario starts from a small number of core factors that you shock directly. These are the factors you care about or believe drive the stress, for example an equity index falling sharply. The moves in the remaining peripheral factors are not chosen by hand. They are inferred from how those factors have historically moved with the core factors.

This matters because hand-picked scenarios can be inconsistent. If you shock equities down 30% but leave credit spreads unchanged, the scenario is unlikely to occur in real markets. Inferring the other moves from the historical joint behaviour keeps the scenario coherent.

Plausibility is a judgement about how likely the shocked combination is, given the historical joint distribution of factors. A shock is more plausible when it is in line with the observed volatilities and correlations. A scenario with a very large core shock can still be plausible if the implied moves are consistent with that joint behaviour. A scenario that needs factors to behave against their usual relationships is less plausible.

The logic is a conditional expectation. Given the core shock, you ask: what is the expected move in each other factor? Under a joint normal assumption this is a regression-style calculation. You should also know its limit. Correlations can change in a crisis, so the implied moves depend on the data window and the assumed distribution.

Key formulas to remember

Implied move for one peripheral factor (single core factor, joint normal)
E[Y | X = x] = μY + ρ × (σY ÷ σX) × (x − μX)
With zero means, implied move = ρ × (σY ÷ σX) × shock to X. Use it to infer a peripheral factor Y from a core shock X.
Regression beta form
β = ρ × σY ÷ σX = Cov(X, Y) ÷ Var(X)
Implied move in Y equals β times the shock in X (zero-mean case).
Shock size in standard deviations
z = shock ÷ σX
Measures how extreme the core shock is. Larger z means a less likely scenario.
Multi-factor conditional expectation
E[Y | X = x] = μY + Σ_YX × Σ_XX⁻¹ × (x − μX)
Σ_YX is the covariance between peripheral and core factors; Σ_XX is the core factors' covariance matrix. Applies under joint normality.

How to solve Plausibility and Construction of Market-Driven Scenarios questions

Use this order for any question on building or judging a market-driven scenario.

  1. 1Identify the core factors being shocked and the peripheral factors to be inferred.
  2. 2Write down the given volatilities, correlations and means. Make sure all are on the same time horizon.
  3. 3Express each core shock in standard deviations to see how extreme it is.
  4. 4Compute the implied move for each peripheral factor using β = ρ × σY ÷ σX times the core shock (add means if given).
  5. 5Check signs and sizes: do the implied moves match known behaviour, such as equities down and credit spreads up?
  6. 6Judge plausibility: a scenario is more plausible when the implied moves follow the historical joint behaviour.
  7. 7State limits: correlations may shift in a crisis and the normal assumption can understate tail moves.

Quickest way: Beta shortcut

When to use it: Use when the question gives one core shock and asks for the implied move in one other factor, with zero means.

  1. Compute β = ρ × σY ÷ σX.
  2. Multiply β by the core shock.
  3. Check the sign matches the sign of ρ.
  4. Eliminate options with the wrong sign or a move larger than the shock when σY ÷ σX is below one and ρ is at most one.

Common mistakes in Plausibility and Construction of Market-Driven Scenarios

  • Using ρ × shock without the volatility ratio

    Students remember the correlation but forget it is not the same as the slope.

    Fix: Always multiply by σY ÷ σX. Correlation only sets the sign and strength.

  • Inverting the volatility ratio

    It is easy to write σX ÷ σY under time pressure.

    Fix: Y is the factor being inferred, so σY goes on top and σX, the shocked factor, goes below.

  • Mixing volatility horizons

    Daily and annual volatilities appear in the same question.

    Fix: Convert to one horizon first. The ratio is unaffected only if both are on the same horizon.

  • Calling a large shock automatically implausible

    Students link plausibility only to shock size.

    Fix: Plausibility covers the full set of moves. A large core shock with consistent implied moves can be plausible. Inconsistent moves are the real problem.

  • Assuming correlations stay fixed in a crisis

    The formula treats historical correlation as given.

    Fix: Mention that correlations can rise in stress, so inferred moves may be understated. Treat the result as an estimate.

  • Shocking every factor by hand

    It feels more thorough.

    Fix: The market-driven approach shocks only a few core factors and infers the rest, which keeps the scenario internally consistent.

Worked examples

Example 1

A risk team shocks an equity index by −20%. Over the same horizon, the index volatility is 16% and a credit spread index has volatility 8%. Their correlation is −0.6, and means are zero. Treating the spread move as a percentage change, what is the implied move in the credit spread index?

Show the solution
  1. β = ρ × σY ÷ σX = −0.6 × 8 ÷ 16.
  2. 8 ÷ 16 = 0.5, so β = −0.6 × 0.5 = −0.3.
  3. Implied move = β × shock = −0.3 × (−20%) = +6%.

Answer: The credit spread index is expected to rise by 6%. The sign is positive because equities and spreads are negatively correlated.

Example 2

An equity index has horizon volatility 10%. A scenario shocks it by −25%. Another factor has volatility 15% and correlation 0.4 with the index, with zero means. (a) How many standard deviations is the core shock? (b) What is the implied move in the other factor?

Show the solution
  1. (a) z = −25 ÷ 10 = −2.5 standard deviations.
  2. (b) β = 0.4 × 15 ÷ 10 = 0.4 × 1.5 = 0.6.
  3. Implied move = 0.6 × (−25%) = −15%.
  4. Check: the sign is negative, matching the positive correlation.

Answer: The core shock is −2.5 standard deviations, and the implied move in the other factor is −15%.

Exam tips

  • Read which factor is core and which is peripheral before computing. The question often swaps the roles.
  • Check units and horizons first. Mismatched horizons are a common trap.
  • Use sign logic to remove options quickly. The implied move has the same sign as ρ times the shock.
  • For plausibility questions, choose answers about consistency with historical joint behaviour, not just shock size.
  • When asked about limits, think of changing correlations in stress and the normal assumption.

Practice questions from Market-Driven Scenarios: An Approach for Plausible Scenario Construction

Plausibility and Construction of Market-Driven Scenarios: frequently asked questions

What is a market-driven scenario?

It is a stress scenario built by shocking a few key market factors directly. The moves in the other factors are inferred from their historical relationships with those core factors.

What makes a stress scenario plausible?

The set of factor moves should fit the historical joint behaviour of the factors, including volatilities and correlations. A scenario with moves that contradict these relationships is less plausible.

Why not just choose every factor move by judgement?

Hand-picked moves can be inconsistent, such as a large equity fall with no change in credit spreads. Inferring peripheral moves from the core shocks keeps the scenario coherent.

What is the main weakness of this approach?

It relies on historical correlations and often on a normal assumption. In a real crisis correlations can shift and tails can be heavier, so the implied moves may be too mild.