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

A risk manager builds a market-driven scenario by stressing one core risk factor (equity index) and then setting the other factors to their conditional expected shocks given that stress. Which statistical relationship is used to derive these conditional expected shocks under a multivariate normal assumption?

Under multivariate normality, the conditional expected shock of another factor equals its covariance with the stressed factor divided by the stressed factor's variance, times the stress size. This is a regression beta applied to the shock, so correlation drives how other factors move.

  1. AThe conditional mean, which is the factor's covariance with the stressed factor divided by the stressed factor's variance, multiplied by the stress sizeCorrect
  2. BThe unconditional mean of each other factor, unchanged by the stress
  3. CThe factor's own volatility multiplied by the stress size, ignoring correlation
  4. DThe inverse of the correlation matrix applied to the stress size only

Explanation

Under joint normality, E[Y|X=x] = mu_Y + (Cov(X,Y)/Var(X))(x - mu_X). With zero means this is beta times the shock. Ignoring correlation or using unconditional means would not reflect co-movement.

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