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FRM Part II · FRM Exam Part II · Stress Testing Banks

A bank has a portfolio exposed to two risk factors. A stress scenario specifies a shock of -20% to equities directly. Using a multi-factor model, the bank also wants to propagate the shock to an unshocked factor, credit spreads, whose conditional expected change is derived from a joint normal distribution. Equity change has standard deviation 10%, spread change has standard deviation 40 bp, correlation is -0.5, and means are zero. What is the conditional expected spread change in basis points given the equity shock?

The conditional expected spread change is +40 basis points. With zero means, it equals correlation times the ratio of standard deviations times the shock: -0.5 times 4 times -20 gives +40. Negative correlation means an equity fall implies wider spreads.

  1. A+40 bpCorrect
  2. B-40 bp
  3. C+20 bp
  4. D+80 bp

Explanation

E[S|E=e] = rho*(sigmaS/sigmaE)*e = -0.5*(40/10)*(-20%) = -0.5*4*(-20) = +40 bp. Using the wrong sign for the correlation gives -40. Omitting the 0.5 factor gives +80. Using 0.5 with only half the ratio gives +20.

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