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FRM Part I · FRM Exam Part I · Stress Testing

A portfolio has two risk factors, equity returns and credit spreads, which are positively related in stress (spreads widen when equities fall). Under a hypothetical scenario, equity shock is -30%. Historical regression over stress periods gives: spread change (bp) = -4 x equity return (in %), i.e., a 1% equity fall corresponds to a 4bp widening. The portfolio has equity exposure of USD 50 million (beta 1) and credit spread DV01 of USD 20,000 per bp. Using the regression to set the conditional spread shock, what is the scenario loss?

The scenario loss is USD 17.4 million. The 30% equity fall costs 15 million on a 50 million position, and the regression implies a 120 basis point spread widening, which costs 20,000 times 120, or 2.4 million. Both losses add because the factors move adversely together.

  1. AUSD 15.0 million
  2. BUSD 17.4 millionCorrect
  3. CUSD 15.0 million plus USD 2.4 million less a diversification offset of USD 1.0 million, i.e., USD 16.4 million
  4. DUSD 12.6 million

Explanation

Equity loss = 50 x 30% = 15 million. Spread shock = 4 x 30 = 120 bp; credit loss = 20,000 x 120 = 2.4 million. Total = 17.4 million. Ignoring the conditional credit shock gives 15.0; no offset applies since both lose; subtracting credit gives 12.6.

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