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FRM Part I · FRM Exam Part I · Stress Testing

A portfolio manager holds USD 40 million of equities with a beta of 1.2 to the market index and USD 60 million of bonds with a modified duration of 5. In a stress scenario, the market index falls 20% and yields rise by 1.5 percentage points (parallel). Assume bond price change is approximated by -modified duration x yield change, and ignore convexity and any other effects. What is the total stressed loss on the portfolio?

The total stressed loss is USD 14.1 million. Equities lose 40 million times 1.2 beta times 20 percent, which is 9.6 million. Bonds lose 60 million times duration 5 times 1.5 percent, which is 4.5 million. Adding the two gives 14.1 million.

  1. AUSD 9.6 million
  2. BUSD 4.5 million
  3. CUSD 14.1 millionCorrect
  4. DUSD 12.3 million

Explanation

Equity loss = 40 x 1.2 x 20% = USD 9.6 million. Bond loss = 60 x 5 x 1.5% = USD 4.5 million. Total = 9.6 + 4.5 = USD 14.1 million. Option A omits the bond loss; option B omits equities; option D uses a beta of 1.0 for equities (8.0) plus bonds is 12.5, not matching, so it is simply an incorrect sum.

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