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FRM Part I · FRM Exam Part I · Measures of Financial Risk

A portfolio has a current risk measure of USD 20 million. The firm adds USD 5 million of risk-free cash to the portfolio. If the risk measure satisfies translation invariance, what is the new risk measure, assuming risk is expressed as the capital needed to make the position acceptable?

The new risk measure is USD 15 million. Translation invariance says that adding a risk-free amount of cash reduces the required capital by exactly that amount, so 20 million minus 5 million gives 15 million.

  1. AUSD 25 million
  2. BUSD 20 million
  3. CUSD 5 million
  4. DUSD 15 millionCorrect

Explanation

Translation invariance states ρ(X + k) = ρ(X) − k when adding k of risk-free cash. So 20 − 5 = 15. Adding the cash rather than subtracting gives 25, a sign error. Leaving it unchanged ignores the property.

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