FRM Part I · FRM Exam Part I · Measures of Financial Risk
A coherent risk measure rho is applied to portfolio losses. A portfolio's risk is rho(X) = 8 million. A risk-free cash amount of 3 million is added to the portfolio (a gain that reduces loss with certainty). Under translation invariance, what is the risk of the new portfolio?
The risk falls to 5 million. Translation invariance says that adding a sure amount of cash reduces the risk measure by exactly that amount, so 8 million minus 3 million equals 5 million.
- A11 million
- B5 millionCorrect
- C8 million
- D2.67 million
Explanation
Translation invariance states rho(X + n) = rho(X) - n for a sure gain n. So the risk is 8 - 3 = 5 million. Adding 3 million (11) uses the wrong sign; dividing by 3 confuses it with homogeneity.
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