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FRM Part II · FRM Exam Part II · Risk, Regulation and Organizational Structure

A pension fund's board sets a risk appetite that the probability of the funded ratio falling below 90% over one year must not exceed 5%. The current funded ratio is 100%, and the surplus return is assumed normal with zero mean and 6% annual standard deviation. Using a one-tailed 95% z-value of 1.645, what is the maximum surplus volatility consistent with the appetite, and is the current portfolio compliant?

Maximum volatility is about 6.08%, from 10% divided by 1.645. The current 6% volatility gives a 95% loss of about 9.87%, which is inside the 10% tolerance, so the fund is compliant, though with little headroom.

  1. AMaximum about 6.08%; compliant, since 6% is below itCorrect
  2. BMaximum about 5.00%; not compliant, since 6% exceeds it
  3. CMaximum about 10.0%; compliant, since 6% is below it
  4. DMaximum about 6.08%; not compliant, since 6% exceeds it

Explanation

A 10-point shortfall must be at the 5% tail: 1.645 × σ ≤ 10%, so σ ≤ 10/1.645 = 6.08%. Current σ of 6% is below this, so the fund complies (VaR = 9.87% < 10%). Using 10% directly ignores the z-multiplier.

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