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

Two portfolios have the same expected return and the same standard deviation. Portfolio A has a symmetric return distribution, while Portfolio B has a large negative skew and excess kurtosis. Which statement about standard deviation as a risk measure is most accurate?

Standard deviation cannot distinguish the two portfolios, so it understates B's tail risk. It depends only on the second moment and treats gains and losses symmetrically, ignoring the negative skew and excess kurtosis that make B's extreme losses more likely.

  1. AStandard deviation fails to distinguish the tail risk of the two portfolios, so B's extreme loss risk is understated relative to ACorrect
  2. BStandard deviation shows B is riskier because of its skew
  3. CStandard deviation is a coherent risk measure, so it captures the difference in tail losses
  4. DStandard deviation implies A is riskier since it is symmetric

Explanation

Standard deviation uses only the second moment and treats upside and downside deviations equally, ignoring skewness and kurtosis. Thus the two portfolios appear equally risky though B has fatter left-tail risk. It is also not a coherent measure in general.

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