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"Monotonicity" Is the Requirement of a Risk-Measure That If Portfolio

Question 4

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"Monotonicity" is the requirement of a risk-measure that if Portfolio A dominates Portfolio B (in the sense of always doing at least as well as B in every state of the world and strictly better in some states) , then the risk of Portfolio A should be less than the risk of Portfolio B. Which of the following statements is correct?


A) Standard deviation (SD) fails to satisfy monotonicity.
B) Value-at-Risk (VaR) fails to satisfy monotonicity.
C) Expected shortfall (ES) fails to satisfy monotonicity.
D) All three of these portfolio risk-measures (SD, VaR, and ES) fail monotonicity.

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