"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.

Question

Quizplus · Accepted Answer

Standard deviation fails to satisfy monotonicity because it measures the spread of returns around the mean, not the actual risk of loss, and can assign higher risk to a portfolio with better outcomes.

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