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

question 4

Multiple Choice

"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.

---

Definitions:

Merchandise Inventory

The total value of a retailer's goods that are available for sale to customers.

Estimated Cost

A prediction or forecast of the future cost of a project, operation, or production based on current data and trends.

Gross Profit Rate

A financial metric that measures the difference between sales and the cost of goods sold, expressed as a percentage of sales.

Merchandise Inventory

The goods a company holds for the purpose of resale to customers.