Given two portfolios $P _ { 1 }$ and $P _ { 2 }$ , which risk measure $R ( )$ does not always satisfy the "sub-addivity" property (i.e., that $R \left( P _ { 1 } + P _ { 2 } \right) \leq R \left( P _ { 1 } \right) + R \left( P _ { 2 } \right)$ where $R ( )$ is the measure of portfolio risk)?
A) VaR.
B) Expected shortfall.
C) Variance.
D) Standard deviation.

Question

Quizplus · Accepted Answer

VaR (Value at Risk) does not always satisfy the sub-additivity property, which means that the risk of a combined portfolio can be greater than the sum of the risks of the individual portfolios. This is a limitation of VaR as a risk measure, especially when assessing the risk of diversified portfolios.

Given Two Portfolios P1P _ { 1 }P1​ And P2P _ { 2 }P2​

Given Two Portfolios $P _ { 1 }$ And $P _ { 2 }$