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Answer: When cash is added to a portfolio, the value of W for that portfolio should decrease by the amount of cash that is added.
According to the property of translation invariance, adding an amount of cash, K, into a portfolio will decrease the risk measure by K. Therefore, choice A correctly describes translation invariance. This property ensures that the risk measure is consistent and predictable when cash is added to a portfolio, as it should reflect a reduction in risk proportional to the amount of cash added. The other options, B, C, and D, describe different properties of risk measures: subadditivity, monotonicity, and homogeneity, respectively, which are not related to translation invariance.
Author: LeetQuiz Editorial Team
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To accurately determine whether the new risk measure W exhibits the property of translation invariance, which of the following tests should the Chief Risk Officer (CRO) employ?
A
When cash is added to a portfolio, the value of W for that portfolio should decrease by the amount of cash that is added.
B
When W is used to measure the risk of two portfolios A and B, then W(A) + W(B) should be less than or equal to W(A+B).
C
When W is used to measure the risk of two portfolios A and B, and if portfolio A always produces a worse outcome than portfolio B, then W(A) should always be higher than w(B).
D
When W is used to measure the risk of portfolio A, and if all exposures in portfolio A are increased by a constant factor, then W(A) should increase proportionally by that factor.