Which of the following risk measures is not translation invariant (i.e., does not satisfy the property that if we add a risk-free asset to a portfolio with a return of$r$ , the risk of the portfolio should come down by the extent of this addition)?
A) VaR.
B) Expected shortfall.
C) Kurtosis.
D) Standard deviation.

Question

Quizplus · Accepted Answer

Translation invariance implies that if a constant is added to all outcomes of a portfolio, the risk measure should adjust accordingly. VaR, Expected Shortfall, and Standard Deviation are translation invariant because adding a risk-free asset (constant return) to a portfolio directly reduces the risk by that amount. Kurtosis, however, measures the "tailedness" of the distribution and is not affected by shifting the distribution up or down (adding a constant to all outcomes), hence it does not satisfy the property of translation invariance in the context of risk measurement.

Which of the Following Risk Measures Is Not Translation Invariant rrr

Which of the Following Risk Measures Is Not Translation Invariant $r$