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

Kurtosis is not translation invariant because it measures the "tailedness" of the distribution of returns, which is not affected by adding a constant (risk-free asset return) to all returns. Translation invariance applies to measures that assess risk based on deviations from the mean or expected value, which is not what kurtosis does.

Which of the Following Risk Measures Is Not Translation Invariant rrr

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