Abstract: Estimation or mis-specification errors in the portfolio return distribution can have a considerable impact on risk measures. This paper investigates the sensitivity of tail-related risk measures including the Value-at-Risk, expected shortfall and the expectile-quantile transformation level in an epsilon-contamination neighbourhood. The findings give the different approximations according to the tail heaviness of the contamination models and its contamination levels. Illustrating examples and an empirical study on the Royalton CRIX capturing and displaying the market movements are given. The codes used to obtain the results in this paper are available via QuantLet/SRMC.

Key words and phrases: Expected shortfall, expectile, risk measures, Royalton CRIX, sensitivity.