  Expectile bears some interesting properties in comparison to the industry
wide expected shortfall in terms of assessment of tail risk. We study the
relationship between expectile and expected shortfall using duality results and
the link to optimized certainty equivalent. Lower and upper bounds of expectile
are derived in terms of expected shortfall as well as a characterization of
expectile in terms of expected shortfall. Further, we study the asymptotic
behavior of expectile with respect to expected shortfall as the confidence
level goes to $1$ in terms of extreme value distributions. We use concentration
inequalities to illustrate that the estimation of value at risk requires larger
sample size than expected shortfall and expectile for heavy tail distributions
when $\alpha$ is close to $1$. Illustrating the formulation of expectile in
terms of expected shortfall, we also provide explicit or semi-explicit
expressions of expectile and some simulation results for some classical
distributions.
