  Quantiles and expected shortfalls are usually used to measure risks of
stochastic systems, which are often estimated by Monte Carlo methods. This
paper focuses on the use of quasi-Monte Carlo (QMC) method, whose convergence
rate is asymptotically better than Monte Carlo in the numerical integration. We
first prove the convergence of QMC-based quantile estimates under very mild
conditions, and then establish a deterministic error bound of $O(N^{-1/d})$ for
the quantile estimates, where $d$ is the dimension of the QMC point sets used
in the simulation and $N$ is the sample size. Under certain conditions, we show
that the mean squared error (MSE) of the randomized QMC estimate for expected
shortfall is $o(N^{-1})$. Moreover, under stronger conditions the MSE can be
improved to $O(N^{-1-1/(2d-1)+\epsilon})$ for arbitrarily small $\epsilon>0$.
