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 the 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
)
O(N^{-1/d})
for the quantile estimates, where
d
d
is the dimension of the QMC point sets used in the simulation and
N
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
)
o(N^{-1})
. Moreover, under stronger conditions the MSE can be improved to
O
(
N
−
1
−
1
/
(
2
d
−
1
)
+
ϵ
)
O(N^{-1-1/(2d-1)+\epsilon })
for arbitrarily small
ϵ
>
0
\epsilon >0
.