We formulate the service composition problem as a multi-objective stochastic program which simultaneously optimizes the following quality of service (QoS) parameters: workflow duration, service invocation costs, availability, and reliability. All of these quality measures are modelled as decision-dependent random variables. Our model minimizes the average value-at-risk (AVaR) of the workflow duration and costs while imposing constraints on the workflow availability and reliability. AVaR is a popular risk measure in decision theory which quantifies the expected shortfall below some percentile of a loss distribution. By replacingthe random durations and costs with their expected values, our risk-aware model reduces to the nominal problem formulation prevalent in literature. We argue that this nominal model can lead to overly risky decisions. Finally, we report on the scalability properties of our model.