A promising application of swarm robotics is environmental monitoring, whereby large numbers of self-organizing agents are deployed concurrently to gather information on a short-or long-term basis. The greater resilience and attritability of a swarm system may be particularly valuable in hazardous or adversarial environments where a proportion of agents are likely to be damaged or destroyed. In such contexts the profitable information gathered by sensor payloads on robots is associated with material risk. Relatively little work has been done to consider how to manage this risk autonomously and effectively at the individual and system level. The field of financial risk management provides pre-existing tools and frameworks to get a head-start on this challenge. The method of Value at Risk (VaR) allows the easy quantification of prospective losses over a defined time period and confidence interval. Here, we consider VaR in a multi-agent context where the environment is intrinsically risky, for example containing damaging radiation sources. In agent-based simulations, individuals calculate VaR in real time and broadcast a self-triggered alert to their neighbors when their VaR limit is breached, helping them to avoid the area. This minimal communication system is effective at decreasing overall swarm exposure to hazards, while permitting agents to make risk-weighted explorations of hazardous areas. We further discuss the opportunity for finance-inspired risk management frameworks to be developed in the multi-agent systems context.