There is a huge difference between responding to risk and proactively reducing risk. By following the process of the latter, you can reduce the cost of rework and the sunk costs associated with project-stopping risks. This article found on Leading Answers discusses how an agile approach can lend itself to this risk driven development, and the benefits because of it:
Over the course of the project, agile teams use tools such as risk burn-down graphs and risk profiles to illustrate the effectiveness of the risk-driven approach. The goal is to rapidly reduce risks on the project”
Another benefit of tackling risky work early is the cost of change-curve savings possible in software projects. By proactively undertaking risky work early, we can reduce the overall impact to the project compared to if those risks occurred later when their effect (in terms of rework or revision of approach) would be much higher. Simply put, risks solved early are more valuable than risks solved late. The constant reprioritization within agile methods makes the actions associated with risk management occur early and often, allowing for a mitigation of risks before they halt the project. Keep in mind, however, that agile methods aren't a catch all for risk management either; if your organization isn't currently using agile methods, the implementation of the new agile-centric risk driven development can in itself be a risk.