Assessing the vulnerability of large heterogeneous systems is crucial to IT operational decisions such as prioritizing the deployment of security patches and enhanced monitoring. These assessments are based on various criteria, including (i) the NIST National Vulnerability Database which reports tens of thousands of vulnerabilities on individual components, with several thousand added every year, and (ii) the specifics of the enterprise IT infrastructure which includes many components.Defining and computing appropriate vulnerability metrics to support decision making remains a challenge. Currently, several IT organizations make use of the CVSS metrics that score vulnerabilities on individual components. CVSS does allow for environmental metrics, which are meant to capture the connectivity among the components; unfortunately, within Section 2.3 of [1] there are no guidelines for how these should be defined and, consequently, environmental metrics are rarely defined and used.We present a systematic approach to quantify and automatically compute the risk profile of an enterprise from information about individual vulnerabilities contained in CVSS scores. The metric we propose can be used as the CVSS environmental score. Our metric can be applied to the problem of prioritizing patches, customized to the connectivity of an enterprise. It can also be used to prioritize vulnerable components for purposes of enhanced monitoring.