Cardiac Implantable Electronic Devices (CIED) are fast becoming a fundamental tool of advanced medical technology and a key instrument in saving lives. Despite their importance, previous studies have shown that CIED are not completely secure against cyber attacks and especially those who are exploiting their Radio Frequency (RF) communication interfaces. Furthermore, the telemetry capabilities and IP connectivity of the external devices interacting with the CIED are creating other entry points that may be used by attackers. In this paper, we carry out a realistic risk analysis of such attacks. This analysis is composed of three parts. First, an actor-based analysis to determine the impact of the attacks. Second, a scenario-based analysis to determine the probability of occurrence of each threat. Finally, a combined analysis to determine which attack outcomes (i.e. attack goals) are riskiest and to identify the vulnerabilities that constitute the highest overall risk exposure. The conducted study showed that the vulnerabilities associated with the RF interface of CIED represent an acceptable risk. In contrast, the network and internet connectivity of external devices represent an important potential risk. The previously described findings suggest that the highest risk is associated with external systems and not the CIED itself.