Accurate assessment of patients' risk against a certain disease is pivotal to healthcare management and personalized medicine. Although a variety of risk prediction models have been proposed in the literature, these models are mostly single-task, i.e. they only predict the risk of one disease at a time. However, in practice, the risks of multiple related diseases are often studied together. By separately applying single-task model to these diseases, the relation between them, such as the common risk factors, will likely be lost. To address this problem, in this work we propose a multi-task framework that can jointly predict the risk of multiple related diseases. We characterize the disease relatedness by assuming that the co morbidities underlying these diseases have overlap. We develop an optimization-based formulation that can simultaneously predict the risk for all diseases and learn the shared comorbidities. To validate our model, we apply it to a real Electronic Health Record database with patients at risk of Congestive Heart Failure and Chronic Obstructive Pulmonary Disease. We demonstrate that our model not only achieves good prediction accuracy but more importantly identifies a meaningful set of shared comorbidities that leads to deeper understanding of the association between the two diseases.