The offspring of older fathers have higher risk of psychiatric disorders such as schizophrenia and autism. Paternal-age-related de novo mutations are widely assumed to be the underlying causal mechanism, and, although such mutations must logically make some contribution, there are alternative explanations (for example, elevated liability to psychiatric illness may delay fatherhood). We used population genetic models based on empirical observations of key parameters (for example, mutation rate, prevalence, and heritability) to assess the genetic relationship between paternal age and risk of psychiatric illness. These models suggest that age-related mutations are unlikely to explain much of the increased risk of psychiatric disorders in children of older fathers. Conversely, a model incorporating a weak correlation between age at first child and liability to psychiatric illness matched epidemiological observations. Our results suggest that genetic risk factors shared by older fathers and their offspring are a credible alternative explanation to de novo mutations for risk to children of older fathers.