The term 'co-primary endpoints', which was historically used for different meanings in different clinical trial protocols, statistical analysis plans and journal articles, was recently clarified in the FDA guidance 'Multiple Endpoints in Clinical Trials' and the EMA guidance 'Guideline on multiplicity issues in clinical trials'. The FDA guideline claimed that a positive correlation between two endpoints can increase the (overall) power compared to that when the two endpoints are independent, but no detail has been provided. We examined the loss and gain in power of clinical trials with two correlated co-primary endpoints through simulation. Assuming normality of the two endpoints and two-sample t-test applicable, the results indicated that the loss and gain in power depend not only on the correlation but also on the two effect sizes. The gain increases with a positive correlation when the two effect sizes are equal; it can be ? 5% only if that the two effect sizes are equal and that the correlation is ? 0.5, which could be very rare in practice. The loss and gain can be ignorable otherwise. Thus a big gain in power due to positive correlation should not be generally expected.