A falling out-of-sample R squared

A prediction model has negative out-of-sample R squared. What does that mean, and which baseline must be specified?

It means the model's squared error exceeds the squared error of the baseline used in the denominator. Define that baseline explicitly: a training-window mean, zero return, and a test-sample mean are different comparators. A test mean is unavailable at prediction time even if used as a descriptive statistic. Also assess uncertainty, costs and regime stability before drawing an investment conclusion.