There is, however, plenty of evidence that professional investors outperform individuals, reliably. And professionals make most of their money from non-linear derivatives (or make their own).

People say that hedge funds are worse than passive investing, and that's often true, but it's true because that's after fees - professional investors routinely beat the market by 3% YoY long term averages, it's just that they are basically paid as much as they make you.