They should actually regress senator returns against Ken French's research factors [1] and measure the statistical/economic significance of the intercept and the volatility of the residuals.

If I return 2% per year, but do so at 1% volatility and zero market exposure, then I can be a highly successful hedge fund after applying 10x leverage.

[1] https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data...

Yeah this will probably end up being one of our benchmarks -- it's commonly used in academic literature to measure abnormal returns.

Where does this signal come from in a time-sequence series? I looked up "common mode signal" and in EE it looks like line to line interference, or line to ground interference. Does the existence of this signal presume a Senate's portfolio performance is somehow coupled to some index fund performance (S&P in this case)?

The common-signal would just be the general stock market performance. S&P is one way to approximate "the market". The idea being that you want a plot to show you how well they're doing in terms of market performance, not in terms of absolute share price (which is kind of meaningless here). Otherwise every shock to the general market ends up getting rendered in every line in the plot which is pretty distracting and makes it hard to see what's going on.

I'm not entirely sure either but you could use some combination of dS/dt dI/dt where S is the senator and I is the market?

What is the partial derivative of a sitting US senator?

Their portfolio