To test this out, I took the weekly S&P 500 movements throughout each presidency. I tried a bunch of ideas but the visualizations were not very easy to read. An example is overlaying histograms of the weekly results to see how the distributions varied. The visualization that ended up being cleanest in my opinion is a box plot.
There is one problem I could never settle on, and that's 'who gets credit for the first year in office?' For example, 2017 followed 8 years of Obama policy but Trump was the current president. Is 2017's stock market Obama's or Trump's? To deal with that, I have the analysis for all permutations below.
In case you aren't familiar with this type of plot...The shaded rectangle represents the middle 50% of the weeks. The dotted triangles are the mean +/- standard deviation. The solid line is the median. The dotted line is the mean. If you hover, you can read the values. Basically...the vertical lines tell you the most typical, and the width of the rectangle and triangles tells you the variability.
Looking at the results, the market doesn't seem extremely chaotic under Trump. It looks pretty typical.
Unfortunately, I could not find daily data going back this far or weekly data going back earlier than this, so there might be a more interesting result with that data.
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