My interpretation: It is meaningless.
I can imagine good reasons for being a Democrat (see this link), but stock market returns are not one of them. First of all, the stock market is hardly a barometer of economic well-being. Second, as David Backus wisely points out, the President's policies are only a small part of what drives the economy. Third, it is nearly impossible to get the timing right to do this kind of comparison.
Let me explain this last point.
According to the efficient markets hypothesis, financial markets are forward-looking. If so, you would expect the entire impact of a candidate's election on the market to occur on election day, or maybe even during the days leading up to the election, as the market learns about the party of the next administration. By the time the new President takes office, the news has been fully priced in, and it will not show up in returns during his term.
But suppose you thought that stock investors were not forward-looking, or did not understand the differences between the parties. If so, the stock market would respond to economic events only as they unfold. In that case, you would have to wonder whether the timing is off in the other direction. Does the President influence the direction of the economy from the first day he takes office? Do the effects of his policies disappear the day after he leaves office? Of course not. Policy influences the economy with long and variable lags.
The bottom line: Trying to isolate the differences between the parties using this kind of stock market data is silly at best.
Addendum: Related readings here and here. Meanwhile, a PhD candidate in economics suggests this explanation:
Suppose what New York Times finds is econometrically correct. They might have just found another risk factor for abnormal returns. Democrats sitting in the White House do bring about more risks in stock holdings. Therefore, investors demand higher return to compensate for extra risks they are bearing.
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