re: Why has the Dow Jones done so well under the two recent Democratic presidents?

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This details the start of the QE program (at the very END of W's presidency) and it's effect on the market. The US president has no control over the Federal Reserve and their actions, therefore any gains or losses in the stock market cannot be credited with Barack Obama or his policies. The Fed's policy of easy money has artificially pumped the stock market up.

Bill Clinton just happened to be president when the Dawn of the Internet Age came upon us and transformed commerce. The market became enamored with anything with a "dot com" behind it. Investors threw massive amounts of money into companies that developed an online presence whether they produced a profit or not. Evidence of this happened when the tech bubble burst at the end of Clinton's presidency. While the internet age was taking hold during the 90's, the subprime mortgage industry grew 100 fold due to Clinton's repeal of Glass-Steagal Act and fundamental changes to Jimmy Carter's Community Reinvestment Act of 1977. Close examination of these actions show that the government made banks abandon sound lending practices and forced them to give mortgage loans to people who couldn't really afford them. Through Freddy and Fannie, the government acted as a backstop to defaulting loans. Literally these companies could not lose. These actions grew balance sheets for banks and mortgage companies pumping stocks further up.
Also, during this time period, companies like Enron and WorldCom showed that certain liberties could be taken in accounting practices, leading to further stock pumping. How many companies that engaged in practices like this and got away with it?

So your basic premise that "Democratic presidents are engaging in policies that are good for stocks" is a somewhat faulty argument. A truly objective look proves that