Looking ahead, some analysts think the stock market will keep soaring as Trump pushes for deregulation and tax cuts during his second term. For instance, while on the campaign trail, he proposed lowering the corporate tax rate to 15% for domestic manufacturers. That could boost net profit margins and send the stock market higher.

President Donald Trump used his inaugural address to focus on ways to "resurrect the old economy by making it cheaper to build it here, using taxes, regulations, tariffs and abundant energy," according to Steven Blitz,

President Trump will have little direct impact on the stock market, but his policies, initiatives and posts certainly can make prices move. Here's how.