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.

Donald Trump's inauguration on Monday could herald a more volatile period for markets, with the Republican seen moving quickly on a wide swath of issues including trade and immigration that are expected to swing asset prices.

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.