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It's been just over a week since voters in the U.S. went to the polls and elected Donald Trump as their next president. That's caused some volatility in the stock market, which has since stabilized, even making some gains since.

But some investors are concerned about how some individual companies, including Amazon.com (AMZN 1.49%), will fare under President Trump. So, let's take a look at what Trump has said about Amazon specifically, what policies could affect the company, and why Amazon ultimately stands on its own. 

Creating problems 

Speaking back in February at a campaign rally, Trump spoke to supporters about Amazon and its CEO Jeff Bezos, saying:

I have respect for Jeff Bezos, but he bought The Washington Post to have political influence, and I gotta tell you, we have a different country than we used to have. He owns Amazon. He wants political influence so that Amazon will benefit from it. That's not right. And believe me, if I become president, oh, do they have problems. They're going to have such problems.

Trump says Bezos used his purchase of the newspaper (which is unprofitable) to help keep more taxes away from Amazon. It's worth mentioning here that The Washington Post isn't a part of Amazon in any way. Bezos purchased the company personally, so forging the two together and making the accusation that one is helping the other pay lower taxes is inaccurate. Amazon paid $273 million in income taxes in 2015.

Trump might have talked a lot about causing problems for Amazon when it comes to taxes, but it's not very likely to play out that way.  

Antitrust accusations

President-elect Trump has also accused Amazon of violating antitrust laws. He said back in May that Bezos is worried because:

He thinks I would go after him for antitrust because he's got a huge antitrust problem. Amazon is controlling so much of what they're doing ... What he's got is a monopoly and he wants to make sure I don't get in.

The accusation that Amazon is a monopoly isn't a new one. An article in the New Republic argued as much back in 2014. But there's been plenty of pushback on this idea as well, including articles by major news sources here, here, and here.

An article from New York Magazine said at the time:

The evidence for this is thin. Amazon is surely the biggest player in e-commerce, with about $75 billion in revenue last year. But that comes out of a $263 billion market, and the National Retail Federation estimates that Amazon makes up only about 15 percent of total e-commerce sales.

The article went on to mention how Amazon is facing increased online sales pressure from brick-and-mortar stores. 

Amazon has certainly grown since 2014, but it's unlikely the current antitrust laws could be applied to the company. As David Goldman wrote in a CNNMoney article a few months ago:

According to the Sherman Antitrust Act, a judge would need to find that Amazon is a monopoly that abuses its power and harms consumers as a result. That's a high bar. Amazon is hardly the largest retailer. Its sales are about a fifth of Walmart's.

This could actually help Amazon

As I mentioned in different article about Trump's potential impact on another tech giant, there could actually be a benefit for Amazon under a Trump presidency. 

The president-elect has said he would be open to offering American companies a 10% tax rate for repatriated money. Companies often leave their foreign profits in other countries because it costs them a hefty 35% tax fee if they bring it back into the U.S. 

But Trump has said he wants to make it easy to bring those profits back: "We'll bring it back, and it'll be taxed only at the rate of 10% instead of 35%. And who would bring it back at 35%? Obviously nobody, because nobody's doing it."

Amazon doesn't keep as much of its profits in other countries as others do, but it could still benefit from a lower repatriation rate to bring back the $5.8 billion the company held in foreign subsidiaries as of the end of 2015.

Amazon stands on its own

As expected with any unforeseen outcome, there have been some short-term jitters following Trump's election, and Amazon's stock price is currently down over 5% since election day. It would be slightly naive to assume Trump could have zero impact on Amazon, but it's more likely than not that the company will continue to operate as usual. 

Amazon pays taxes, and Trump's correlation between The Washington Post and Amazon doesn't exactly hold up, nor is it likely for the government to go after (or win) any type of antitrust litigation against Amazon. If anything, the company might benefit from a Trump presidency if the repatriation rate drops some time over the next four years.

While it's easy to get caught up in what's happening right now, investors should remember that the fundamentals of Amazon's business haven't changed over the past week -- and that's reason enough to remain calm.