One of the biggest risks to Teladoc Health (TDOC 1.26%) was the ability of a big tech giant like Amazon (AMZN -1.04%) to steal market share away from the telehealth company. Amazon, after all, has made multiple acquisitions into the healthcare industry and also has a telehealth business, Amazon Care. But in August, Amazon announced it was shutting Amazon Care down. 

The news seems like it should be positive for a stock like Teladoc. However, as an investor in the company, there are a couple of scenarios that I still worry about today. Here's why.

1. Amazon could invest in a Teladoc rival

Amazon's decision to halt its telehealth services suggests that maybe it wasn't as easy getting into telehealth as the tech giant may have assumed. While it undoubtedly has the technical resources to get it done, it's quite another issue to get subscribers to sign up for its service and trust the tech company. As perhaps a sign that things may not have been going all that well, Amazon highlighted in February that Whole Foods (its own subsidiary) was a new customer for its service.

The company's decision to abandon Amazon Care could lead Amazon to pursue an acquisition of a telehealth company, a potential rival of Teladoc's. That would be a much quicker and more efficient way to jump-start a telehealth business, as opposed to starting from the ground up. Amazon has clearly shown an interest in telehealth and the healthcare industry as a whole. In 2018, it announced it was acquiring online pharmacy PillPack for $753 million. This year, it signed an agreement to buy primary care company 1Life Healthcare, also known as One Medical, for $3.9 billion.

Acquiring a telehealth company may not cost all that much, either. Amwell, which is a Teladoc rival, has a market capitalization of just $1.3 billion right now. The danger for Teladoc is that with Amazon's resources, a competing telehealth company could become more of a threat.

2. The tech company could buy Teladoc

You might be thinking that if Amazon acquired Teladoc, that would be great news for Teladoc investors. But there's a significant downside to this scenario, and it's the biggest risk I always worry about: an acquisition that values the business at less than it was worth a year ago.

I'm confident that Teladoc can do well and recover in the long term, which is why I think it's a mistake to give up on the stock. However, if Amazon comes in and makes a bid for the stock, it may garner a premium that leaves investors in the red.

For example, Amazon is paying $18 per share for One Medical. That's a huge premium -- but only from where the stock was previously trading at prior to the announcement (around $10). For One Medical investors who bought the stock a year ago at more than $23, they will receive $18 for their shares in the all-cash deal; if the transaction goes through, there's no hope of them turning a profit, regardless of how much patience they have.

The same could happen to Teladoc, which has been down 78% over the past year. Even though the future looks promising for Teladoc, an acquisition would effectively put a ceiling on how high the stock can go. 

Should you invest in Teladoc?

The first risk I'm not terribly worried about, because Teladoc has proven itself to be a top telehealth company, earning top marks from a J.D. Power survey last year for customer satisfaction. Pumping more money into a competitor may not necessarily be enough to hurt Teladoc's market share.

The second risk largely pertains to investors who have been holding onto the stock for more than a year. If you've bought the healthcare stock recently (or are on the verge of doing so), an acquisition would certainly be good news as you could walk away with a nice profit.

For investors who have been hanging on for a while, this could create an incentive to buy more of Teladoc's stock today. That's because regardless of whether an acquisition ends up taking place, by averaging down you can put yourself in a better position to profit from owning Teladoc shares in the long run.

The company's continued growth opportunities make it a fantastic buy, and Amazon throwing in the towel on its own telehealth business lends credibility to the idea that big tech may not be that much of a threat to Teladoc as was once feared.