Many investors dream of their stocks becoming 10-baggers -- soaring at least tenfold in value -- over several years. AMC Entertainment (AMC 7.19%) has gone far past the realm of those dreams in a much shorter period of time. The movie theater chain stock is a 25-bagger in just the first half of 2021.

What's next for AMC? There are some starkly contrasting views, to say the least. Some believe the stock can keep moving higher. Others think it's a question of when and not shares will plunge. Regardless of what your take is, here are three stocks to buy that are critically important to AMC's future.

Smiling people sitting in a movie theater.

Image source: Getty Images.

AMC and the big three

AMC CEO Adam Aron said in the company's Q1 conference call, "I watch those vaccination statistics closely all the time because, let's say what it is, vaccination is our way out of all of this." He's right: COVID-19 vaccines are absolutely key to AMC's business returning to pre-pandemic levels.

The three most important companies in the COVID-19 vaccine market are, without question, Pfizer (PFE 0.87%), BioNTech (BNTX 1.54%) (Pfizer's partner), and Moderna (MRNA 1.04%). AMC's fortunes are largely intertwined with those of these three vaccine makers.

What about other companies with COVID-19 vaccines? Johnson & Johnson (JNJ 0.61%) already has a vaccine on the market in the U.S. Novavax (NVAX 2.06%) hopes to soon win Emergency Use Authorization for its COVID-19 vaccine. AstraZeneca's (AZN 0.44%) vaccine is available in many of the European countries where AMC owns movie theaters.

However, none of these vaccine makers are in the same league as Pfizer, BioNTech, and Moderna are right now. Johnson & Johnson has experienced manufacturing problems. A top European official is warning people to avoid AstraZeneca's vaccine because of a rare blood-clotting issue. Novavax had to delay its filings for authorization for its vaccine candidate.

Comparing the correlations

Aron also stated in AMC's Q1 update, "I said a few months back that Albert Bourla, the CEO of Pfizer, might just be the most important human in directing the come back on the immediate future of the entire cinema industry. I meant that then, and I mean that still today." 

Does this mean that for AMC stock to perform well, Pfizer stock must also perform well? Not necessarily. While AMC has skyrocketed so far this year, Pfizer's share price has risen only 7%. 

While Pfizer's COVID-19 vaccine is certainly a key growth driver, its stock performance also depends on lots of other factors. In the first quarter of 2021, for example, Pfizer's other products generated more than three-fourths of its total revenue. 

Unsurprisingly, the correlation between AMC's and Pfizer's share prices is lower than the correlation between AMC stock and the other two biotech stocks. Moderna's share price has the highest correlation coefficient with AMC -- 0.93. (A coefficient of 1.0 reflects a perfect correlation.) 

Stocks to buy? 

There's no question that Pfizer, BioNTech, and Moderna are critically important to AMC's future. But does that automatically make these three stocks smart picks to buy? Of course not. However, the three vaccine stocks appear to be good picks nonetheless.

The key thing to watch with each of these stocks is how strong recurring sales of their COVID-19 vaccines will be. Moderna president Stephen Hoge recently stated that he thinks "that there's going to be a chronic booster need." If he's right, Moderna (and probably its top rivals as well) will be able to count on significant COVID-19 vaccine sales for years to come.

I suspect that annual vaccinations will be required. I also think that Pfizer, BioNTech, and Moderna will reinvest the enormous amounts of cash they make from their COVID-19 vaccines into building up their pipelines and potentially making strategic acquisitions.

No, it's not likely that any of these three vaccine stocks will be 25-baggers as AMC has been. However, AMC won't be able to deliver such sizzling gains going forward, either.