Being big isn't always easy. Large-cap stocks face a harder time delivering the level of growth that they had when they were smaller. It's also tempting the big companies to rest on their laurels, which increases the chances that innovative rivals disrupt their businesses.

However, these potential issues don't mean that investors must look to smaller stocks for great ideas. Here are three monster stocks to buy without any hesitation.

1. Amazon

With a market cap of nearly $1.4 trillion, Amazon (AMZN -0.66%) is one of the biggest companies in the world. It dominates e-commerce. Amazon Web Services (AWS) ranks No. 1 in the cloud services market. Is the company running out of ways to generate strong growth? Not at all.

There's still significant room for Amazon to grow in e-commerce. In the second quarter of 2023, e-commerce accounted for only 15.4% of total U.S. retail sales. Market penetration in some countries is even smaller. No company is as well positioned as Amazon to expand the e-commerce market.

AWS has even better growth prospects. The surging adoption of generative AI will especially serve as a tailwind. Amazon CEO Andy Jassy predicts that the cloud services market will increase from around 5% of IT spending to more than 90% within the next 10 to 15 years. This isn't an unrealistic scenario. If Jassy's right, Amazon's AWS business should deliver explosive growth.

The company has also moved into new areas, including healthcare, self-driving cars, and supply chain management, all of which present tremendous opportunities. With improving profitability and free cash flow, Amazon should keep up its winning ways for years to come.

2. Mastercard

Mastercard (MA -0.64%) is a financial services giant with a market cap of nearly $380 billion. It's the second-largest payment-processing company in the world, trailing behind only Visa

The company boasts two economic moats. It enjoys network effects as more consumers use its credit cards, and the more merchants accept its cards, the stronger its business becomes. Mastercard also has scale advantages thanks to its capital-light model. Importantly, the company doesn't assume any credit risk at all with its credit cards; it only processes payments.

We can easily see the fruit of these moats in Mastercard's recent financial performance. The company's revenue jumped 14% year over year in the second quarter of 2023 to $6.3 billion. Its adjusted earnings soared 29% to $2.7 billion. Mastercard's operating margin rose to an impressive 58.3%. 

Wall Street looks for strong growth in the future, too. Analysts project that Mastercard's earnings will grow by an average of close to 17% annually over the next five years. That's a much higher growth rate than the company generated over the last five years -- a period when its share price nearly doubled. 

3. Vertex Pharmaceuticals

Vertex Pharmaceuticals (VRTX -0.08%) now stands as one of the biggest biotech companies with a market cap approaching $100 billion. A decade ago, the company was worth less than $20 billion. Vertex's cystic fibrosis (CF) franchise drove its spectacular growth.

CF drugs continue to make the big biotech boatloads of money. It will be years before Vertex's nearest potential competition in treating the underlying cause of the rare genetic disease can even have a shot at launching a rival therapy. In the meantime, Vertex hopes to move forward with seeking regulatory approvals next year for a triple-drug combo that should be its most powerful and profitable CF therapy yet. 

But CF isn't Vertex's biggest growth opportunity these days. The company awaits approvals for exa-cel in curing the rare blood disorders sickle cell disease and transfusion-dependent beta-thalassemia. It appears to be in great shape for a near-term commercial launch of the non-opioid pain drug VX-548 as well. Both have huge market opportunities.

Looking a little farther into the future, Vertex could have the first approved drug for treating APOL1-mediated kidney disease on the way. This indication affects more patients than CF does. In addition, Vertex's pipeline features three programs in early stage testing that hold the potential to cure type 1 diabetes.

You might think the biotech stock would be priced at a premium with its exceptional growth prospects. That's not the case, though. Vertex's price-to-earnings-to-growth (PEG) ratio is a ridiculously low 0.53. This monster stock is a no-brainer buy right now, in my view.