Cathie Wood is the CEO of Ark Invest, whose widely followed investment funds own shares of lots of different stocks -- many of which have performed quite poorly in the stock market downturn. And to be fair, some of them have serious unanswered questions from a long-term perspective.

However, there are some Wood stocks that look like excellent opportunities for long-term investors. Here are three in particular that make up significant portions of one or more Ark ETFs that look attractive to buy and hold for the next decade or more.

E-commerce is still in its early stages

Shopify (SHOP 0.81%) is one of the largest holdings in Wood's funds, and it's one that she continues to buy.

There's a lot to like about Shopify right now. Its recent results were much stronger than expected, and the company demonstrated impressive pricing power by rolling out price increases earlier this year. In the first quarter, gross merchandise volume increased by 15% year over year, and thanks to the aforementioned price increases, revenue grew by 25%. Shopify Payments continues to gain traction, and the company's recent decision to exit the logistics business and focus on its core e-commerce platform seems to be a smart one.

Furthermore, it's worth noting that Shopify could still be in the relatively early stages of capturing its market opportunity. Just 15% of all retail sales currently take place over e-commerce, but that figure has been on a clear upward trajectory for about two decades.

Excellent momentum despite poor stock performance

Wood is a big fan of financial technology, or fintech, and one of Ark Invest's largest fintech holdings, Block (SQ 3.04%), looks like an attractive opportunity right now.

Although the stock is down by more than 75% from its 2021 highs, the business continues to grow at an impressive pace, especially on the Cash App side, where gross profit was up 49% year over year in the first quarter. Cash App now has 53 million active users, 36% more than in 2021, and the company has done a great job of monetizing adjacent products such as the Cash App Card, which 20 million customers use. On the Square side of the company, gross payment volume is now over $180 billion on an annualized basis, up 55% over 2021 levels.

Block may be just scratching the surface of its potential, especially when it comes to global expansion. Sixteen percent of its gross profit now comes from outside the U.S. -- up from just 8% in 2021, but still a relatively small part of the total. Cash App and Square will certainly continue to roll out new monetizable features over time, and the acquisition of Afterpay is starting to produce results.

One of Cathie Wood's biggest winners

On average, Ark Invest's funds have nearly quintupled their money on Nvidia (NVDA 0.66%). The tech giant is near its all-time high as of this writing on strong results and optimism about AI applications, but there's reason to believe the company could become much larger in the years ahead.

In the first quarter, Nvidia's revenue jumped by 19% sequentially. Growth was especially strong in the data center side of the business -- which makes up well over half of the revenue -- but the entire company performed quite well. The automotive segment in particular is one to watch as electric-vehicle and autonomous technology evolves, as it makes up a relatively small part of Nvidia today but has more than doubled its revenue over the past year.

In short, Nvidia should be a major beneficiary of several major tech trends (artificial intelligence, autonomous driving, cloud computing, augmented reality, and more), and it's difficult to see how its growth will end anytime soon.

Buy for the long term

As a final thought, while all three of these businesses have tremendous long-term potential, I have absolutely no idea what their stocks will do over the coming weeks and months. Even if things go well, it's wise to expect significant volatility. So these are best suited as long-term investments, and I'm confident that those who buy with a decade or more on the horizon will be glad they did.