Ark Invest CEO Cathie Wood has earned a reputation for bold predictions. Her asset management firm became a Wall Street sensation during the early days of the pandemic as the Ark Innovation ETF delivered triple-digit returns in 2020. Unfortunately, those gains have since evaporated, but Wood hasn't budged from her medium-term price targets on Tesla (TSLA -2.44%) and Roku (ROKU 0.57%), both of which rank among the top three holdings in the Ark Innovation ETF.

Specifically, Ark estimates Tesla will trade at a split-adjusted $1,533 per share by 2026, which implies 688% upside from its current share price. And it estimates Roku will trade at $605 per share by 2026, which implies 924% upside from its current share price.

Are those forecasts realistic?

Tesla: $1,533 per share by 2026

Tesla has been a disruptive force in the auto industry from day one. In addition to popularizing electric vehicles (EVs), the company uses a novel direct-to-consumer sales strategy to drive efficiency by eliminating dealerships from the equation. It has also cultivated a premium brand image and inspired incredible demand without traditional advertising. In fact, Tesla topped the industry in battery electric car sales in the first half of the year, capturing 19% market share.

The company has also become a case study in operating efficiency. Thanks to innovative battery cell technology, Tesla pays less (per kilowatt-hour) for battery packs than any other automaker, according to Cairn Energy Research Advisors, and its leadership is expected to last through the decade's end. Additionally, its single-piece casting technique -- meaning the front and rear body of the Model Y are cast as a single piece of metal -- has greatly reduced welding robot count (and time spent welding) at the new Gigafactories in Texas and Berlin.

That relentless pursuit of manufacturing efficiency continued to pay off in the third quarter as Tesla once again achieved the highest operating margin in the auto industry. Despite missing deliveries estimates, the company still grew revenue 56% to $21.5 billion, and it generated record free cash flow of $3.3 billion.

Looking ahead, management says full self-driving technology will eventually be the greatest source of profitability. That is the cornerstone of Ark's investment thesis. Wood expects robotaxi revenue to approach $290 billion by 2026, while lower-margin EV sales will contribute about $480 billion to total revenue. That prediction is very ambitious at best and wildly unrealistic at worst. Tesla won't have a robotaxi in production until 2024, and scaling an autonomous ride-hailing service to $290 billion by 2026 sounds a bit farfetched.

That said, Tesla does have more miles' worth of autonomous driving data than its rivals, and data is the cornerstone of the artificial intelligence that will one day drive these vehicles. Tesla has also demonstrated its capacity for innovation on countless occasions, so it's reasonable to assume robotaxis will be a key part of its business at some future point.

While 688% returns by 2026 are probably unrealistic, this growth stock is still worth buying for patient investors.

Roku: $605 per share by 2026

Roku is the most popular streaming platform in the world, both in terms of devices and viewing time. In fact, Roku holds nearly twice as much market share in both categories as the next closest competitor. That makes Roku a valuable advertising partner, and it monetizes brand relationships with OneView, an ad tech platform that allows marketers to run targeted cross-channel campaigns on connected televisions (CTV), desktops, and mobile devices.

Unfortunately, many brands have cut their ad budgets due to softening demand as people continue to battle high inflation, and that trend hit Roku hard in the third quarter. Revenue rose just 12% year over year to $761 million, and the company posted a GAAP loss of $0.88 per share, down from a profit of $0.48 per share in the same period last year.

But investors shouldn't read too much into those results. Roku's still growing faster than several other ad tech companies. In fact, Alphabet reported 3% growth in ad revenue in the third quarter, while Meta Platforms actually saw sales decline 4%. Moreover, Roku is the most popular streaming platform by a wide margin, and that positions it for strong growth as the economic climate stabilizes.

Omdia estimates online video advertising will surpass traditional television advertising this year, growing into a $259 billion market by 2026. That's the cornerstone of Ark's investment thesis. Wood assumes Roku will see approximately $10 billion in online video advertising revenue in 2026, meaning it would have about 4% market share.

That estimate isn't unreasonable, but Ark also expects Roku to reach 157 million active accounts by 2026, up from 65.4 million in the most recent quarter. That implies annualized growth of 23% through the end of 2026 -- a meaningful acceleration from the 16% growth reported last quarter.

Roku will benefit as more ad dollars shift to online video, but economic uncertainty will probably slow active account growth in the near term as high inflation continues to suppress demand for streaming players and smart TVs. It seems unlikely shareholders will see 924% gains by 2026, but this growth stock is worth buying and holding.