Catherine Wood, founder and chief executive of money management firm ARK Invest, stands by her call that Tesla stock could go to $4,000 per share.

Wood told CNBC on Tuesday she plans to send a letter "today or tomorrow" to Tesla's board, outlining how she gets to that lofty number, which would represent a 1,200 percent increase and about a $700 billion stock market value.

ARK is an investor in Tesla.

On "Squawk on the Street," Wood said her bull case on Tesla has not wavered in the past two weeks since Elon Musk's tweet that he was considering taking the company private stunned Wall Street and drew the attention of regulators.

"Our conviction has increased recently because of their new chip. We think they're three years ahead of any other auto manufacturer," she said, also citing Tesla's advanced battery technology.

On the second-quarter conference call earlier this month, Musk touted the strengths of its upcoming autopilot hardware, featuring an artificial intelligence processor developed by Tesla.

Wood said going private would be the wrong decision for Tesla.

"He's showing us quarterly statements. He'll have to show private equity monthly [statements]," she said. "He won't be able to scale that company the way he wants to."

Wood, a money manager known for making bold calls, first revealed her prediction of $4,000 per share on Tesla in February. At the time, she said her "bear case" was $600, which would still be nearly double Monday's $308 close.

Shares of Tesla were turning in a second straight day of gains Tuesday after a 14 percent, four-session losing streak. However, the stock was still about 6 percent lower than its Aug. 6 close, the day before Musk's go-private tweet.

Musk has expressed the hope that if Tesla were to become a private company that public investors would keep their money in.

But many fund managers might have no choice but to get out, given the rules of their investment products to generally only put money into public companies.

Wood said she might be in this camp. "Given what we know of structure, we can't do it" because of ARK's exchange-traded funds.



