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Brian Armstrong, founder and CEO of Coinbase; Cathie Wood, founder and CEO of ARK Invest.
Getty Images North America for Armstrong; ARK Invest for Wood.

Cathie Wood's Ark Invest reduced its Coinbase holdings on Monday for the first time, selling as the stock rose in the wake of a rally in bitcoin to a five-month high.

The crypto exchange's stock gained nearly 6% to reach $262.91 per share in intraday trading Monday, but closed 3.3% higher at $256.50 per share. Bitcoin topped $57,000 the same day, taking its year-to-date gains to 96%.

Wood's Ark Innovation ETF sold 98,427 shares in Coinbase, worth more than $25 million at Monday's closing price. The stock is still the flagship fund's fourth-largest holding after Tesla, Teladoc Health, and Roku, according to company data.

Despite its recent gains, Coinbase's stock is down 21% so far this year. It was changing hands at $254.76 per share, down 0.7% in early trading Tuesday.

The crypto company's share movements track bitcoin prices and trading volumes, some analysts suggest. "As bitcoin prices go, so goes Coinbase's stock," said David Trainer, CEO of investment research firm New Constructs.

Wood's key investing strategy typically involves a buy-the-dip approach. At various points this year, her funds have bought into short-term declines in bitcoin, Peloton, Zoom, and Ginkgo Bioworks after it was slammed by a short-seller. She has predicted that bitcoin will surge to $500,000 in five years.

Two other funds, Ark Next Generation Internet ETF and Ark Fintech Innovation ETF, also hold Coinbase stock. Together, all three combined have 6.3 million shares worth about $1.6 billion. The crypto exchange made its trading debut on the Nasdaq in April.

Separately on Monday, the Ark Innovation ETF increased its exposure to Teladoc, Crispr Therapeutics, and Intellia Therapeutics. It also sold about 16,000 in Warren Buffett-backed Chinese electric-vehicle company BYD.

Read More: A 'bitcoin maximalist' old school value investor breaks down why he thinks the cryptocurrency will hit $100,000 this year - and reveals the 2 altcoins he holds as speculative plays

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