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Cryptocurrency exchange Gemini (NASDAQ: $GEMI ) has been thrashed since it held its initial public offering (IPO) last September. But there's now reason for cautious optimism with the stock.

Gemini is the crypto exchange run by twin brothers Tyler and Cameron Winklevoss, who famously claimed that Mark Zuckerberg stole their idea for Facebook, now Meta Platforms (NASDAQ: $META ).

The brothers plowed a legal settlement they received from Meta into Bitcoin (CRYPTO: $BTC ), buying the cryptocurrency early on and holding through thick and thin.

The Winklevoss twins founded Gemini in 2014 as a crypto exchange and custodian bank. The company had the misfortune of going public last September right before the crypto winter descended.

The result has been that GEMI stock has plunged 77% since the IPO to currently trade at $7.25 U.S. per share.

The stock has sunk as the prices of Bitcoin (BTC) and Ethereum (CRYPTO: $ETH ) have effectively been cut in half since last August.

Gemini, which remains unprofitable, has also issued its first few earnings reports, which failed to impress Wall Street.

Despite the drubbing GEMI stock has suffered, there's reasons for optimism that the share price might turnaround, especially as cryptocurrencies recover.

In recent months, Gemini has cut 25% of its workforce and announced that it is winding down its overseas operations.

Gemini said that it will cease operations in the United Kingdom, European Union (EU), and Australia so that it can focus on the U.S. market.

The exchange also announced the departure of several senior executives in a broad house cleaning.

Gemini parted ways with its Chief Operating Officer (COO) Marshall Beard, Chief Financial Officer (CFO) Dan Chen, and Chief Legal Officer (CLO) Tyler Meade, all at once.

Additionally, Gemini is pushing into the red-hot prediction market space, launching its own betting site on its platform.

While most Wall Street analysts don't yet recommend GEMI stock, they do like the renewed focus on the U.S. market, streamlined operations, and gamble on prediction markets.

With a market capitalization of only $855 million U.S., Gemini is best described as a micro-cap stock, a term reserved for securities valued at less than $1 billion U.S.

For investors, it might be best to view Gemini as a startup company and speculative investment. But it could be a good way to play the eventual rebound in crypto prices.