Umit Turhan Coskun | Nurphoto | Getty Images

The price of bitcoin could rise to $150,000 by 2025, Bernstein said Tuesday in a note citing optimism about a bitcoin exchange-traded fund. 

Bernstein analyst Gautam Chhugani said the firm expects the U.S. Securities and Exchange Commission to approve a bitcoin ETF by the first quarter of 2024.

The bullish estimate is about five times the current price of around $34,000 and more than double bitcoin's all-time high of more than $67,000 set in November 2021.

Bernstein also expects that ETF approval would shift up to 10% of bitcoin's circulating supply toward ETFs. The approval would allow conventional investors to get bitcoin exposure directly from their investment portfolios. The only similar product is Grayscale's Bitcoin Trust, or GBTC, which presently holds around 3% of outstanding bitcoin, according to the note.

"You may not like Bitcoin as much as we do, but a dispassionate view of Bitcoin as a commodity, suggests a turn of the cycle," Chhugani wrote. "A good idea is only as good as its timing - SEC approved ETFs by world's top asset managers (BlackRock, Fidelity et al), seems imminent."

The prediction came in a note where Chhugani initiated coverage on several bitcoin mining firms, saying that the bitcoin "halving" in April 2024 — in which bitcoin rewards will be halved as part of a planned and recurring event baked into the currency's underlying code — will force "losing miners" to be "washed out," paving the way for big gains by the survivors.

Last week, the price of bitcoin reached $35,000, its highest level since May 2022. Investors have said they remain hopeful for a green light on the ETF by the end of the year after the SEC declined to appeal a key court ruling in Grayscale's lawsuit against it.

However, the court ruling does not guarantee the SEC will approve a bitcoin ETF. SEC Chair Gary Gensler has long criticized the crypto industry as being rife with "fraudsters and scam artists," so whether the regulator will continue to fight against crypto ETFs is an open question.

• Want to retire in 5 years? Here's how to invest for it, according to the pros
• Morgan Stanley says the average stock is breaking down, S&P 500 to fall to 3,900 by year-end
• This highly profitable industry is booming as the population ages
• This chip stock is getting a ton of love from Wall Street, and it's not Nvidia