Anthropic's roadshow is selling the future of AI. Four centuries of hot IPOs say the first trade is rarely the best one.

The AI lab is asking for as much as $1.4 trillion at the top of its $70-to-$78 range, counting every possible share. Trading could start as soon as next week. Rival OpenAI (OPAI.PRV) may not be far behind: OpenAI president Greg Brockman said last week the company could be ready to go public next year.

History has a warning for anyone planning to buy on the first day. The world's first IPO, the Dutch East India Company, began trading in 1602. Its stock took about three decades to double.

This year brought two fresh reminders. SpaceX (SPCX) opened at $150 in June, $15 above its IPO price, and soared about 40% in its first week. By August, it was in a nearly 30% hole. Five months later, SpaceX is still below its first trade.

SpaceX shot above $200 in its first week, then fell below its $135 IPO price by mid-July. · Yahoo Finance AlphaSpace

Cerebras (CBRS) had it worse. The AI chipmaker opened at nearly double its $185 IPO price in May. Its first close is still its best, and the stock now trades at about half what IPO buyers paid.

The price tag problem

Anthropic's growth is anything but typical. Revenue in the first nine months of the year was 13 times what it was a year earlier. But investors are being asked to pay up for it. At $78 a share, Anthropic would trade at about 29 times its sales over the past year, by Yahoo Finance calculations.

University of Florida professor Jay Ritter tracked more than 4,000 IPOs of companies with at least $100 million in sales since 1980. Those priced at 20 to 40 times sales gained about 3% on average over three years from their first close. The cheapest gained about 41%.

Jay Ritter, University of Florida, Yahoo Finance analysis

There's a bright spot for Anthropic. IPOs of the biggest companies, those with more than $1 billion in sales, did about as well as the market.

A big first-day pop would make the math worse. A jump of about 40% would push Anthropic past 40 times sales, where IPOs lost nearly half their value over three years.

That pop goes to whoever buys at the IPO offering price, usually big Wall Street firms and their wealthy clients. It has averaged nearly 20% since 1975, Ritter's data shows, and everyone buying after the open pays for it. This time, Anthropic is setting aside up to a fifth of its shares for retail brokers including Schwab, Fidelity, and Robinhood.

Other companies are racing to sell stock before the deal, competing for the same investors' dollars. "The Anthropic IPO is almost becoming this magnet where everybody's trying to raise liquidity in front of them," Peachtree Creek Investments founder Conor Sen said on Yahoo Finance's Market Hang in November.