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Anthropic's initial public offering, expected no earlier than mid-October, will test how hungry the financial markets still are for exposure to artificial intelligence, with backers seeking a valuation of $2 trillion or more that would top Space Exploration Technologies as the biggest IPO ever. Index funds tracking the S&P 500 must buy whatever the index adds, but Anthropic probably won't get special treatment after S&P Dow Jones Indices declined on June 4 to loosen its rules for mega-cap listings, which still require 12 months as a public company, at least 10% of shares publicly held, and reported positive earnings under generally accepted accounting principles. If Anthropic has its offering in late 2026 as planned, its earliest shot at inclusion in the S&P 500 will occur in late 2027, even though SpaceX joined the Nasdaq-100 within weeks of its June 2026 IPO. Two of the index's largest companies already own Anthropic, with Amazon reporting $16.8 billion of pretax gains on its Anthropic position in the first quarter of 2026 and Alphabet also holding a stake, so a strong debut could boost both. Per finance professor Jay Ritter at the University of Florida, across 9,343 U.S. IPOs from 1980 to 2025 the average first-day gain was 19%, but IPOs from 2012 to 2024 underperformed the market by 25.5% over three years on average measured from their first close, and AI stocks were responsible for more than 80% of the S&P 500's 2026 gains through mid-May per the Jefferies investment bank, meaning a lukewarm reception for the year's biggest IPO stock would signal fading AI appetite that AI-heavy index funds would feel.