St. Petersburg Paradox (Valuation)

📝 Overview

In the context of the 2004 Meeting, Warren Buffett and Charlie Munger discussed the St. Petersburg Paradox to warn investors about the mathematical dangers of projecting high growth rates into perpetuity when valuing businesses.

🧠 The Mathematical Trap

The original paradox describes a theoretical lottery game with an infinite expected value, yet no rational person would pay a huge sum to play it. In investing, the paradox manifests when a growth stock's valuation is calculated using a discount rate that is equal to or less than the projected growth rate.

• The Formula Failure: If a business is projected to grow its earnings at 15% per year indefinitely, and an investor uses a 10% discount rate, the resulting "intrinsic value" becomes infinite.
• The "St. Petersburg" Warning: Buffett uses the paradox to show that even slight adjustments to growth assumptions (moving from 14% to 15%) can collapse the valuation model or produce astronomical numbers that have no basis in economic reality.

⚠️ Investing Implications

• The Danger of Growth: Buffett notes that growth is "a much more dangerous variable" to estimate than profitability. While high-growth companies like Google (discussed as an inspiration for the Owner's Manual in 2004) are attractive, the mathematical penalty for being even slightly wrong about the duration or rate of that growth is catastrophic.
• The Ceiling of Reality: Munger often adds that no business can grow faster than the overall economy forever. Therefore, any growth assumption must eventually transition to a terminal rate lower than the discount rate to avoid the St. Petersburg trap.

💬 Direct Quotes

• "If you find a business that can truly grow at a rate higher than your discount rate forever, its value is infinite. The problem is, businesses rarely do that, and investors' math often fails them before the business does." — (Synthesized from 2004 Meeting)

🔗 Connections

• Source: 2004 Meeting
• Concept: Intrinsic Value, Owner's Manual
• Related: Discounted Cash Flow

• References: 2004 Meeting
• Index: index