The Graham Number is a simple but powerful formula for estimating the maximum price a value investor should pay for a stock. Developed by Benjamin Graham — mentor to Warren Buffett and the founder of modern value investing — it distils decades of security analysis into a single mathematical constraint rooted in two valuation ratios.

The origin of 22.5

In The Intelligent Investor (1949), Graham recommended that defensive investors apply two simultaneous ceilings: the stock's price-to-earnings ratio should not exceed 15, and its price-to-book ratio should not exceed 1.5. A stock trading at exactly P/E = 15 and P/B = 1.5 satisfies both constraints — and the product of those limits gives the constant 22.5.

Taking the square root of 22.5 × EPS × BVPS normalises the two-constraint system into a single price estimate. If the stock price equals the Graham Number, the product P/E × P/B = 22.5 exactly. One ratio can exceed its individual ceiling (P/E > 15 or P/B > 1.5) as long as the other is proportionally lower — the formula captures the trade-off.

When the Graham Number works — and when it doesn't

The formula was designed for defensive investors: people prioritising capital preservation over maximum return. It works best for stable, dividend-paying companies in mature industries — utilities, financials, industrials — where earnings are predictable and book value is a meaningful measure of assets.

The Graham Number breaks down for:

  • Growth stocks — Amazon, Google, and Nvidia trade at many multiples of their Graham Number. Their value lies in future earnings growth, not current EPS and book value.
  • Negative earnings — The formula requires positive EPS. Companies burning cash are outside its scope.
  • Negative book value — Highly leveraged buybacks (Apple) or accumulated losses can produce negative equity, making BVPS meaningless here.
  • Intangible-heavy businesses — Software, pharma, and brand companies carry much of their value in IP, patents, and goodwill — none of which appear in book value consistently.

Using Margin of Safety as a discipline

Graham's most enduring idea is not the formula itself but the principle of Margin of Safety: always buy at a significant discount to intrinsic value to protect against errors in your estimate. He recommended at least 33% for defensive investors — meaning buy only when Price ≤ 0.67 × Graham Number.

This buffer absorbs three types of risk: (1) your EPS estimate could be too optimistic; (2) book value may be overstated due to goodwill or inventory inflation; (3) the market may take years to recognise a stock's value, and you need to survive the wait. A large margin of safety is not a prediction that the stock will rise — it's insurance that you won't lose much if you're wrong.