Graham Number

The Graham number is a formula Benjamin Graham developed to set an upper bound on what an investor should pay for a stock. It uses the square root of (22.5 × earnings per share × book value per share) to produce a single fair-value estimate that blends profitability and balance-sheet strength.

Graham’s philosophy: quantifying a margin of safety

Benjamin Graham—the father of value investing and author of The Intelligent Investor—believed that safety comes from a margin of safety: buying a stock at a price well below its intrinsic value. But what is intrinsic value? How does an investor calculate it without intuition or guesswork?

The Graham number is Graham’s answer. Rather than elaborate discounted-cash-flow models or subjective judgment calls, it uses a straightforward mechanical formula applied to two financial realities: what the company earns (earnings per share) and what it owns (book value per share). The formula balances income and assets, producing a single fair-value ceiling.

The formula broken down

The Graham number is:

√(22.5 × EPS × Book Value per Share)

The constant 22.5 encodes Graham’s view of reasonable valuation: it assumes a fair price-to-earnings ratio of about 15 and a fair price-to-book ratio of about 1.5. Multiply them together and you get 22.5. Taking the geometric mean (square root) of (22.5 × earnings × book value) reflects the idea that a stock’s fair value should rest somewhere between its earnings power and its asset backing.

Example: A company with earnings per share of $5 and book value per share of $20 would have a Graham number of:

√(22.5 × 5 × 20) = √(2,250) ≈ $47.43

If the stock trades at $35, it is trading below the Graham number, suggesting a margin of safety. If it trades at $55, it has climbed above it, suggesting caution.

Why earnings and book value together?

Earnings tell you how much profit the business generates each year. Book value tells you how much capital is invested in the business. A company could have high earnings but weak assets (perhaps it operates asset-light, or has written down past investments); it could have substantial assets but generate weak returns.

By taking both into account, the Graham number avoids overvaluing a business with temporarily inflated earnings or undervaluing one with hidden asset value. The geometric mean naturally penalises companies that excel in only one dimension.

When Graham number is most reliable

The formula works best on mature, stable, profitable companies: industrials, banks, utilities, established consumer brands. For these businesses, historical earnings are a reasonable proxy for future earnings, and book value roughly reflects what the assets are genuinely worth.

It is much less reliable for technology companies, growth stocks, or turnarounds. A software company might have minimal book value yet generate enormous earnings; applying the Graham number would dramatically undervalue it. Conversely, a company in distress might have a high book value that is about to be written down; the Graham number would suggest false safety.

The margin of safety in practice

Graham himself suggested buying only when the stock price was at least 25% below the Graham number. This extra cushion accounts for forecast error, business deterioration, and plain bad luck. A stock at the Graham number might be fairly valued but offers no room for error. A stock at 75% of the Graham number offers genuine protection.

Over decades, investors who stuck to this discipline—buying stocks at deep discounts to their Graham numbers—tended to outperform those who chased full valuations. The margin of safety is not a guarantee, but it shifts the odds in the investor’s favour.

Modern criticisms and evolution

The Graham number treats past earnings as equivalent to future earnings, which is reasonable for stable companies but risky in a changing world. A company facing technological disruption, new competition, or regulatory headwinds might have solid historical earnings but terrible forward prospects. The Graham number would not flag this.

Additionally, the constant 22.5 was set in an era of lower inflation and different interest rates. Some investors adjust it upward or downward to reflect current discount rates or macro conditions—though this introduces judgment back into what was meant to be a mechanical method.

For these reasons, modern value investors often use the Graham number as a starting point rather than a final answer. They pair it with discounted cash flow analysis, industry trends, competitive positioning, and management quality. But as a quick screening tool—a way to identify stocks trading at a clear discount to a defensible fundamental benchmark—it remains powerful.

See also