WarrenCo

Margin of Safety.

What separates investing from gambling is the gap you insist on between what something is worth and what you pay for it. Graham called this the margin of safety, and condensed it into three words because he thought it was the only motto an investor needed. The chart below is the visual reason why.

Chart 1 · The cushion

Three buyers, one company. Same intrinsic value of $100, three different prices.

The tan band is the margin of safety — the gap between what you paid and what it’s worth. A wider band buys two things at once: a bigger return if you’re right, and more room to be partly wrong without losing money.

Intrinsic value = $100 10% $90 paid Tight Buy at $90 · 10% MoS Implied return: +11% 33% $67 paid Good Buy at $67 · 33% MoS Implied return: +49% 50% $50 paid Wide Buy at $50 · 50% MoS Implied return: +100%

Two free options. When the price you pay is well below what something is worth, you get two things for one decision. One: if you’re right about intrinsic value, the price eventually converges and you earn the gap as return. Two: if you were partly wrong, the gap absorbs the error before it eats your capital. Graham’s phrase for the second one was protection against analyst overconfidence and bad luck. Both are paid for in the same currency: patience to wait for a wide cushion.

Chart 2 · The reward shape

If you’re right about value, the price converges. Your implied return is m ÷ (1 − m).

Same convex math you saw on the loss page, mirror-imaged. Each 10% deeper discount doesn’t add 10% to your reward — it multiplies it.

0% 50% 100% 200% 300% 400% Implied return when price converges to intrinsic value MoS 10% +11% MoS 20% +25% MoS 30% +43% Graham’s minimum. MoS 40% +67% MoS 50% +100% MoS 60% +150% MoS 70% +233% MoS 80% +400%

The math. Buy at price p, intrinsic value v. Margin of safety m = (v − p) ÷ v. If price eventually returns to v, your gain is r = m ÷ (1 − m). This is the same convex function as the recovery curve on the loss page, looked at from the other end of the telescope. The loss page asks: how far must the climb back be after a fall? This page asks: how steep is the climb up if the fall already happened to someone else.

Margin of safety m = (v − p) ÷ v, where v is your intrinsic-value estimate and p is the price paid. Implied return when price converges to v: r = m ÷ (1 − m). The model assumes a one-shot convergence and ignores time-to-convergence; in practice the speed of convergence varies, which is why Graham coupled margin of safety with diversification and held positions for years. Cross-reference: the Patience Curve shows the corresponding empirical relationship at the index level.