P/E and P/B: what they are and how not to get the math wrong

The two most-used multiples for judging whether a stock is cheap or expensive. Also the two most misread — because "cheap" by the math and "cheap" for real don't always line up.

P/E — Price to Earnings

P/E = market cap ÷ earnings (or share price ÷ earnings per share)

It tells you how many years of current profit you pay for the company. A P/E of 8 means "8 years of earnings". Lower looks cheaper — but the denominator is the trap. Negative earnings give a meaningless negative P/E; peak-cycle earnings make the P/E look low exactly when the stock is expensive.

P/B — Price to Book

P/B = market cap ÷ shareholders' equity

It tells you how much you pay per real of book equity. A P/B below 1 means buying the company for less than its book value — which can be a bargain, or a warning that the market doesn't trust those assets.

A low P/E isn't the same as cheap. Cyclical companies (commodities) show a minimum P/E at the top of the cycle, when profit is inflated — and a sky-high or negative P/E at the bottom. Buying "low P/E" without looking at where the profit comes from is the classic trap. P/E and P/B are the start of the question, not the answer.

Real B3 examples (2024)

Ticker	P/E	P/B	Reading
WEGE3	33.2	9.04	expensive — the market pays for quality and growth
LREN3	12.0	1.34	moderate multiple, retail
VALE3	7.7	1.18	"cheap" — but it's a commodity, mind the cycle
SUZB3	−10.2	2.23	negative P/E: it posted a loss that year

WEG at 33× and Vale at 7.7× doesn't mean "buy Vale". Expensive WEG reflects 38% returns and growth; cheap Vale reflects commodity earnings that can shrink. The multiple must be read together with quality and the cycle.

The detail almost nobody gets right

At Dados B3, the price behind P/E and P/B is that of the first session after the report was actually published — never the Dec-31 close paired with earnings that only came out months later. Without that, the history "knows the future" and the multiple lies. Details in Look-ahead-free backtesting.

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Honest limitations

P/E is useless for negative or cyclical earnings without context; P/B misleads for intangible-heavy businesses.
They're backward-looking and say nothing about the future price.
Not investment advice. Cheap by the math can be expensive in reality.