PIN: The Probability Of Informed Trading

A market maker quoting a stock loses money specifically on trades from counterparties who know something about the stock's true value that hasn't been priced in yet — an informed trader who just learned bad news sells into the bid before the price adjusts, and the market maker who bought that stock is left holding it as the price then falls. This is adverse selection, and PIN — the probability of informed trading — puts a number on how much of it a given stock's order flow contains, estimated purely from counting buys and sells each day, with no access to who actually placed each order.

The model imagines each trading day as one of two types: a no-news day, where both buy and sell orders arrive purely from uninformed liquidity traders at some background rate, or a news day (which happens with probability $\alpha$), where in addition to the usual background flow, informed traders arrive at a higher rate $\mu$, all trading in the same direction — buying if the news is good, selling if it's bad. Fitting this model to the observed daily counts of buy and sell trades (via maximum likelihood) yields estimates of the arrival rates, and PIN is defined as

$\text{PIN} = \frac{\alpha \mu}{\alpha \mu + 2\varepsilon}$

where $\alpha$ is the probability any given day is a news day, $\mu$ is the informed-trader arrival rate on a news day, and $\varepsilon$ is the background (uninformed) arrival rate on each side. In words: PIN is the informed order-flow rate as a fraction of total order flow (informed plus both sides of uninformed background flow) — the share of all trading that comes from people who know something.

Worked example. Suppose fitting the model to a stock's daily buy/sell counts over a year yields $\alpha = 0.25$ (a news event occurs roughly one day in four), $\mu = 60$ (informed traders submit about 60 orders on a news day), and $\varepsilon = 25$ (uninformed buy orders and, separately, uninformed sell orders each arrive at about 25 per day in the background). Then $\text{PIN} = \frac{0.25 \times 60}{0.25 \times 60 + 2 \times 25} = \frac{15}{15 + 50} = \frac{15}{65} \approx 0.23$ — about 23% of this stock's total order flow is estimated to be informed.

Second example, comparing two stocks. A heavily covered large-cap with many analysts and near-continuous public information flow might show $\alpha = 0.15$, $\mu = 40$, $\varepsilon = 80$: $\text{PIN} = \frac{0.15 \times 40}{6 + 160} = \frac{6}{166} \approx 0.036$, or about 3.6%. A thinly covered small-cap with sporadic disclosure might show $\alpha = 0.40$, $\mu = 30$, $\varepsilon = 8$: $\text{PIN} = \frac{0.4 \times 30}{12 + 16} = \frac{12}{28} \approx 0.43$, or 43%. The small-cap's order flow is estimated to be more than ten times as informed — consistent with the intuition that names with less continuous public information are exactly where a market maker faces the most adverse selection risk per trade.

What this means in practice

Market makers use PIN-style reasoning (even informally) to set wider spreads on names where informed trading risk is higher, since the spread must compensate for adverse-selection losses in addition to covering inventory and operational costs. Academic finance has also used PIN as a proxy for information asymmetry when studying cost of capital, liquidity, and corporate disclosure policy, since a firm with sustained high PIN suggests a persistent information gap between insiders/informed traders and the rest of the market.

PIN formalizes the same adverse-selection intuition behind the The Kyle Model using observable trade counts instead of a continuous-time price-impact framework; see Order-Flow Imbalance for a simpler, more commonly used real-time proxy for the same underlying informed-flow concern.