Hasbrouck's Information Share

A stock trades on its primary exchange, three other lit exchanges, and a handful of dark pools; its futures contract trades on a derivatives exchange; an ETF that holds it trades everywhere else too. All of these venues' prices track the same underlying value, but they don't all learn new information at the same instant — one venue typically reacts first and the others catch up a few milliseconds or seconds later. Information share asks: of the total genuine price movement (not noise, not bounce — the permanent, information-driven component), what fraction originates in each venue?

The intuition: if venue A's price changes tend to predict venue B's subsequent price changes, but not the reverse, then A is where information arrives first — A is "leading" price discovery and B is following. Hasbrouck formalizes this using the same efficient-price/pricing-error decomposition as Hasbrouck's Pricing Error Variance, fit with a vector autoregression (VAR) across the linked price series, and computes each venue's information share as its contribution to the variance of innovations (surprises) in the common efficient price $m_t$.

Worked example, simplified. Suppose a stock trades on Exchange A (its primary listing) and is also tracked via a highly liquid futures contract on Exchange B. A VAR fit to five-second returns on both series finds that innovations to A's price explain 70% of the variance of the shared efficient-price innovation, while innovations to B's price explain the remaining 30%. Interpreted directly: Exchange A contributes roughly 70% of genuine price discovery, and the futures market contributes 30% — new information tends to show up in the primary listing first, with the futures market largely (but not entirely) following.

Second example, contrast with a stale market. For a heavily traded index name, a common empirical finding is closer to the reverse: futures markets, being more liquid and attracting the fastest informed traders, often show information shares well above 50%, sometimes 70–90%, with the underlying cash equities market largely reacting to futures moves rather than leading them. This is a genuinely useful, testable empirical question rather than something you can assume in advance — it depends on relative liquidity, the trader population in each venue, and market structure, and it can shift over time as venues change.

What this means in practice

Information share tells regulators and market participants which venue actually deserves to be treated as the "reference price" for surveillance, best-execution obligations, and circuit-breaker triggers — a venue with a low information share is mostly a follower, not a discoverer, of price. It's also directly relevant to trading strategy: if a fast venue reliably leads a slower one, that lead-lag relationship is potentially exploitable (subject to being fast enough and having access to both venues), which is exactly the kind of relationship latency-sensitive strategies are built to capture.

The technique reuses the efficient-price decomposition from Hasbrouck's Pricing Error Variance and depends on the same Vector Autoregression (VAR) machinery; see Market-By-Order Versus Market-By-Price Feeds for the underlying data granularity such a VAR typically needs.