Trade run structure

Here's a microstructure concept that rarely gets discussed outside market-making desks: trade runs — consecutive sequences of same-direction trades. Their statistical properties reveal the hidden structure of order flow in ways that aggregate volume metrics completely miss.

The theoretical basis

Lillo & Farmer (2004) made a striking empirical discovery: order flow in equity markets exhibits long-range autocorrelation, with a Hurst exponent significantly above 0.5. Buys tend to follow buys, and sells follow sells, at horizons far longer than can be explained by individual order splitting. They attributed this to the herding behavior of institutional investors and the mechanical persistence of algorithmic execution.

Earlier, Hasbrouck (1991) showed that the autocorrelation structure of trade signs (buy/sell sequences) carries information about the permanent price impact of trades. Trades that cluster into runs tend to have higher permanent impact than isolated trades — because runs are the signature of informed order flow that the market hasn't yet fully absorbed.

Bouchaud et al. (2004) formalized this in their propagator model, showing that the long memory of order flow, combined with a power-law decay in individual trade impact, produces a market that is approximately efficient despite highly predictable order flow.

What we measure

• Maximum run length (buy/sell separately) — the longest uninterrupted same-direction streak. Long runs signal sustained directional pressure — either a large order executing incrementally or multiple participants leaning the same way.
• Mean run length — average persistence before a direction flip. Higher means more serial correlation in the tape.
• Run imbalance ratio — (max_buy_run − max_sell_run) / (max_buy_run + max_sell_run). Captures asymmetry in directional persistence.
• Flip rate — fraction of trades that change direction. High flip rate = choppy, mean-reverting tape. Low flip rate = persistent flow.
• Price change on direction flip — how much price moves when a run ends. Large price changes on flips indicate that runs represent genuine information being incorporated; small changes suggest noise.

Practical implications

The flip rate is directly related to the Roll (1984) model of the bid-ask bounce: in a pure noise-trading world with constant spreads, every trade should alternate between bid and ask, producing a flip rate near 1.0 and negative first-order return autocorrelation exactly equal to the squared half-spread. Deviations from this benchmark — particularly low flip rates — indicate that something beyond the mechanical bid-ask bounce is driving the tape.

Run imbalance is particularly powerful: if buy runs average 8 trades but sell runs average 3, buyers are sustaining pressure longer. This asymmetry often precedes continued price movement — it's the microstructure expression of the order flow autocorrelation that Lillo & Farmer documented at daily horizons, compressed into intrabar timescales.

References:

• Lillo, F. & Farmer, J.D. (2004). "The Long Memory of the Efficient Market." Studies in Nonlinear Dynamics & Econometrics, 8(3).
• Hasbrouck, J. (1991). "Measuring the Information Content of Stock Trades." Journal of Finance, 46(1), 179–207.
• Bouchaud, J.-P., Gefen, Y., Potters, M. & Wyart, M. (2004). "Fluctuations and Response in Financial Markets: The Subtle Nature of 'Random' Price Changes." Quantitative Finance, 4(2), 176–190.
• Roll, R. (1984). "A Simple Implicit Measure of the Effective Bid–Ask Spread in an Efficient Market." Journal of Finance, 39(4), 1127–1139.