Trend arbitrage, bid-ask spread and market dynamics
Trend arbitrage, bid-ask spread and market dynamics
This paper introduces a novel approach to studying market microstructure by analyzing linear trends in tick-level bid-ask data. The author derives a trend arbitrage inequality that relates the bid-ask spread to the absolute trend slope, market reaction time, stock-specific latency, and transaction costs. Using tick data from 33 stocks across five European exchanges, the paper identifies trends via a linear fitting algorithm with a chi-squared trigger. The key empirical finding is that the distribution of the response time (τ_resp = spread/|trend| - average update time) is log-normal, with a sharp front edge that defines the market reaction time τ_M. This τ_M is found to be exchange-specific, ranging from about 1.2 seconds in Frankfurt to 5.5 seconds in Madrid, and is interpreted as the latency of the exchange system. The analysis also shows that the product of trend and update time (μ·τ_u) is normally distributed with a standard deviation such that three sigma lies within the tick size, indicating that price updates occur frequently enough to prevent trend arbitrage. When tick size is subtracted from the spread, the measured τ_M values across exchanges converge to a narrow range of 0.6-1.2 seconds, suggesting that tick size absorbs much of the stock-specific latency. The paper further identifies three investor groups (fast, medium, slow) with different fee and latency characteristics. A simulation using a random walk model reproduces the normal distribution of μ·τ_u, suggesting a duality between trend-based and return-based descriptions of price dynamics. Overall, the study provides a microstructure framework linking trend, spread, latency, and tick size, with implications for understanding market efficiency and arbitrage opportunities.
Highlights
- 1Introduces linear trend as a novel tool for analyzing market microstructure and bid-ask spread dynamics.
- 2Derives and tests a trend arbitrage inequality linking trend, spread, market reaction time, and update frequency.
- 3Measures market reaction time (latency) from tick data, showing it is exchange-specific and ranges from 0.6 to 5.5 seconds.
- 4Demonstrates that tick size influences price update frequency and absorbs stock-specific latencies.
- 5Shows equivalence between trend-based and random walk descriptions of price dynamics via simulation.
Methods
- MLinear trend fitting to intraday mid-prices with a chi-squared trigger to detect trend changes.
- MTrend arbitrage inequality derived from a simple investor-specialist game, tested on tick data.
- MStatistical analysis of distributions of response time (τ_resp) and product of trend and update time (μ·τ_u).
- MSimulation of random walk model to compare trend properties with empirical data.
Results
- RMarket reaction time τ_M is exchange-specific: Amsterdam 1.9s, Frankfurt 1.22s, Madrid 5.5s, Milan 5.1s, Paris 2.1s.
- RDistribution of τ_resp = Spr/|μ| - τ_u is log-normal, with a sharp front edge corresponding to τ_M.
- RProduct μ·τ_u follows a normal distribution with 3σ within the tick size, indicating efficient price updating.
- RAfter subtracting tick size, τ_M values across exchanges converge to 0.6-1.2 seconds, suggesting tick size absorbs latency.
- RInvestor groups (fast, medium, slow) are identified in the τ_resp vs 1/|μ| plot, with distinct fee and latency parameters.
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