Almgren Thum Hauptmann Li 2005

“Direct Estimation of Equity Market Impact” by Robert Almgren, Chee Thum, Emmanuel Hauptmann and Hong Li (Risk, July 2005) fits a market-impact model to a large dataset of US equity-desk trades from Citigroup. It is the empirical companion to Almgren Chriss 2000: the 2000 paper assumed permanent and temporary impact functions of a particular shape; this paper measures them from real institutional trade data. Impact is decomposed into a permanent component — a lasting price shift, taken as linear because a linear permanent impact is the only specification consistent with no statistical arbitrage — and a temporary component, a concave, mean-reverting cost of demanding liquidity that depends on the trading rate.

The headline empirical result is that the authors reject the pure square-root law for temporary impact in favour of a 3/5 power law (exponent ≈ 0.6) across the order-size range they study. Impact is parameterised by the dimensionless trade size X/(V·T) — shares traded relative to average daily volume over the trading interval — and scaled by the security’s volatility σ. The model “can be directly incorporated into optimal trading strategies,” i.e. it operationalises the Almgren Chriss 2000 framework by supplying the impact coefficients that the 2000 model left as free parameters.

Almgren Thum Hauptmann Li 2005 [defines] Transaction Costs and Slippage Almgren Thum Hauptmann Li 2005 [supports] Almgren Chriss 2000 Almgren Thum Hauptmann Li 2005 [contradicts] Square-Root Law of Market Impact

The 3/5 finding sits in productive tension with the broader Square-Root Law of Market Impact. Later, much larger studies — notably the 2024 complete survey of the Tokyo Stock Exchange (arXiv 2411.13965), which measured the impact exponent across every trading account over eight years — find δ = 1/2 with high precision and argue for strict universality of the square-root form. The reconciliation is that the two results emphasise different objects: the √ law is most robustly supported for the peak impact of a metaorder, whereas Almgren et al. fit temporary impact as a function of trade rate over a specific order-size range on one desk’s data. The honest reading is that the temporary-impact exponent is concave and well below 1, somewhere in the 0.5-0.6 region depending on definition and dataset, and that the √ form remains the standard reduced-form approximation while this paper stands as evidence the exponent is not pinned to exactly 1/2 for every impact definition.

It appears in this vault as the empirical foundation for why a flat basis-point cost is structurally wrong: impact rises with trade size relative to average daily volume and with volatility, so a constant fee silently understates costs for large or fast trades. That makes it a load-bearing input to Transaction Costs and Slippage and the reason high-turnover Markov strategies face a nonlinear, turnover-driven cost penalty. Its profitability_evidence_grade is inconclusive — out of scope for alpha: the paper estimates a cost function, not a trading strategy. It reports no return, no Sharpe ratio and no backtest; it is a market-microstructure measurement that makes Optimal Execution and realistic backtesting possible, not a profitable model in itself.

Robert Almgren [proposes_model] Almgren Thum Hauptmann Li 2005 Almgren Thum Hauptmann Li 2005 [relates] Optimal Execution

Connections

• Robert Almgren — proposes_model, lead author, source: https://www.cis.upenn.edu/~mkearns/finread/costestim.pdf
• Citigroup — uses_dataset, the data is from Citigroup US equity trading desks, source: https://www.cis.upenn.edu/~mkearns/finread/costestim.pdf
• Transaction Costs and Slippage — defines, empirically estimates a permanent+temporary market-impact model, source: https://www.cis.upenn.edu/~mkearns/finread/costestim.pdf
• Square-Root Law of Market Impact — contradicts, prefers a 3/5 power law for temporary impact over pure square-root, source: https://www.cis.upenn.edu/~mkearns/finread/costestim.pdf
• Almgren Chriss 2000 — relates, empirically calibrates the impact functions used in the Almgren-Chriss framework, source: https://www.cis.upenn.edu/~mkearns/finread/costestim.pdf
• Optimal Execution — includes_costs, results feed directly into optimal trading strategies, source: https://www.cis.upenn.edu/~mkearns/finread/costestim.pdf

Sources

• Almgren, R., Thum, C., Hauptmann, E. & Li, H. (2005), “Direct Estimation of Equity Market Impact”, Risk, July 2005 — https://www.cis.upenn.edu/~mkearns/finread/costestim.pdf
• Sato, Y. & Kanazawa, K. (2024), “Strict universality of the square-root law in price impact” (arXiv 2411.13965) — https://arxiv.org/html/2411.13965v3