The New Demands of Optimal Execution

Alpha is harder to find than ever. Markets are more efficient, signals decay faster, and competition for every basis point has never been more intense. In that environment, how you trade matters as much as what you trade.

So how much does it really cost to act on a good investment idea?

For large institutional investors, the answer is often dominated by price impact: the adverse price movement a large order causes against itself. A fund manager buying 2% of average daily volume does not execute at the quoted price. The act of buying pushes prices up before the order is complete. Frazzini, Israel, and Moskowitz (2018) estimate that these costs at AQR were an order of magnitude larger than bid-ask spreads. Yet price impact is still often modeled too simply.

Three features matter most.

First, price impact is concave in trade size. Larger trades do cost more, but not proportionally more. This is the well-known square-root law: doubling the size of an order does not double its cost. That matters for how orders are split and scheduled.

Second, impact does not decay at a single rate. Some of it fades within hours, while some can persist for weeks or months and may appear close to permanent. Models that assume a single exponential decay rate miss this multi-timescale structure and can misestimate both the timing and magnitude of execution costs.

Third, liquidity matters directly. In less liquid markets, the same order has greater impact. Any realistic execution model must therefore estimate liquidity accurately. Mis-specifying those parameters has direct and asymmetric costs: underestimating impact can lead to overly aggressive trading and can turn a profitable signal into a losing strategy, even when the alpha is right.

A fourth effect becomes important when trading portfolios rather than single securities: cross-impact. A large trade in one asset can move not only its own price, but also the prices of related assets. For highly correlated instruments, such as futures on the same underlying with different maturities, this effect can be substantial. A futures roll looks expensive when each leg is analyzed in isolation. Once cross-impact is taken into account, the true cost may be much lower, because selling one contract can partially offset the impact of buying the other. Ignoring that interaction risks systematically mispricing execution.

Before asking what to trade, investment professionals need to understand what it will cost to trade and whether their execution model can answer that question accurately enough to be trusted.

Machine learning has transformed signal generation. Applying it to execution, however, is a different problem.

The difficulty is that market data are endogenous: prices and order flow are shaped by the actions of the same participants the model is trying to learn from. A model trained naively on historical trading data may therefore struggle to distinguish between predicting price moves and causing them.

Consider a simple example. A model observes that aggressive buying in an illiquid market is often followed by short-term price appreciation. Statistically, that may look like alpha. But what the model may actually be learning is that buying moves prices, not that it predicts future value. In the extreme, a backtest can mistake self-induced price moves for genuine predictive power.

That is not just a technical problem. A strategy that appears profitable only because it moves prices is not discovering value. In many settings, it would raise clear market-manipulation concerns.

A more practical alternative is to use structured price impact models. Models built on explicit no-manipulation conditions help ensure that profitability comes from genuine forecasting rather than from mechanically moving prices. They also narrow the set of plausible models and make calibration more reliable. In the multi-asset setting, those conditions constrain cross-impact in ways that make an otherwise difficult problem both tractable and auditable.

In institutional settings, execution logic must be explainable, auditable, and robust enough to withstand scrutiny from risk managers, compliance teams, and regulators. A model that cannot clearly separate forecasting from its own market impact will be difficult to deploy.

In traditional markets, institutional order flow is largely anonymized. Large positions are not directly visible, and while other participants may infer activity, they usually cannot observe exactly where a position becomes vulnerable.

Decentralized finance changes this. On some blockchain-based trading platforms, positions, leverage, and liquidation thresholds can be visible in real time. In effect, other market participants can see where forced buying or selling may occur.

That transparency creates a more adversarial execution environment. A trader who identifies a large position near its liquidation threshold has a clear incentive to push prices toward that level, trigger forced liquidation, and profit from the resulting order flow. In most traditional markets, conduct of that kind would raise obvious manipulation concerns. In decentralized markets, however, it can arise directly from the market’s design.

The same problem also runs in reverse. A trader executing a large order must consider not only their own price impact, but also whether their trading could trigger liquidation cascades in other positions, moving the market much further than intended and worsening their own execution.

In stress scenarios, a third layer of risk appears. If exchange insurance funds are exhausted, loss-allocation mechanisms such as auto-deleveraging can force healthy counterparties to absorb losses from positions they did not initiate. Execution in that setting depends not only on modeling one’s own impact, but also on understanding the incentives of other participants and the rules by which the venue redistributes risk under stress.

The broader point extends beyond decentralized finance. As markets become faster, more correlated, and more algorithmic, execution is no longer just a question of minimizing spread and impact under stable assumptions. It is increasingly a problem of operating in an environment shaped by feedback, strategic interaction, and evolving market design.

Optimal execution is therefore not an academic afterthought. It is a core part of investment performance. Every basis point lost to misestimated impact or poorly understood market structure is a basis point transferred to someone else.

References:

1. Frazzini, A., Israel, R., and Moskowitz, T.J. (2018). Trading Costs. AQR Capital Management Working Paper. Available at: https://www.aqr.com/Insights/Research/Working-Paper/Trading-Costs
2. Bouchaud, J.-P., Bonart, J., Donier, J., and Gould, M. (2018). Trades, Quotes and Prices: Financial Markets Under the Microscope. Cambridge University Press, Cambridge.
3. Webster, K.T. (2023). Handbook of Price Impact Modeling. CRC Press, Boca Raton, FL.
4. Brokmann, X., Serie, E., Kockelkoren, J., and Bouchaud, J.-P. (2015). Slow Decay of Impact in Equity Markets.Market Microstructure and Liquidity, 1(2), 1550007.
5. Bucci, F., Benzaquen, M., Lillo, F., and Bouchaud, J.-P. (2019). Slow Decay of Impact in Equity Markets: Insights from the ANcerno Database. Market Microstructure and Liquidity, 4(03n04), 1950006.
6. Hey, N., Mastromatteo, I., Muhle-Karbe, J., and Webster, K.T. (2025). Trading with Concave Price Impact and Impact Decay — Theory and Evidence. Operations Research. Published Online: March 21, 2025. Available at: https://pubsonline.informs.org/doi/10.1287/opre.2023.0620
7. Bouchaud, J.-P., Hey, N., Mastromatteo, I., Muhle-Karbe, J., and Webster, K.T. (2024). The Cost of Misspecifying Price Impact. Risk, January 2024. Available at: https://www.risk.net/investing/7958754/the-cost-of-mis-specifying-price-impact
8. Tomas, M., Mastromatteo, I., and Benzaquen, M. (2022). How to Build a Cross-Impact Model from First Principles: Theoretical Requirements and Empirical Results. Quantitative Finance, 22(6), 1017–1036.
9. Hey, N., Mastromatteo, I., and Muhle-Karbe, J. (2025). Concave Cross Impact. Preprint, available at ssrn.com.
10. Gatheral, J. (2010). No-Dynamic-Arbitrage and Market Impact. Quantitative Finance, 10(7), 749–759.
11. Chitra, T. (2025). Autodeleveraging: Impossibilities and Optimization. arXiv preprint arXiv:2512.01112. Available at: https://arxiv.org/abs/2512.01112
12. Campbell, R., Hey, N., Nutz, M., and Moallemi, C. (2026). Risk-Based Auto-Deleveraging. arXiv preprint arXiv:2603.15963. Available at: https://arxiv.org/abs/2603.15963
13. U.S. Securities and Exchange Commission (2020). Staff Report on Algorithmic Trading in U.S. Capital Markets.August 5, 2020. Available at: https://www.sec.gov/files/algo_trading_report_2020.pdf