Kyle-Obizhaeva Inelastic Market Impact Model
The Formal Definition
A structural quantitative market microstructure model that characterizes price formation and market impact as an inelastic process governed by order flow duration and volume invariance, predicting that large institutional orders generate square-root price impact regardless of execution venue.
Permanent Market Impact ΔP = Y × σ × √( Order Size / Average Daily Volume )
Cole Barrett's Reality Check
The Unvarnished Bottom Line"The Kyle-Obizhaeva model proved what institutional traders feared: the market is not a bottomless pool; it is an inelastic spring. If you trade 10% of a stock's daily volume, the market impact doesn't grow linearly—it follows a square-root law. The harder and faster you push, the more the price bends against you, making large block execution exponentially more expensive."
Interactive Simulator: Test the Math
Real-World Example: Scenario Breakdown
Examining the real numbers for: An institution executing an order to purchase 100,000 shares of a mid-cap equity representing 15% of the security's Average Daily Volume
| Execution Metric | Inelastic Model-Calibrated Execution Desk | Single-Session Aggressive Execution Desk |
|---|---|---|
| Fee / Rate | $0.0035/share DMA rate | $0.0035/share rate |
| Spread / Buffer | Calculated non-linear market impact; spaced execution over 3 full trading sessions (capping daily participation to 5% of ADV) | Attempted to force all 100,000 shares into a single 2-hour morning window (absorbing 40% of morning volume) |
| Execution / Status | Minimized the square-root impact function; captured an average fill price of $50.15 against a $50.00 arrival price | Inelastic market depth buckled; price impact accelerated non-linearly, pushing the stock from $50.00 up to $51.80 |
| Total Cost / Result | Minimized market impact via square-root volume pacing | Suffered outsized execution losses from violating market impact limits |
How Brokers Weaponize This Term
When analyzing institutional Transaction Cost Analysis (TCA) benchmarks, evaluate whether your broker's algorithms utilize square-root market impact modeling. Algorithms that pace orders linearly without accounting for inelastic price elasticity consistently cause adverse price impact on large orders.
Broker Evaluation Matrix
Cole Approves
Interactive Brokers: Provides institutional execution algorithms (IBKR Algos, VWAP, Percentage of Volume) designed around quantitative market impact models to minimize execution slippage.
Read Audit →Cole Flags / Avoids
Basic Retail Investing Apps: Lacks quantitative algorithmic order slicing, forcing users to submit large orders that trigger severe market impact.
View Trap Details →Frequently Asked Questions
What is the 'Square-Root Law' of market impact?
It is an empirical finding in quantitative finance showing that the price impact of a trade is proportional to the square root of the trade size relative to daily volume, holding true across equities, futures, and currencies.
What is the difference between temporary and permanent market impact?
Temporary impact is the transient price concession required to incentivize liquidity providers right now. Permanent impact is the lasting price change caused by the information content of your order.