How to use the market impact calculator
- Choose dollars or shares and enter the order size and the average daily volume (ADV) in the same unit. A 20-day or 60-day average is typical; in shares mode, also enter the price.
- Enter the daily volatility in percent. Annual volatility divided by √252 converts it: 32% a year is about 2% a day. The stock volatility calculator computes it from prices.
- Enter the quoted bid-ask spread in basis points. You pay about half of it on the way in.
- Set the impact coefficient Y. Values from about 0.5 to 1 are typical in the literature; your own fills are the best calibration.
- Set the participation rate, your share of market volume while the order works. It determines the execution time and the timing risk.
The formula
The participation rate ρ sets how long the order takes and how much the price can drift meanwhile. For an order worked at a constant rate over T days, the standard deviation of that drift, as a share of the order value, is:
Timing risk = σ × √(T ÷ 3)T is in trading days (a regular US session is 390 minutes). The factor 1/3 is the average of the squared unfilled fraction, (1 − t/T)², over a linear schedule: the position at risk shrinks as the order fills.
The square-root form has been documented across many markets; Tóth et al. (2011) is a widely cited study of it, and Almgren et al. (2005) fitted a concave power law to a large sample of US equity orders, with an exponent of about 0.6 for the temporary impact.
A worked example
You want to buy $2,000,000 of a stock that trades $100,000,000 a day, 2.00% of ADV. Its daily volatility is 2% and its spread is 4 bps.
- Half the spread costs 2.0 bps.
- Impact is 1 × 2% × √0.0200 = 28.3 bps.
- The expected cost is 30.3 bps, or $6,057.
At 10% participation the order takes 78 minutes, and the price could drift by about 51.6 bps ($10,328) either way in that time, one standard deviation. That drift has no expected direction, but it is larger than the expected cost itself.
Why impact grows with the square root
The square-root law is concave: the first slice of liquidity is the cheapest, and each additional share costs a little more than the last, but less than proportionally. In numbers:
| Order | Share of ADV | Impact per share | Total cost | Cost in dollars |
|---|---|---|---|---|
| $500,000 | 0.50% | 14.1 bps | 16.1 bps | $807 |
| $2,000,000 | 2.00% | 28.3 bps | 30.3 bps | $6,057 |
| $8,000,000 | 8.00% | 56.6 bps | 58.6 bps | $46,855 |
Each fourfold increase in size doubles the impact per share and multiplies the dollar impact by eight, because dollar impact grows with size to the power 1.5. That is the arithmetic behind strategy capacity: returns per dollar fall as a fund grows, so profit eventually stops growing with assets.
Volatility enters linearly. A stock with 1% daily volatility instead of 2% halves the impact, to 14.1 bps, at the same share of volume. The intuition is that impact is measured in units of the stock’s normal daily price range: a large order in a quiet stock still moves its price by a fraction of a typical day’s move.
Choosing the participation rate
| Participation | Execution time | Expected cost | Timing risk (1 s.d.) |
|---|---|---|---|
| 5% | 2.6 hours | 30.3 bps | 73.0 bps |
| 10% | 78 minutes | 30.3 bps | 51.6 bps |
| 25% | 31 minutes | 30.3 bps | 32.7 bps |
In the pure square-root law, the expected cost does not depend on speed, so the table shows the same cost in every row while the timing risk falls as you trade faster. Real executions are not that simple. Very high participation makes you the dominant flow, and the impact tends to exceed the formula; very low participation exposes the order to drift and to other traders noticing it. Optimal execution models in the Almgren–Chriss tradition balance the expected cost of speed against the variance of waiting; a VWAP or TWAP schedule is the common practical compromise.
Calibrating Y
The coefficient is the least certain input and it scales the impact directly: with Y of 0.5 instead of 1, the example cost falls to 16.1 bps. Estimate it from your own executions: for each order, measure the shortfall against the arrival price, subtract half the spread and divide by σ × √(Q/V). The average of that ratio over many orders is your Y. Individual orders scatter widely because the price would have moved anyway, so a few dozen orders give only a rough figure.
What this calculator does not include
- It is an average, not a prediction for one order. News, the time of day and other traders’ flow can make a single execution far cheaper or far more expensive.
- Permanent versus temporary impact. Part of the impact persists after the order and part decays. The square-root law here describes the average total cost during execution, not the price path afterward.
- Multi-day orders and very large sizes. Above roughly a fifth of daily volume, data on impact become thin, and overnight gaps add risk that the timing-risk formula ignores beyond the one-session horizon.
- Commissions, fees and the full spread on exit. Add those separately, for example with the trading cost calculator.