Slippage and market impact with worked numbers

What you will learn

• How to measure slippage in euros and basis points against a clear benchmark.
• How to calculate the average fill price when an order walks through several book levels.
• The difference between temporary and permanent market impact, and a rough rule for estimating impact.
• How implementation shortfall captures every cost, including the cost of not trading.

Explanation

How spreads and slippage behave during the trading day is covered in the course "Day Trading & Intraday Execution", and how to include costs in a backtest in "Systematic Trading & Backtesting". This lesson gives you the measurement tools.

Slippage needs a benchmark

Slippage is the difference between the price you expected and the average price you received. Always state the benchmark:

• Arrival price: the mid price at the moment your order reaches the market. This is the standard benchmark.
• Decision price: the price when you decided to trade, which can be minutes or hours earlier.
• Stop price: for stop orders, the trigger price.

For a buy: Slippage per share = Average fill price − Benchmark. For a sell, reverse the sign. In basis points: Slippage (bps) = Slippage per share ÷ Benchmark × 10,000.

Walking the book

When an order is larger than the size at the best price, it uses several levels. Its volume-weighted average price (VWAP) of the fills is:

Average fill = Σ (price × shares at each level) ÷ total shares

Market impact

Market impact is the price change caused by your own trading. Temporary impact fades after you stop trading, because new orders refill the book. Permanent impact remains, because other participants read your trades as information.

A widely used rule of thumb from market microstructure research is the square-root rule:

Impact ≈ Y × σ × √(Q ÷ V)

Here σ (sigma) is the daily volatility in %, Q your order size, V the average daily volume (ADV), and Y a constant of roughly 1 that differs by market. Doubling the order does not double the impact; it raises it by about 41% (√2 ≈ 1.41). Treat the result as an order-of-magnitude estimate, not a precise forecast.

The participation rate is your volume as a share of all volume traded while you execute. Splitting a large order over time lowers it and usually reduces impact, but exposes you longer to price moves.

Implementation shortfall

Implementation shortfall compares a "paper" trade, filled completely at the decision price with no costs, with what really happened. It adds:

1. Execution cost: (average fill − decision price) × shares filled.
2. Opportunity cost: (later price − decision price) × shares not filled.
3. Explicit fees.

This prevents a common illusion: a limit order that never fills shows zero slippage, but missing the trade can cost more.

Worked example

Hypothetical example A (walking the book): bid €15.00, asks €15.02 × 800, €15.03 × 1,000, €15.04 × 700, €15.05 × 1,500. Arrival mid: €15.01. You buy 3,000 shares with a market order.

1. Fills: 800 × €15.02 = €12,016; 1,000 × €15.03 = €15,030; 700 × €15.04 = €10,528; 500 × €15.05 = €7,525.
2. Total: €45,099. Average fill: €45,099 ÷ 3,000 = €15.033.
3. Slippage: €15.033 − €15.01 = €0.023 per share = €69.00 in total ≈ 15.3 bps.
4. For comparison, 3,000 shares at the best ask alone would have cost only €0.01 × 3,000 = €30.00 above the mid. Walking the book more than doubled the cost.

Example B (square-root estimate): an order of 20,000 shares at about €15 (≈ €300,000), ADV 400,000 shares, daily volatility 2%, Y = 1. Q ÷ V = 5%, √0.05 ≈ 0.224. Impact ≈ 2% × 0.224 ≈ 0.45% ≈ €0.067 per share ≈ €1,342, before the half-spread.

Example C (implementation shortfall): you decide to buy 3,000 shares at €15.01. You fill 2,000 at an average of €15.06 and cancel the rest; the price later reaches €15.20. Fees €5.00. Execution cost: 2,000 × €0.05 = €100. Opportunity cost: 1,000 × €0.19 = €190. Total: €100 + €190 + €5 = €295, ≈ 65.5 bps of the €45,030 paper value. Exclusions: taxes; all prices hypothetical.

Common mistake

Practice activity

Hypothetical: bid €30.00, ask €30.04. Asks: €30.04 × 300, €30.05 × 400, €30.07 × 600. You buy 1,000 shares at market.

1. Calculate the average fill price and the slippage against the arrival mid in euros and bps.
2. Estimate the impact of a 10,000-share order with the square-root rule: ADV 250,000 shares, daily volatility 1.5%, Y = 1, price €30.

Key takeaways

• Slippage is meaningful only against a stated benchmark, usually the arrival mid.
• Orders larger than the best level pay a volume-weighted average across levels.
• Impact grows roughly with the square root of order size relative to daily volume.
• Implementation shortfall includes the opportunity cost of shares you did not buy.

Next step

The next lesson explains the EU best execution rules and the debate on payment for order flow.