Learn about slippage assumptions

What is Slippage?

WHY it exists: Markets are not infinitely liquid. Large orders consume available liquidity at each price level, forcing subsequent fills at worse prices. Even small orders face the bid-ask spread—a guaranteed minimum slippage.

HOW it manifests: You decide to buy when price is $50.00 (mid-market). By the time your order arrives, the ask is$50.05. You get filled at $50.05. Slippage =$0.05 = 10 basis points.

Deriving Slippage Models from First Principles

1. Fixed Slippage Model

Assumption: Every trade pays a constant slippage $s$ (in basis points or absolute dollars).

Derivation:

• Expected fill price when buying: $P_{\text{fill}} = P_{\text{decision}} \times (1 + s)$
• Expected fill price when selling: $P_{\text{fill}} = P_{\text{decision}} \times (1 - s)$

WHY this form? It's the simplest model: assumes average market conditions and ignores volatility, order size, and liquidity variations.

Example: Buy 100 shares at $50,$s = 0.001$ (10 bps)

• Expected fill: $50 \times 1.001 = 50.05$
• Slippage cost: 100 \times 50 \times 0.001 = \5$

Why this step? Multiplying by price converts basis points to dollars. The absolute value $|Q|$ ensures slippage is always a cost, never a gain. Watch the conversion: 5 bps is $0.0005$ (not $0.005$)—a factor-of-10 slip here silently inflates your costs tenfold.

2. Volume-Dependent Slippage Model

Assumption: Larger orders relative to average volume experience worse slippage.

Derivation from market microstructure:

• The order book has depth $D_i$ at each price level $P_i$
• Your order $Q$ walks up the book, consuming liquidity
• Average fill price is the volume-weighted average of levels consumed

For a market order of size $Q$ in a market with average volume $V$: $\text{Market Impact} \propto \sqrt{\frac{Q}{V}}$

WHY the square root? This is the empirical "square-root law" of market impact, documented across many later microstructure studies (e.g., Almgren, Toth, Bouchaud). Note: Kyle's original 1985 lambda model implies linear impact ($\Delta P = \lambda \cdot Q$); the $\sqrt{Q/V}$ scaling is an empirical regularity observed in real trade data, not a direct consequence of Kyle's model. Intuitively, the square root captures diminishing marginal impact—informed traders splitting orders can't extract unlimited profit.

Example: $\alpha = 0.1$, $Q = 1000$, $V = 100{,}000$

• $s = 0.1 \times \sqrt{1000/100000} = 0.1 \times 0.1 = 0.01 = 100$ bps
• On a $50 stock: slippage cost =$1000 \times 50 \times 0.01 = $500$

Why this step? The square root captures diminishing returns—doubling order size doesn't double impact. Dividing by volume normalizes across different liquidity regimes.

3. Volatility-Adjusted Slippage

Assumption: High volatility → prices move faster → more slippage.

Derivation:

• During latency $\tau$ (time to execution), price follows random walk with volatility $\sigma$
• Expected price move: $\Delta P \sim \sigma \sqrt{\tau}$
• Worst-case (directional): $\Delta P = \sigma \sqrt{\tau}$ against you

Unit convention for $\tau$: Since $\sigma$ is annualized, $\tau$ must be expressed as a fraction of a year. Examples:

• Half a trading day: $\tau = \dfrac{0.5}{252} \approx 0.00198 \approx 0.002$ years
• One full trading day: $\tau = \dfrac{1}{252} \approx 0.00397 \approx 0.004$ years
• A few seconds of latency: $\tau$ is essentially $0$ on this scale, so intraday HFT models often use per-second volatility instead.

Example (half-day latency): $\sigma = 0.30$ (30% annual), $\tau = 0.5/252 \approx 0.002$ years

• $s_{\text{vol}} = 0.5 \times 0.30 \times \sqrt{0.002} = 0.5 \times 0.30 \times 0.0447 \approx 0.0067 = 67$ bps

Why this step? We use $\sqrt{\tau}$ because price diffusion scales with square root of time (Brownian motion). The factor $k$ acknowledges you won't always get hit by the worst-case move.

4. Combined Slippage Model

Real-world: All effects occur together.

$s_{\text{total}} = s_{\text{fixed}} + \alpha \sqrt{\frac{Q}{V}} + k \sigma \sqrt{\tau}$

Example: Trade 500 shares, $V = 50{,}000$, $\sigma = 0.25$, $\tau = 0.001$ years (~a quarter trading day)

• Fixed: $s_{\text{fixed}} = 0.0005 = 5$ bps
• Volume: $0.1 \times \sqrt{500/50000} = 0.1 \times 0.1 = 0.01 = 100$ bps
• Volatility: $0.5 \times 0.25 \times \sqrt{0.001} = 0.5 \times 0.25 \times 0.0316 \approx 0.00395 = 39.5$ bps
• Total: $\approx 0.0145 = 144.5$ bps

Why this step? Note carefully: the volume term $0.01$ equals $1\% = 100$ bps (since $1\% = 100$ bps, and $0.01 = 100 \times 0.0001$), not 10 bps. A 500-share order that is 1% of daily volume already generates significant impact—another reminder to keep bps conversions straight ($1 \text{ bp} = 0.0001$).

Implementing Slippage in a Backtest

Step-by-step:

1. Choose your model based on strategy frequency:

   • High-frequency (seconds): use volatility + volume model
   • Medium-frequency (minutes-hours): use volume + fixed
   • Low-frequency (daily+): fixed slippage often sufficient

2. Calibrate parameters from real execution data:

   • Measure actual fill prices vs. decision prices over 100+ trades
   • Fit $s$, $\alpha$, $k$ to minimize error
   • If no real data: use conservative estimates (10-20 bps for retail, 2-5 bps for institutional)

3. Apply on every trade:

   # Pseudocode for backtest engine
   def execute_order(decision_price, quantity, volume, volatility):
       s_fixed = 0.0005  # 5 bps  (recall: 1 bp = 0.0001)
       s_volume = 0.1 * sqrt(abs(quantity) / volume)
       s_volatility = 0.5 * volatility * sqrt(latency_in_years)
       total_slippage = s_fixed + s_volume + s_volatility
    
       if quantity > 0:  # Buy
           fill_price = decision_price * (1 + total_slippage)
       else:  # Sell
           fill_price = decision_price * (1 - total_slippage)
    
       return fill_price

Why this structure? Slippage is directional—always hurts you. Buys get worse fills (higher price), sells get worse fills (lower price).

Connections

• Transaction costs and their impact – slippage is one component of total transaction costs
• Realistic order execution modeling – extends slippage with partial fills and fill probability
• Market microstructure basics – order book dynamics explain why slippage exists
• Look-ahead bias – ignoring slippage is a form of look-ahead bias (assumes perfect execution)
• Position sizing – slippage costs scale with position size, affecting optimal sizing

#flashcards/stock-market

Concept Map

Hinglish (regional understanding)