Lesson 18: Trading Cost Modeling and Tradability

Alpha exists = (Gross Alpha - Cost) > 0

A Typical Scenario (Illustrative)

Note: The following is a synthetic example to illustrate common phenomena; numbers are illustrative and do not correspond to any specific team/account.

In 2019, a quant team showed me their machine learning strategy:

Backtest Results (2015-2019):
- Annual Return: 45%
- Sharpe Ratio: 2.3
- Maximum Drawdown: 8%
- Monthly Win Rate: 78%

"This is the best strategy we've ever seen!" they said excitedly.

I asked one question: "What's your daily turnover rate?"

Answer: 300%.

This means buying and selling stocks equivalent to 3 times the principal every day.

I asked them to recalculate, adding the following real-world costs:

• Trading commission: 0.03% (round trip)
• Market impact: 0.1% (conservative estimate)
• Slippage: 0.05%

Cost Calculation:
- Daily cost = 300% x (0.03% + 0.1% + 0.05%) = 0.54%
- Annual cost = 0.54% x 252 = 136%

Adjusted Backtest:
- Gross return: 45%
- Cost: -136%
- Net return: -91%

Their "money printer" turned into a "money shredder."

This is why trading cost modeling is so important - it determines whether your Alpha is real or an illusion.

18.1 The True Composition of Costs

18.1.1 Explicit Costs vs. Implicit Costs

18.1.2 Explicit Costs in Detail

US Stock Explicit Cost Example:

Buying $100,000 of AAPL:
- Commission: $0-5 (depends on broker)
- Exchange fees: ~$1
- Total: ~$5 = 0.005%

Same for selling, round trip about 0.01%

18.1.3 Implicit Costs: The Invisible Killer

Slippage

Definition: The difference between your expected execution price and actual execution price

Expected to buy AAPL at $100.00
Actual execution price $100.05
Slippage = $0.05 = 0.05%

Sources of Slippage:

Market Impact

Definition: Your trading itself pushes prices in an unfavorable direction

Scenario: You want to buy 10,000 shares of AAPL

Order Book:
  Ask 1: $100.00 x 2,000 shares
  Ask 2: $100.02 x 3,000 shares
  Ask 3: $100.05 x 5,000 shares

If you use a market order to buy all at once:
  First 2,000 shares: $100.00
  Next 3,000 shares: $100.02
  Last 5,000 shares: $100.05

Weighted average price: $100.029
Ideal price: $100.00
Market impact: 0.029%

Moreover: You've consumed Ask 2 and Ask 3
         The next buyer can only buy at higher prices
         This is "permanent impact"

Opportunity Cost

Definition: Potential returns lost due to inability to execute or delayed execution

Scenario:
  Price when signal fired: $100
  Your limit order: $99.50
  Price immediately rises to $105
  Your order never fills

Opportunity cost = $105 - $100 = 5%

18.2 Slippage Modeling

18.2.1 Linear Model

The simplest model assumes slippage is proportional to order size:

Slippage = k x OrderSize / ADV

Where:
- k = empirical coefficient (typically 0.1-0.5)
- OrderSize = order amount
- ADV = Average Daily Volume

Paper Exercise:

You want to buy $500,000 of stock, assuming k = 0.3

Discovery: On small caps, a $500K order could generate $7,500 in slippage!

18.2.2 Square-Root Model

A more precise model considers nonlinear relationships:

Slippage = k x sigma x sqrt(OrderSize / ADV)

Where:
- sigma = daily volatility
- k = empirical coefficient (typically 0.5-1.5)

Paper Exercise:

Key Findings:

• Slippage grows sub-linearly with order size (square root relationship)
• High volatility stocks have larger slippage
• Small cap slippage can be 60x that of large caps

18.2.3 Estimating Slippage with Tick Data

With Level-2 data, you can estimate more precisely:

Method: Simulate order walking through the order book

1. Obtain historical order book snapshots
2. Simulate market order consuming each level
3. Calculate weighted average price vs. mid-price
4. Gather slippage distribution for different order sizes

def estimate_slippage(order_size: float,
                     order_book: dict,
                     side: str = 'buy') -> float:
    """
    Estimate slippage based on order book data

    order_book = {
        'bids': [(price1, size1), (price2, size2), ...],
        'asks': [(price1, size1), (price2, size2), ...]
    }
    """
    if side == 'buy':
        levels = order_book['asks']  # Buying consumes asks
    else:
        levels = order_book['bids']  # Selling consumes bids

    mid_price = (order_book['bids'][0][0] + order_book['asks'][0][0]) / 2
    filled = 0
    cost = 0

    for price, size in levels:
        if filled >= order_size:
            break
        fill_amount = min(size, order_size - filled)
        cost += fill_amount * price
        filled += fill_amount

    if filled < order_size:
        # Order book depth insufficient for full execution
        return float('inf')

    avg_price = cost / order_size
    slippage = (avg_price - mid_price) / mid_price

    return slippage if side == 'buy' else -slippage

18.3 Market Impact Modeling

18.3.1 Temporary Impact vs. Permanent Impact

18.3.2 Almgren-Chriss Model

This is the most famous market impact model:

Total Cost = Temporary Impact + Permanent Impact + Volatility Risk

Where:
  Temporary impact is proportional to trading speed (volume per unit time)
  Permanent impact is proportional to total trading volume
  Volatility risk is proportional to execution time x volatility

Trade-off:
  Trade fast -> High temporary impact, but low volatility risk
  Trade slow -> Low temporary impact, but high volatility risk

Intuitive Explanation:

Imagine pouring a bucket of water into a pond. Pour fast (all at once) -> Big splash (temporary impact), but water settles quickly Pour slow (drop by drop) -> Small splash, but wind and rain may occur during (volatility risk)

18.3.3 Paper Exercise: Execution Strategy Selection

You want to buy $10M of AAPL (ADV = $10B), volatility = 1.5%/day

Optimal Solution: Balance based on urgency and risk preference

18.4 Tradability Assessment

18.4.1 Fill Probability Modeling

The Limit Order Problem: Your orders may not get filled

Fill probability P(fill) depends on:
1. Distance of limit price from current price
2. Queue depth at the price level
3. Price volatility range
4. Waiting time

Estimation formula (simplified):
P(fill) ~ 1 - exp(-lambda x time)

Where lambda relates to price distance and volatility

Paper Exercise:

You place a $99 limit buy order on a $100 stock (1% below market)

Problem: High fill probability means prices often drop - might not be a good signal

18.4.2 Liquidity Cost Metrics

18.4.3 Alpha Purification: From Gross to Net

Gross Alpha: Predicted return (from backtest)

Minus:
  - Explicit costs (commission, taxes)
  - Slippage (Bid-Ask + latency)
  - Market impact
  - Opportunity cost

Equals:
  Net Alpha: Actually achievable return

Key Formula:
  Strategy viable <=> Net Alpha > 0
  Strategy viable <=> Gross Alpha > Total Cost

Paper Exercise:

Findings:

• Strategy E has highest gross Alpha but lowest net return
• Strategy A has lowest gross Alpha but highest net return
• High turnover is the Alpha killer

18.5 Strategy Crowding: When Everyone Trades the Same Signal

Cost modeling focuses on your own orders. But there is a systemic cost that no individual model can estimate: what happens when hundreds of funds hold the same positions and try to exit at the same time.

Case Study: 2024 China Small-Cap Quant Crisis

In early 2024, many of China's top quantitative funds suffered simultaneous drawdowns of 8-13% within weeks. Ubiquant, Lingjun, and High-Flyer -- firms managing tens of billions -- all posted double-digit losses in their CSI 500 enhanced products. The cause was not a single bad trade but strategy homogenization: most funds had overweighted small and micro-cap stocks using similar momentum and size factors. When regulatory tightening restricted micro-cap trading, forced liquidations triggered a positive feedback loop -- selling compressed liquidity, which forced more selling. Backtested slippage models, calibrated on normal conditions, wildly underestimated the impact.

The lesson: your cost model must account for crowding risk. If your strategy uses widely published factors on capacity-constrained stocks, your true cost includes the tail risk of correlated unwinding.

For a deeper analysis of strategy homogenization dynamics, capacity estimation methods, and countermeasures, see Background: Strategy Homogenization and Capacity Bottlenecks.

18.6 Why Many ML Alphas Are Untradable

18.6.1 Signal Decay Rate vs. Execution Delay

18.6.2 Capacity Constraints of High-Frequency Alpha

Key Insight:

ML models easily discover short-term Alpha (because signal-to-noise ratio is high) But these Alphas often decay too fast for retail traders to execute

18.6.3 Case Study: High Win-Rate Strategy's Live Trading Collapse

Backtest Results:

• Daily win rate 65%
• Daily average return 0.3%
• Sharpe 3.0

Strategy Characteristics:

• Signal decay half-life: 2 minutes
• Average execution delay: 5 minutes

Problem:

When signal fires: Expected return +0.5%
After 2 minutes: Expected return +0.25% (50% decay)
After 5 minutes (actual execution): Expected return +0.06%

Minus 0.1% cost: Net return -0.04%

65% win rate x (-0.04%) = Continuous losses

18.7 Multi-Agent Perspective

18.7.1 Cost Estimator Agent

18.7.2 Cost-Aware Strategy Design

Acceptance Criteria

After completing this lesson, use the following criteria to verify learning:

Lesson Deliverables

After completing this lesson, you will have:

1. Cost Classification Framework - Explicit, implicit, opportunity costs
2. Slippage Estimation Models - Linear and square-root models
3. Tradability Assessment Method - Gross Alpha to Net Alpha
4. Cost Estimator Agent Design - Cost estimation and decision collaboration

Key Takeaways

• Trading cost = Explicit cost + Slippage + Market impact + Opportunity cost
• Slippage has a square-root relationship with order size/ADV
• Strategy viability = Net Alpha > 0 = Gross Alpha > Total Cost
• High turnover is the Alpha killer
• ML Alpha easily discovers short-term signals, but execution delay may make them uncapturable

Further Reading

• Lesson 19: Execution System - From Signal to Real Fill - More details on execution
• Background: HFT and Market Microstructure - Market microstructure basics, Kyle's Lambda
• Background: Execution Simulator Implementation - Code implementation of 4-level execution simulator
• Appendix A: Live Trading Logging Standards - What data to record

Next Lesson Preview

Lesson 19: Execution System - From Signal to Real Fill

Cost modeling tells us "how expensive trading is." In the next lesson, we dive into execution: How to design orders? How to handle slippage? How to turn signals into actual fills in real markets?