Trade Execution Modeling

Idealized backtest: filled at the close, zero slippage
Real world:
1. The order book has a bid-ask spread
2. Large orders push prices (market impact)
3. Execution is delayed (there is latency from signal to fill)

No slippage model -> overly optimistic backtest -> losses in live trading

def fixed_slippage(price: float, direction: int, bps: float = 5.0) -> float:
    """
    Args:
        price: Original price
        direction: 1=buy, -1=sell
        bps: Slippage in basis points (1bp = 0.01%), default 5bp
    Returns:
        Execution price after slippage
    """
    slippage = price * bps / 10000
    return price + direction * slippage

def linear_impact(price: float, direction: int,
                  volume_traded: float, adv: float,
                  impact_coeff: float = 0.1) -> float:
    """
    Linear market impact: impact ∝ traded volume / ADV

    Args:
        price: Original price
        direction: 1=buy, -1=sell
        volume_traded: Trade size (shares or notional)
        adv: Average Daily Volume
        impact_coeff: Impact coefficient, usually 0.05-0.2
    Returns:
        Execution price after impact
    """
    participation_rate = volume_traded / adv
    impact = impact_coeff * participation_rate
    return price * (1 + direction * impact)

import numpy as np

def sqrt_impact(price: float, direction: int,
                volume_traded: float, adv: float,
                volatility: float, eta: float = 0.5) -> float:
    """
    Square-root market impact (more accepted in academia):
    impact = η × σ × sqrt(V/ADV)

    Args:
        price: Original price
        direction: 1=buy, -1=sell
        volume_traded: Trade size
        adv: Average daily volume
        volatility: Daily volatility (standard deviation)
        eta: Impact elasticity coefficient, usually 0.3-0.8
    Returns:
        Execution price after impact
    """
    participation = volume_traded / adv
    impact = eta * volatility * np.sqrt(participation)
    return price * (1 + direction * impact)

Backtest capital vs instrument ADV:
├── Capital < 0.5% of ADV -> fixed slippage (5bps) is enough
├── Capital 0.5-5% -> linear impact model
└── Capital > 5% -> square-root impact model (required)

Goal: execute at the day's volume-weighted average price

VWAP = Σ(Price_i × Volume_i) / Σ(Volume_i)

Execution logic:
1. Forecast the intraday volume profile (typically U-shaped)
2. Split the order according to the predicted profile
3. Execute proportionally in each time slice

Typical China A-share VWAP volume profile (U-shaped):
09:30-10:00  15%  (active open)
10:00-11:30  25%  (normal morning session)
13:00-14:00  15%  (weak afternoon session)
14:00-14:30  15%  (afternoon recovery)
14:30-15:00  30%  (active close)

VWAP in backtests:
- Daily backtest: use the VWAP field directly as the fill price
- Minute backtest: simulate VWAP order slicing

Goal: execute evenly over a specified time window

TWAP = simple time-sliced execution

Execution logic:
1. Define an execution window (for example 09:30-11:30)
2. Divide it into N time buckets
3. Execute total_size / N in each bucket

Pros and cons:
+ Simple, no need to forecast volume
- Easier to cause impact during low-volume periods
- Less adaptive than VWAP

def delayed_execution(signal_series: pd.Series, delay_bars: int = 1) -> pd.Series:
    """
    Simulate the delay from signal generation to execution

    Args:
        signal_series: Original signal
        delay_bars: Number of bars to delay, default 1 (T+1 execution)
    Returns:
        Delayed signal

    China A-shares: delay_bars=1 (T+1 rule)
    Crypto: delay_bars=0 or 1
    """
    return signal_series.shift(delay_bars)

Total trading cost = explicit cost + implicit cost

Explicit cost:
- Commission: China A-shares 2-3 bps, crypto 0.02-0.1%
- Stamp duty (China A-share sell side): 0.05% (sell orders only)
- Transfer fee: negligible

Implicit cost:
- Bid-ask spread: 0.5-5bps
- Market impact: depends on trade size and liquidity
- Opportunity cost: loss from not filling at the best price

{
  "commission": 0.001,
  "comment": "0.1% one-way commission, already includes stamp duty and spread"
}

{
  "commission": 0.001,
  "engine": "daily",
  "interval": "1D"
}

class SignalEngine:
    def __init__(self):
        # Execution assumption parameters
        self.execution_delay = 1       # T+1 delay
        self.slippage_bps = 5          # Fixed 5bps slippage
        self.max_participation = 0.05  # Maximum participation rate 5%

    def generate(self, data_map):
        for code, df in data_map.items():
            # 1. Generate raw signal
            raw_signal = self._compute_signal(df)

            # 2. Apply execution delay
            delayed_signal = raw_signal.shift(self.execution_delay)

            # 3. Apply volume filter (do not trade when liquidity is too low)
            volume_ok = df['volume'] > df['volume'].rolling(20).mean() * 0.3
            delayed_signal[~volume_ok] = 0

            signals[code] = delayed_signal

Step 1: Estimate annual turnover
  Annual turnover = annual trade count × 2 (buy + sell) / number of positions

Step 2: Compute annual cost drag
  Annual cost = annual turnover × total one-way cost

Step 3: Evaluate the impact on returns
  Net return = gross return - annual cost

Example:
  Annual turnover = 12 (monthly rebalance)
  One-way cost = 0.1%
  Annual cost = 12 × 0.1% = 1.2%
  If annualized return is only 5% -> costs eat 24% of returns!

### Backtest Results Under Different Slippage Assumptions

| Slippage (bps) | Annual Return | Sharpe | Max Drawdown |
|-----------|---------|--------|---------|
| 0 (ideal) | 15.2% | 1.35 | -18.5% |
| 3 | 13.8% | 1.22 | -19.0% |
| 5 | 12.9% | 1.15 | -19.2% |
| 10 | 11.1% | 0.98 | -19.8% |
| 20 | 7.5% | 0.65 | -20.5% |

Conclusion: the strategy still has meaningful profitability under 10bps slippage

## Execution Cost Analysis

### Strategy Trading Characteristics
| Metric | Value |
|------|-----|
| Average annual trade count | 48 |
| Annual turnover | 4.8x |
| Average holding days | 25 |
| Average order size | ¥50,000 |

### Cost Estimate
| Cost Item | Per Trade | Annualized |
|--------|------|------|
| Commission | 0.025% | 0.24% |
| Stamp duty | 0.025% | 0.12% |
| Estimated slippage | 0.03% | 0.29% |
| **Total** | **0.08%** | **0.65%** |

### Cost Impact
- Gross return: 12.5%
- Net return: 11.85%
- Cost drag: -0.65% (5.2% of gross return)
- Conclusion: cost impact is manageable

### Optimization Suggestions
1. Lower turnover (lengthen holding period)
2. Avoid trading during low-liquidity windows
3. Use limit orders instead of market orders