Transaction Cost Modelling for Realistic Backtests

1. Why Fixed Costs Are Wrong

The standard approach to transaction costs in backtesting is to assume a fixed cost per trade — typically 1–2 basis points for liquid futures or 5–10 basis points for equities. This assumption is convenient but wrong in three important ways.

First, transaction costs are not constant over time. The bid-ask spread widens during periods of high volatility, market stress, and low liquidity. A strategy that trades actively during these periods faces costs that can be 3–5× the calm-period average. Since many systematic strategies increase their turnover precisely during volatile periods (due to changing signals), the correlation between turnover and costs amplifies the total cost burden.

Second, transaction costs are not constant across trade sizes. Market impact — the price movement caused by the execution of the trade itself — scales nonlinearly with order size. A $1 million order in E-mini S&P 500 futures has negligible market impact; a $50 million order moves the market measurably. For institutional-scale strategies, market impact typically dominates the spread component.

Third, transaction costs are not symmetric. Selling into a declining market (as occurs during stop-loss execution) is more expensive than buying into a rising market, because the urgency of the exit reduces the trader's ability to wait for favourable fill prices.

2. A Three-Component Cost Model

We decompose total transaction cost into three components, each modelled separately:

Spread cost. Half the bid-ask spread, which is the minimum cost of a round-trip transaction. We model the spread as a function of realised volatility using a log-linear relationship calibrated to tick data:

where σ(t) is the trailing 5-day realised volatility. The coefficients a and b are instrument-specific and estimated from historical tick data. For E-mini S&P 500 futures, a ≈ 0.25 ticks and b ≈ 0.18 ticks. During the March 2020 volatility spike, this model estimates the effective spread at approximately 1.5 ticks, compared to the normal-period value of 0.25 ticks — a 6× increase.

Slippage cost. The difference between the signal price (the price at which the signal was generated) and the execution price (the price actually achieved). For strategies that generate signals at the close and execute at the open, slippage arises from overnight price movements. For intraday strategies, slippage arises from the delay between signal generation and order placement. We model slippage as a function of the signal-to-execution delay and the current volatility:

where Δt is the execution delay in trading days and c is a calibration constant (typically 0.5–1.0).

Market impact cost. For larger orders, the execution itself moves the market. We use the square-root impact model of Almgren et al. (2005), which has strong empirical support:

where η is a constant (typically 0.1–0.3 for futures), σ is daily volatility, Q is order size in contracts, and V is average daily volume. The square-root scaling means that doubling the order size increases impact by only 41% — but for large orders relative to volume, the cost can be substantial.

import numpy as np

class DynamicCostModel:
    """
    Three-component transaction cost model for futures.
    """
    def __init__(self, spread_a, spread_b, slippage_c,
                 impact_eta, avg_daily_volume, tick_value):
        self.spread_a = spread_a
        self.spread_b = spread_b
        self.slippage_c = slippage_c
        self.impact_eta = impact_eta
        self.adv = avg_daily_volume
        self.tick_value = tick_value

    def total_cost(self, realised_vol, order_size,
                   execution_delay=0.0):
        """
        Compute total round-trip cost in basis points.

        Args:
            realised_vol: trailing realised vol (annualised)
            order_size: number of contracts
            execution_delay: delay in trading days
        """
        daily_vol = realised_vol / np.sqrt(252)

        # Spread (half-spread per side, so full spread RT)
        spread = self.spread_a + self.spread_b * np.log(
            max(daily_vol, 1e-6))
        spread_cost = max(spread, self.spread_a) * 2  # round trip

        # Slippage
        if execution_delay > 0:
            slip = daily_vol * np.sqrt(execution_delay) * self.slippage_c
        else:
            slip = 0

        # Market impact (per side, doubled for round trip)
        impact = (self.impact_eta * daily_vol *
                 np.sqrt(order_size / self.adv))
        impact_cost = impact * 2

        # Convert to basis points
        total_bps = (spread_cost + slip + impact_cost) * 10000
        return total_bps

# E-mini S&P 500 example
es_model = DynamicCostModel(
    spread_a=0.25e-4, spread_b=0.18e-4,
    slippage_c=0.7, impact_eta=0.15,
    avg_daily_volume=1_500_000, tick_value=12.50
)

# Normal vol (15%), 10 contracts, no delay
print(f"Normal: {es_model.total_cost(0.15, 10):.1f} bps")
# Stress vol (40%), 10 contracts, no delay
print(f"Stress: {es_model.total_cost(0.40, 10):.1f} bps")
# Normal vol, 500 contracts (institutional)
print(f"Large order: {es_model.total_cost(0.15, 500):.1f} bps")

3. Calibration Results

Table 1: Transaction cost estimates (round-trip, 10-contract order) under fixed assumptions versus the dynamic model. "Calm" and "Stress" correspond to the 25th and 95th percentile of realised volatility over 2020–2023.

The dynamic model's time-weighted average cost is consistently higher than the fixed assumption — by a factor of 1.6× for liquid instruments (ES, ZN) and up to 1.8× for less liquid instruments (CL). During stress periods, costs can be 4–5× the fixed assumption. Since many systematic strategies trade more actively during stress (stop-losses trigger, signals change), the actual cost burden over a full backtest period can be 2–4× the fixed-cost estimate.

4. Impact on Strategy Performance

We re-run a standard trend-following backtest on a diversified futures portfolio using both fixed costs and the dynamic model. The difference is material: the annualised Sharpe ratio drops from 0.84 (fixed costs of 1 bp per contract) to 0.61 (dynamic costs). Approximately half of this difference comes from higher average costs, and half from the correlation between costs and trading activity — the strategy trades most when costs are highest.

For a mean-reversion strategy with higher turnover, the impact is larger: the Sharpe drops from 0.72 to 0.38. Mean-reversion strategies are particularly sensitive because they trade against momentum, executing during periods of high volatility when spreads are widest.

5. Recommendations

We recommend that all backtests include a volatility-dependent cost component, even if the full three-component model is impractical. A simple improvement over fixed costs is to multiply the base cost by the ratio of current volatility to average volatility:

This single adjustment captures the most important dynamic — cost increases during stress — and can be implemented in a single line of code. For institutional-scale strategies (order sizes above 1% of daily volume), the market impact component should also be included.

Published backtests that use fixed costs should be treated with caution. A useful rule of thumb: multiply the reported cost assumption by 2× for a rough estimate of the dynamic cost burden. If the strategy's profitability does not survive this adjustment, it is unlikely to be profitable in live trading.