Contango, Backwardation & Roll Yield in Futures Backtesting [2026]

1. Term Structure Economics: Contango vs Backwardation

Cost of Carry, Storage Costs, and Convenience Yield

The forward price of a commodity or financial futures contract is determined by the Cost of Carry model: F = S * exp((r + c - y) * T), where r is the risk-free rate, c is storage and insurance costs, and y is the convenience yield.

When storage costs and financing exceed convenience yield, the market enters Contango (upward-sloping curve). When immediate physical demand is high, convenience yield dominates, driving the market into Backwardation (downward-sloping curve).

2. The Mathematical Impact of Roll Yield

Deconstructing Total Futures Return into Spot Return and Roll Yield

The total return of a continuous futures strategy equals: Total Return = Spot Return + Roll Yield + Collateral Yield. If roll yield is negative, even a rising spot price can produce a net loss for buy-and-hold investors.

Market Regime | Curve Shape | Near Contract vs Far | Roll Yield for Long | Roll Yield for Short Severe Contango | Upward Sloping | Near < Far | Negative Drag (-4% to -15%/yr) | Positive Yield (+4% to +15%/yr) Mild Contango | Slight Slope | Near <= Far | Slight Drag (-1% to -3%/yr) | Slight Yield (+1% to +3%/yr) Backwardation | Downward Sloping | Near > Far | Positive Yield (+5% to +20%/yr) | Negative Drag (-5% to -20%/yr)

3. Python Continuous Contract Stitching

Eliminating Artificial Gaps with Ratio Adjustment

When backtesting futures in Python, naive stitching creates massive price discontinuities on expiration day. Below is a Python function implementing multiplicative ratio adjustment for backtesting.

// futures_roll_stitching.py (python) import pandas as pd import numpy as np def ratio_adjust_futures(near_series: pd.Series, far_series: pd.Series, roll_index: int) -> pd.Series: """Adjusts historical contract prices by roll ratio to preserve percentage returns.""" roll_ratio = far_series.iloc[roll_index] / near_series.iloc[roll_index] adjusted_near = near_series.iloc[:roll_index] * roll_ratio continuous_series = pd.concat([adjusted_near, far_series.iloc[roll_index:]]) return continuous_series