2026-04-25

Article 18 — Cointegration Pairs Trading on NSE: An Educational Walkthrough

The Engle-Granger cointegration workflow described pedagogically with anonymised placeholders. Methodology only — not a recommendation on any specific pair.

Educational only. Bharath Shiksha is an educational publisher, not a SEBI-registered Investment Adviser or Research Analyst. Nothing here is investment advice or a recommendation on any security. The methodology is described pedagogically with anonymised placeholders. The variable names below (Stock A, Stock B) are illustrative — substitute with any cointegrated pair the reader chooses to study from their own historical data.

The core idea. Two non-stationary price series can have a stationary linear combination (the spread). If the spread reverts to its mean, a pairs-trading framework can in principle profit from the divergence-then-convergence cycle. The methodology below describes the analytical workflow; it is not a recommendation on any specific pair.

The Engle-Granger 2-step procedure

Step 1: OLS regression of one series on the other

import pandas as pd
import numpy as np
import statsmodels.api as sm
from statsmodels.tsa.stattools import adfuller

# Load 5 years of daily closes for any two candidate cointegrated names: Stock A and Stock B
# (Reader supplies historical data for the pair they wish to study)
df = pd.DataFrame({
    "stock_a": stock_a_data["Close"],
    "stock_b": stock_b_data["Close"]
}).dropna()

# Regress Stock A on Stock B
X = sm.add_constant(df["stock_b"])
model = sm.OLS(df["stock_a"], X).fit()
beta = model.params["stock_b"]  # hedge ratio

Step 2: ADF test on residuals

residuals = df["stock_a"] - beta * df["stock_b"] - model.params["const"]
adf_stat, p_value, *_ = adfuller(residuals)
print(f"ADF stat: {adf_stat:.3f}, p-value: {p_value:.3f}")

If p-value < 0.05, the spread is stationary → the pair is cointegrated → the pairs framework is methodologically applicable.

The z-score framework rule

# Compute z-score of spread
residuals = residuals.dropna()
mean = residuals.rolling(60).mean()
std = residuals.rolling(60).std()
z = (residuals - mean) / std

# Framework definition (NOT a trade recommendation):
# When z < -2: the spread is at a historically wide negative deviation.
#   The framework's long-spread leg would be sized as +1 unit Stock A,
#   -beta units Stock B (hedge ratio).
# When z > 2: the spread is at a historically wide positive deviation.
#   The framework's short-spread leg would be the mirror.
# Exit: |z| < 0.5 (mean reversion completed).

These are the framework's mathematical signals — not directions to act on. Whether to deploy capital, and on which specific securities, is the reader's own decision based on their own research, risk tolerance, and SEBI-compliant adviser consultation.

Indian-market-specific constraints

Short selling. Indian retail can't short cash equity overnight. The framework requires stock futures for the short leg.
Hedge ratio and lot size. A computed hedge ratio may not match F&O lot sizes. Round down; adjust size proportionally.
Physical settlement risk on expiry. A pairs methodology held into expiry week is exposed to physical settlement on the equity leg.

Half-life of reversion

# AR(1) of spread
lag_spread = residuals.shift(1).dropna()
aligned = residuals.iloc[1:]
ar1_model = sm.OLS(aligned, sm.add_constant(lag_spread)).fit()
k = ar1_model.params[1] - 1
half_life = -np.log(2) / np.log(1 + k)
print(f"Half-life: {half_life:.1f} days")

A half-life of 10-30 days is typically considered usable for retail-capital horizons. Under 10 days: noise dominated. Over 60 days: capital tied up too long for the expected mean reversion.

Stage 4 Volume 3 connection

Stage 4 Volume 3 (Time-Series Econometrics) covers cointegration with additional pedagogical examples, ARIMA, GARCH for volatility forecasting, and the 8 common time-series mistakes retail quants make. All examples are historical, anonymised, and presented as methodology — not as trade recommendations.

Disclaimer

About Bharath Shiksha. Bharath Shiksha is an educational publisher. All content is for educational purposes only.

Not investment advice. Nothing here constitutes investment advice, a recommendation to buy, sell, or hold any security, a forecast of price action, or a research report under the SEBI (Research Analyst) Regulations, 2014. We are not a SEBI-registered Investment Adviser (IA) or Research Analyst (RA).

Educational scope only. Examples that reference specific securities or sectors are pedagogical illustrations of methodology applied to historical data — not recommendations, predictions, or guidance on current or future market positioning.

Risk warning. Trading involves substantial risk of loss. SEBI's 2024 study found 89-93% of retail F&O traders incurred losses. Past performance is not indicative of future results.

Consult a registered adviser. Before deploying capital, consult a SEBI-registered Investment Adviser or Research Analyst.