{"id":241435,"date":"2026-04-13T13:45:53","date_gmt":"2026-04-13T17:45:53","guid":{"rendered":"https:\/\/ibkrcampus.com\/campus\/?p=241435"},"modified":"2026-04-13T13:46:09","modified_gmt":"2026-04-13T17:46:09","slug":"statistical-arbitrage-using-cointegrated-stock-pairs-in-indian-equity-market-2015-2025-epat-project","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/statistical-arbitrage-using-cointegrated-stock-pairs-in-indian-equity-market-2015-2025-epat-project\/","title":{"rendered":"Statistical Arbitrage Using Cointegrated Stock Pairs in Indian Equity Market (2015-2025) | EPAT Project"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><em>The article &#8220;Statistical Arbitrage Using Cointegrated Stock Pairs in Indian Equity Market (2015-2025) | EPAT Project&#8221; was originally published on <a href=\"https:\/\/blog.quantinsti.com\/cointegrated-pairs-trading-indian-equity-market-epat-project\/\">QuantInsti<\/a> blog.<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>About the author<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.linkedin.com\/in\/shanttandon\/?originalSubdomain=in\" target=\"_blank\" rel=\"noreferrer noopener\">Shant Tondon<\/a>&nbsp;brings a diverse background blending financial markets analysis, consulting, and entrepreneurship. He holds a Bachelor&#8217;s in Commerce with a focus on Financial Markets from Narsee Monjee College of Commerce and Economics, and completed his High School Diploma in Business\/Commerce at Mayo College, Ajmer. Professionally, Shant gained early analytical experience as an intern at Teach For India and KPMG in Mumbai, followed by a role as an Analyst at PwC.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Project Abstract<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This project builds and evaluates a market-neutral pairs trading strategy focusing on 25 NSE large-cap stocks spanning the Banking, IT, Pharma, Cement, and Auto sectors. The pairs are selected using a residual stationarity test, specifically the ADF(0) with MacKinnon p-value, on a training sample. To ensure statistical robustness and control for false discoveries, the Benjamini\u2013Hochberg False Discovery Rate (FDR) at 5% is applied.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The strategy trades mean-reversion via z-scores of the spread using a walk-forward train\/test split. It represents a clean, defendable academic implementation with no look-ahead bias, explicit transaction costs (5 bps per leg per side), equal capital per active pair (\u20b95,00,000), and comprehensive portfolio-level risk metrics.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"introduction-project-motivation\">Introduction &amp; Project Motivation<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Pairs trading is a classic statistical arbitrage strategy that seeks to exploit temporary price divergences between two related assets while maintaining a market-neutral stance. This project applies this concept to the Indian equity market between January 1, 2015, and June 30, 2025.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The primary motivation was to build a rigorous prototype that addresses common algorithmic trading pitfalls, such as look-ahead bias, incomplete Profit and Loss (PnL) calculations, and inadequate multiple testing controls.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"strategy-implementation-methodology-technical-breakdown-\">Strategy &amp; Implementation Methodology (Technical Breakdown)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The strategy relies on a rolling walk-forward methodology utilizing a 252 trading-day training window and a 21-day test step.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. Pair Selection &amp; Cointegration:<\/strong>&nbsp;During the training phase, the hedge ratio (<em>\u03b2<\/em>) is estimated using Ordinary Least Squares (OLS). Residual stationarity is then tested using the ADF(0) t-stat to generate a MacKinnon p-value. The Benjamini\u2013Hochberg FDR is applied at 5% to limit false positives. Three highly cointegrated pairs emerged from the framework:&nbsp;<strong>HDFCBANK.NS<\/strong>&nbsp;vs&nbsp;<strong>KOTAKBANK.NS<\/strong>,&nbsp;<strong>HEROMOTOCO.NS<\/strong>&nbsp;vs&nbsp;<strong>ULTRACEMCO.NS<\/strong>, and&nbsp;<strong>HCLTECH.NS<\/strong>&nbsp;vs&nbsp;<strong>ICICIBANK.NS<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. Signal Generation Logic:<\/strong>&nbsp;To prevent look-ahead bias, the rolling variables for standard deviation and mean are strictly shifted by 1 day.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Spread Calculation:<\/strong>&nbsp;<code>S<sub>t<\/sub>&nbsp;= A<sub>t<\/sub>&nbsp;- \u03b2 \u00d7 B<sub>t<\/sub><\/code><\/li>\n\n\n\n<li><strong>Z-Score Calculation:<\/strong>&nbsp;<code>z<sub>t<\/sub>&nbsp;= (S<sub>t<\/sub>&nbsp;- \u03bc<sub>t-1<\/sub>) \/ \u03c3<sub>t-1<\/sub><\/code><\/li>\n\n\n\n<li><strong>Execution Rules:<\/strong>&nbsp;Enter when&nbsp;<code>|z<sub>t<\/sub>| &gt; 1.5<\/code>&nbsp;and exit when&nbsp;<code>z<sub>t<\/sub><\/code>&nbsp;crosses 0.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"python-implementation-code\"><strong>Python Implementation Code<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Below is a conceptual Python snippet demonstrating the core mathematical logic utilized in Shant&#8217;s strategy:<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">import pandas as pd\nimport statsmodels.api as sm\n\ndef calculate_signals(train_data, test_data, stock_a, stock_b):\n    # 1. Estimate Hedge Ratio (Beta) using OLS on Training Window\n    model = sm.OLS(train_data[stock_a], train_data[stock_b]).fit()\n    beta = model.params\n\n    # 2. Calculate Out-of-Sample Spread\n    # Spread formula: S_t = A_t - beta * B_t\n    spread = test_data[stock_a] - (beta * test_data[stock_b])\n\n    # 3. Calculate Z-Score strictly avoiding look-ahead bias\n    # z_t = (S_t - mu_{t-1}) \/ sigma_{t-1}\n    rolling_mean = spread.rolling(window=30).mean().shift(1)\n    rolling_std = spread.rolling(window=30).std().shift(1)\n    z_score = (spread - rolling_mean) \/ rolling_std\n\n    # 4. Generate Trading Signals based on Z-Score Thresholds\n    # Enter when absolute z-score &gt; 1.5, Exit when it crosses 0\n    long_entry = z_score &lt; -1.5\n    short_entry = z_score &gt; 1.5\n    exit_signal = (z_score.shift(1) * z_score &lt;= 0)\n\n    return z_score, long_entry, short_entry, exit_signal<\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3. Portfolio &amp; Risk Management:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Sizing:<\/strong>&nbsp;Equal-weight capital allocation, assigning \u20b95,00,000 per active pair.<\/li>\n\n\n\n<li><strong>Costs:<\/strong>&nbsp;Transaction costs are explicitly modeled at 5 bps per leg per side for entry and exit.<\/li>\n\n\n\n<li><strong>PnL Calculation:<\/strong>&nbsp;PnL is mapped from both legs. Any open position is force-closed on the final backtest day to ensure complete reporting.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"key-findings-portfolio-performance\">Key Findings &amp; Portfolio Performance<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The out-of-sample backtest generated the following portfolio-level performance metrics over the test period:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Strategy Performance Snapshot<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">Capital Base<\/td><td class=\"has-text-align-center\" data-align=\"center\">\u20b915,00,000<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Pairs Traded<\/td><td class=\"has-text-align-center\" data-align=\"center\">3<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Backtest Period<\/td><td class=\"has-text-align-center\" data-align=\"center\">Jan 11, 2016 \u2013 Jun 27, 2025<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Total Trades<\/td><td class=\"has-text-align-center\" data-align=\"center\">271<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Win Ratio<\/td><td class=\"has-text-align-center\" data-align=\"center\">63.47%<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Total PnL<\/td><td class=\"has-text-align-center\" data-align=\"center\">\u20b91,65,544.97<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">PnL \/ Capital<\/td><td class=\"has-text-align-center\" data-align=\"center\">11.04%<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Annualized Return<\/td><td class=\"has-text-align-center\" data-align=\"center\">0.30%<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Annualized Volatility<\/td><td class=\"has-text-align-center\" data-align=\"center\">13.34%<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Sharpe Ratio<\/td><td class=\"has-text-align-center\" data-align=\"center\">0.089<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Max Drawdown<\/td><td class=\"has-text-align-center\" data-align=\"center\">-34.31%<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"challenges-limitations\"><strong>Challenges &amp; Limitations<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Sizing Constraints:<\/strong>&nbsp;The allocation is educational (equal capital per pair); it does not dynamically model capacity limits or real margin constraints.<\/li>\n\n\n\n<li><strong>Transaction Costs:<\/strong>&nbsp;Modeled cleanly at 5 bps per leg per side, but real-world execution slippage and bid-ask spreads can differ.<\/li>\n\n\n\n<li><strong>ADF(0) Approximation:<\/strong>&nbsp;The model uses a lag-0 ADF for computational speed. A full ADF test with optimized lags is recommended for future iterations.<\/li>\n\n\n\n<li><strong>Multiple Testing:<\/strong>&nbsp;While the FDR method reduces false discoveries, it does not completely eliminate them.<\/li>\n\n\n\n<li><strong>Survivorship Bias:<\/strong>&nbsp;The 25-stock universe is fixed and does not dynamically account for historical index reconstitution.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"next-steps\"><strong>Next steps<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Improving Strategy Performance<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">While the current strategy provides a clean academic baseline, several targeted enhancements can meaningfully improve its risk-adjusted returns and real-world applicability:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. Optimise the ADF Lag Selection<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Replace the current ADF(0) shortcut with an information-criterion-based lag selector (AIC or BIC). This reduces the risk of spurious cointegration signals and improves pair selection quality, leading to more stable and reliable trade entries.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. Expand the Universe and Diversify Pairs<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The current three-pair portfolio is highly concentrated. Extending the stock universe beyond 25 large-caps to include mid-cap NSE stocks across additional sectors (Energy, FMCG, Metals) would yield a broader set of cointegrated candidates, improve diversification, and reduce the impact of any single pair breaking down.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3. Introduce Dynamic Position Sizing<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The strategy currently uses a fixed \u20b95,00,000 per pair. Replacing this with volatility-scaled sizing (e.g., inverse-volatility or Kelly-criterion weighting) would allocate more capital to pairs showing stronger mean-reversion signals and tighter spreads, improving overall Sharpe ratio and reducing drawdowns.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>4. Refine Entry\/Exit Thresholds Adaptively<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The fixed z-score thresholds of \u00b11.5 for entry and 0 for exit are static across all market regimes. An adaptive threshold model; where entry and exit levels are calibrated to each pair\u2019s rolling volatility or regime classification (trending vs. mean-reverting), can filter out low-quality signals and improve the win ratio beyond the current 63.47%.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>5. Incorporate Stop-Loss Rules to Control Drawdown<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The current maximum drawdown of -34.31% is high relative to the annualised return of 0.30%. Adding a pair-level stop-loss (e.g., exit when the z-score breaches \u00b13.0 or when unrealised loss exceeds a fixed percentage of allocated capital) would cap downside on regime-breaking events and substantially improve the Sharpe ratio.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>6. Address Survivorship Bias with a Rolling Universe<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The fixed 25-stock universe inflates historical performance by only including companies that survived the full 2015\u20132025 period. Using a point-in-time NSE Nifty 50 or Nifty 100 constituent list that reflects actual index composition at each training window would eliminate this bias and produce more realistic forward-looking performance estimates.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>Visit <a href=\"https:\/\/blog.quantinsti.com\/cointegrated-pairs-trading-indian-equity-market-epat-project\/\">QuantInsti<\/a> for more additional information on this topic.<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pairs trading is a classic statistical arbitrage strategy that seeks to exploit temporary price divergences between two related assets while maintaining a market-neutral stance. <\/p>\n","protected":false},"author":1749,"featured_media":67374,"comment_status":"open","ping_status":"closed","sticky":true,"template":"","format":"standard","meta":{"_acf_changed":true,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[339,343,349,338,341],"tags":[6465,4135],"contributors-categories":[13654],"class_list":["post-241435","post","type-post","status-publish","format-standard","has-post-thumbnail","category-data-science","category-programing-languages","category-python-development","category-ibkr-quant-news","category-quant-development","tag-portfolio-diversification","tag-risk-management","contributors-categories-quantinsti"],"pp_statuses_selecting_workflow":false,"pp_workflow_action":"current","pp_status_selection":"publish","acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v26.9 (Yoast SEO v28.1) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Statistical Arbitrage Using Cointegrated Stock 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