Foundations of Statistical Arbitrage: Pairs Trading and Mean Reversion

Statistical arbitrage sounds like a guarantee of profit — find two assets that move together, sell the expensive one, buy the cheap one, and wait for them to converge. The reality is more demanding: the relationship must be statistically valid, stable over time, and large enough to profit from after transaction costs. Many aspiring quant traders discover this only after backtesting a strategy that looks excellent on paper and performs poorly in live markets. This course builds the conceptual foundation that explains both why statistical arbitrage can work and exactly where it breaks down. By the end of this course you will be able to explain the difference between correlation and cointegration and why cointegration is the correct test for a pairs trading relationship, describe what a stationary time series is and why stationarity is required for mean-reversion signals, interpret a Z-score spread signal and understand what the thresholds represent statistically, identify the key assumptions behind pairs trading and the conditions under which those assumptions are violated, and understand how transaction costs, slippage, and capital requirements affect statistical arbitrage viability. What you will learn: - Correlation vs. cointegration: why two assets can be correlated without having a mean-reverting spread - Stationarity: the Augmented Dickey-Fuller test explained conceptually and its role in pairs selection - The spread: constructing a hedge ratio using ordinary least squares regression and interpreting the residuals - Z-score signals: calculating entry and exit thresholds and what confidence level they imply - Pairs selection criteria: economic relationship, statistical validation, and liquidity considerations - Mean-reversion speed: half-life of mean reversion and its effect on strategy holding period and capital efficiency - Common failure modes: regime change, spread divergence, and fundamental news as arbitrage breakdown triggers - Market-neutral properties: why statistical arbitrage is designed to be dollar-neutral and what residual risks remain The course is structured as a series of conceptual readings with worked numerical examples illustrating each statistical concept. Each module closes with a self-assessment exercise. The material progresses from basic time-series concepts through pairs construction and signal generation. This course is designed for individuals new to statistical arbitrage and quantitative strategies who want a rigorous conceptual grounding. No prior background in statistics beyond basic probability is required — all key concepts are introduced from first principles. This course is informational and educational and does not constitute financial or investment advice.