Statistical arbitrage is a family of strategies that earns returns not by predicting where prices go in absolute terms but by betting on how prices relate to one another. The precondition for any such strategy is a residual — a linear combination of price series — that is stationary and mean-reverting. Without stationarity, there is no equilibrium to trade against, no threshold to enter from, and no convergence to profit from.
This topic lays the two conceptual foundations the rest of the unit builds on. First, it establishes why the relevant bet is relative rather than directional: CAPM's decomposition of returns into a market component and an idiosyncratic residual shows that a zero-beta long-short portfolio strips out the direction of the market and leaves only the spread, which earns a return when mispricing corrects. Second, it establishes the statistical precondition: price series are integrated of order one (random walks), so a raw price spread wanders without mean-reverting. Only when the spread can be shown stationary — formally, when the constituent series are cointegrated — is the pair tradeable.
By the end of this topic you should be able to:
- decompose a single stock return into its market component and idiosyncratic residual using CAPM;
- construct a zero-beta long-short portfolio and explain why its P&L depends solely on spread convergence;
- distinguish strong from weak stationarity and state the conditions each requires;
- demonstrate that a random walk is I(1) and that its first differences are I(0);
- interpret the Augmented Dickey–Fuller test and apply it to decide whether a spread is tradeable;
- state why two I(1) price series can form an I(0) spread (cointegration preview);
- locate the relative-value idea within the anatomy of a quantitative trading system.
In this lesson
- Contents
- The big picture
The full lesson is for members.
Read the full lessonNew to SelfMadeQuant.com? See membership options or browse the Statistical Arbitrage syllabus.