Multivariate Cointegration for Dollar-Neutral Mean-Reversion Trading
Summary
This document extends a cointegration-based spread strategy from pairs to three or more assets. It forms a weighted combination of log prices using a cointegration vector, then derives a spread return from the same weights. Under stated stationarity conditions, the spread is expected to mean-revert, providing a basis for trading when the assets move apart. The document illustrates the framework with an empirical application to four European stock indices at daily frequency.
The proposed position in each asset depends on the cointegration weight and the accumulated lagged spread returns. It derives positive expected profit under its assumptions, then describes how to scale long and short legs to make the portfolio dollar-neutral. Since price histories are finite, it replaces the theoretical infinite lag sum with a finite lookback. The result is conditional on the return and covariance assumptions, and the document does not provide empirical performance statistics or transaction-cost analysis. It also notes that positions can change direction and the portfolio is designed to remain invested.
Key ideas
- A stationary weighted combination of asset log prices represents a cointegrating relationship.
- The trading rule takes positions across multiple assets based on lagged returns of the combined spread.
- The stated positive expected profit follows from assumptions about zero-mean returns and their autocovariances.
- Long and short notionals can be scaled to create a dollar-neutral portfolio.
- A finite lookback approximates the theoretically infinite sum because practical price histories are limited.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.