Testing Portfolio Mean Reversion with Cointegration

Summary

The document asks how to test whether rebalancing a portfolio of assets could benefit from mean-reverting behavior. It contrasts this portfolio question with applying a Dickey–Fuller test to a single time series, which can assess evidence of mean reversion in that series over the sample.

The response explains that cointegration among integrated asset-price series implies a linear combination that is stationary and mean-reverting. A portfolio whose weights follow that combination can provide an exposure to the reversion. For a small asset set, vector autoregression or error-correction models are suggested; principal component analysis is mentioned for higher-dimensional settings. The discussion is conceptual: it supplies no test results, trading rules, or evidence that rebalancing would be profitable after costs. Cointegration is a statistical relationship, so an estimated mean-reverting combination still requires validation and careful portfolio design.

Key ideas

• Cointegration can identify a linear combination of integrated price series that is mean-reverting.
• Portfolio weights can be chosen to represent that stationary combination.
• Vector autoregression and error-correction models are options for smaller asset sets.
• Principal component analysis is one approach suggested for larger collections of assets.
• Statistical mean reversion alone does not show that rebalancing will be profitable.

Tags

# Tests for Mean Reversion in a Portfolio Rebalancing


# Tests for Mean Reversion in a Portfolio Rebalancing












On a single time series one can run a Dickey-Fuller test to determine if the asset is mean reverting or at least has been mean reverting during your sample.

Is there a way to test for mean-reversion in a portfolio of assets? In other words is there a way to test if portfolio re-balancing would have offered statistically significant advantage?

## Answer by John (score 4, accepted)

https://quant.stackexchange.com/a/20932

If two or more (I(1)) time series are cointegrated, then this means that you can find a linear combination of them that is mean-reverting. Thus, if you create a portfolio with weights that are proportional to this linear combination, then the portfolio returns will also be mean-reverting.

There is a large literature on cointegration and asset prices and many techniques to try to take advantage of this behavior in asset prices. For a small number of assets, you could fit a VAR or ECM. For larger dimensional problems, PCA is often used.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.