Interpreting Rolling OLS Hedge Ratios in Cointegrated Pairs

Summary

The document discusses a pairs-trading spread formed from the log prices of two stocks, with a hedge ratio estimated by rolling ordinary least squares. The questioner treats deviations in the spread as mean-reversion signals and asks whether a negative estimated coefficient changes the interpretation of the long and short positions or the dollar-neutrality of the hedge.

The answer recommends first checking whether the assets are cointegrated and suggests that a negative coefficient in a short rolling window may reflect instability, proposing a longer estimation window. This is guidance rather than an empirical demonstration. A rolling regression alone does not establish cointegration or dollar neutrality, and a negative coefficient is not by itself proof that a pair cannot be cointegrated; the appropriate interpretation depends on the regression setup, data, and hedge construction.

Key ideas

• The spread in the question uses log prices and a rolling OLS hedge ratio.
• The answer recommends testing for cointegration before treating a pair as a mean-reversion trade.
• A short rolling estimation window may produce unstable hedge-ratio estimates.
• The hedge ratio describes a statistical relationship and does not by itself guarantee dollar neutrality.
• The document offers no test results or detailed method for assessing cointegration.

Tags

# Pairs trading/Cointegration confusion


# Pairs trading/Cointegration confusion












I've been trying to wrap my head around cointegration. Currently I use the log returns of both stocks A and B, calculate the spread given by:

$S = log(A) - n*log(B)$ where $n$ is the Hedge Ratio calculated from a rolling OLS. In the results I've read I've operated under the assumption that if the spread falls below a certain point then long A and short B and vice versa. I believe this is a dollar neutral hedge?

My confusion lies in the Hedge ratio part whereby I'm not sure how to interpret it. I've seen an example that says long A and short $n$ stocks of B. However, I sometimes get negative values of $n$, i.e log returns are inversely correlated. How do I interpret this?

## Answer by Dhruv Mahajan (score 0)

https://quant.stackexchange.com/a/63933

Did you check for cointegration b/w A and B before running the regression? You should not get a negative hedge ratio for 2 assets that are deemed to be co-integrated with a sufficient confidence level.

If they are infact cointegrated, try increasing the look back period for calculation of rolling hedge ratio from OLS, might be the case that beta is negative for a certain small time period.

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