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Cointegration Hedge Ratios and Share-Price Differences

Article Quant Q&A · Author: 43zombiegit
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Summary

The document raises a pairs-trading question about estimating hedge ratios with rolling ordinary least squares on two stocks’ log returns. The author observes that when the stocks have very different share prices, the estimated ratio can still be near zero to one, and worries that this would imply a very small position in the lower-priced stock.

It provides no answer or supporting analysis, so it does not establish whether the method or the author’s interpretation is correct. The question highlights a distinction worth examining: a return-based hedge ratio describes the relationship between return exposures, while translating that ratio into share quantities also involves prices and position sizing. Any practical conclusion would depend on the chosen regression specification and how the resulting exposure is converted into trades.

Key ideas

  • The document asks how to interpret a hedge ratio estimated from stock log returns.
  • Large differences in share prices do not by themselves determine a return-based regression coefficient.
  • Converting a hedge ratio into share quantities requires considering the instruments’ prices.
  • The document poses the issue but supplies no answer or empirical evidence.

Tags

EquitiesPairs tradingStatisticsPosition sizing
Full text
# Cointegration and hedge ratio


# Cointegration and hedge ratio












I've recently been looking into pairs trading through cointegration. So far I've used the log returns of stock A and stock B in a rolling OLS to find the hedge ratio. However, I've noticed that for a pair whereby stock A and B have massive differences in price that the hedge ratio still remains small. Say for example stock A was trading at 600 a share and stock B at 1. The log returns of these two stocks won't be too far off and so the resulting hedge ratio will end up around ~0-1. Therefore I would be shorting a really small position in stock B.

I'm almost certain that I've got something wrong in the above example so feel free to correct me.

Thanks

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