Choosing Price or Return Regressions for Pairs Trading
Summary
The document explains that regression on prices and regression on returns answer different questions in pairs trading. Regressing returns, or examining their correlation, describes how the assets’ short-term movements relate. The resulting weights can help characterize portfolio behavior, but return comovement alone does not establish a mean-reverting spread that can be traded for profit.
Price or log-price analysis is used when investigating long-run relationships such as cointegration and whether a combination of assets has stationary behavior. The answers differ in how they describe price regression: one frames it as searching for a stationary combination, while another cautions that price levels are usually non-stationary and that naive regression can be spurious. The practical lesson is to choose the analysis for the intended hypothesis and account for non-stationarity; the discussion does not specify a complete test, trading rule, or validation process.
Key ideas
- Return regressions describe relationships between assets’ short-term movements.
- Return correlation alone does not establish a profitable mean-reverting spread.
- Price-level analysis can be used to investigate long-run relationships such as cointegration.
- Non-stationary price levels can make naive regressions misleading.
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Full text
# Pairs trading - is regression done on log prices or log returns? # Pairs trading - is regression done on log prices or log returns? I'm getting into pairs trading (statistical arbitrage), but I keep finding different instructions on how it's done. Some sources (like this) run the linear regression (to find hedge ratio) on the log prices of the two assets. Other sources (like this) run the linear regression on the log returns of the two assets to determine hedge ratio. Which one is the correct way to do it? Is there any good source/guide for pairs trading? All I seem to find are random blogs. ## Answer by user61297 (score 1) https://quant.stackexchange.com/a/70038 depends on what you're doing. a quick google search will turn up plenty of results saying that you always want to regress returns against each other (to remove the element of trend), but sometimes you may want to regress prices against each other if trend is the very thing you are testing for https://hudsonthames.org/definitive-guide-to-pairs-trading/ ^ this is an oft recommended resource, theres also a pairs trading book by vidyamurthy and Ernie Chan has some pairs stuff in his algo trading book. check em out ## Answer by Arshdeep (score 0) https://quant.stackexchange.com/a/79527 Both mean different things - depends on what you want to get out of it. . A price regression indicates you are searching for a combination of assets that has stationary properties so any deviation in the value of the combination can be gained off. If the combination value goes far away from usual, you can be sure it will come back, which is a direct statement on your profit. The other just indicates the correlation in the relative movements of the 2 assets. Here, you can't exploit much per se, you can characterize the volatility of your portfolio as you change the weights of asset1 and asset2. It does not say how the price of 1 asset moves w.r.t the other, but how gain in one asset relates with gain in the other. ## Answer by achirikhin (score 0) https://quant.stackexchange.com/a/79531 For short term behavior, you can regress (log) returns, or just compute their correlation. For long term behaviour, you work with prices or log prices, to detect co-integration. You never regress either prices or log prices, because they are usually non-stationary. Your correlation will be oscillating and spurious.
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