Cointegration Residuals and Pair Trading Opportunities

Summary

The document asks whether a tighter linear relationship between two equity prices leaves fewer opportunities for pairs trading. It distinguishes the quality of a cointegrating fit from the behavior of the residual spread, and asks whether a residual with mean-reverting, autoregressive dynamics would provide more useful entry and exit signals. A small simulated example combines a random walk, a sinusoidal component, and noise to illustrate the question.

The document offers no tested trading rule or empirical results, and it does not resolve the question. In particular, it provides no comparison of candidate spreads, trading thresholds, transaction costs, or out-of-sample performance. Its central research prompt is whether residual stationarity and predictable reversion can support trade timing, rather than whether a linear fit is simply close. The simulation is illustrative only; it cannot establish that either pair is tradable or that a particular residual model improves returns.

Key ideas

• A close linear fit between two prices does not by itself establish how profitable a pairs strategy may be.
• The document asks whether autoregressive mean reversion in the spread could provide clearer trade entry and exit points.
• Its toy simulation combines a random walk with sinusoidal variation and noise to motivate the question.
• No trading method, empirical test, or evidence of profitability is supplied.

Tags

# Cointegration and pairs trading


# Cointegration and pairs trading












I have intuition that cointegration between elements of pair of equities somehow contradicts pairs trading strategies. Because the better is linear fit of the model the less opportunities we have for arbitrage (with still holding assumption of stationarity of residuals).

For me it seems that it would be better (from trading point of view) to fit model which assumes that residuals follow autoregressive mean-reverting process (which looks like sinusoid or randomly alternating version of it)

primary school justification of my question in R :

```
set.seed(123)
N=120

x1 <- cumsum(rnorm(N, sd=0.24))
SIN <- sin(seq(0, 20, length.out=N))
x2 <- x1+SIN+rnorm(N, sd=.2)

matplot(cbind(x1, x2, SIN), t="l")
abline(h=0, col=3)
```

if residuals are not correlated isn't it harder to select entry and closing points of pairs trading strategy ?

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