Pair Trading Spread Direction and Residual Sign Conventions

# Pair trading - short / long the spread


# Pair trading - short / long the spread












I am wading into pair trading concepts. Here is one article I've read.

I understand for these strategies our intention is to go long on one asset and short another, however I do not understand what is meant by

> long the spread

and

> short the spread

My guess:

"long the spread" is when we anticipate the pair is converging. Short the overperformer, and long the underperformer.

"short the spread" is the opposite; we anticipate the pair to diverge, so long the overperformer and short the underperformer?

## Answer by amdopt (score 5, accepted)

https://quant.stackexchange.com/a/47279

From the link in your OP, the article is talking about buying one stock versus shorting the other. The distance pair trading system they are describing always plays the distance to converge. It just depends on which stock price has appreciated more.

For example, if "stock 1" has moved up excessively compared to "stock 2", you would short "stock 1" and buy "stock 2". If "stock 2" moved up excessively compared to "stock 1" you would short "stock 2" and buy "stock 1".

Whether or not you call this "long the spread" or "short the spread" depends on which stock you have labeled "stock 1" or "stock 2". It's important to understand that the naming of the trade doesn't mean anything, nor does it affect the mechanics of how you are trading. It's just a name.

## Answer by numerairX (score 5)

https://quant.stackexchange.com/a/47278

first keep in mind how spread is constructed, say it's $y - \beta x$, $y$ being asset $A$'s price and $x$ being that of asset $B$. Then long the spread is when $A$ is under-performing, because our current spread is smaller than "fair value". Short the spread is when $A$ is over-performing.

we always short the overperformer and long the underperformer.

## Answer by madilyn (score 4)

https://quant.stackexchange.com/a/47285

There's 2 ways to remember the sign convention:

If you're trading an exchange-listed spread, then the convention is that going long on the spread A-B implies buying A and selling B. Vice versa, shorting the spread implies selling A and buying B.

If you're trading a synthetically-constructed spread, then this means that you're trading the residual, i.e. the difference between the observed $y_t$ and the $\hat{y}_t$ predicted by your regression model.

The simplest example is a pair trade where you're regressing a series $y_t$ against another series $x_t$. You may assume that there exists a linear relationship between the series and a normally distributed error term $\epsilon_t \sim \mathcal{N}$ such that $\epsilon_t = y_t - \hat{y_t}= y_t -\beta x_t -\alpha $. $\alpha,\beta \in \mathbb{R}$ are parameters that you estimate from past data, e.g. with ordinary least squares.

Often, you'd also assume $\alpha$ falls off at $x_t=0$. Then "buying the spread" implies having positive delta to $\epsilon_t$ which means buying 1 unit of the product with series $y_t$ and selling $\beta $ units of the product with series $x_t$.

You don't even need to remember what it means to "buy a spread" in this case, because the intuition behind your trade is simply that if the observed value $y_t$ is less than the predicted value $\beta x_t$, then you would buy the product with series $y_t$ and sell $\beta$ units of the product with series $x_t$, since the observed value and your prediction should eventually converge somewhere. You just need to remember which variable you used as the predictor $x_t$ and the dependent variable $y_t$ when fitting your model.