Matching Pairs Trading Positions to the Beta Estimation Method
Summary
The document asks how to translate a pairs-trading spread signal into positions in two assets. It defines a spread as one price minus beta times the other and considers entry signals when the spread moves above or below its mean by a standard deviation. The central issue is whether positions should be chosen by the sign of the spread, by relative percentage moves, or by the regression convention used to estimate beta.
The accepted answer says position sizing should match the data used to estimate beta. If beta is estimated from returns, the spread and signal should use returns, with dollar exposures arranged to be cash neutral according to beta. If beta comes from regressing prices, the suggested hedge uses shares in the corresponding beta proportion. The document does not develop a full trading rule, address re-estimation or execution, or provide systematic performance evidence. A separate response describes a ratio-based approach with statistical filters and a small example, but its reported outcomes are anecdotal and do not validate the strategy.
Key ideas
- Pairs-trading position units should match whether beta was estimated from returns or prices.
- A return-based beta calls for a return-based spread and dollar-based hedge sizing.
- A price-regression beta leads to share quantities in the corresponding beta proportion.
- The document provides no systematic evidence that either approach is profitable.
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Full text
# Pairs Trading Signals and Positioning
# Pairs Trading Signals and Positioning
I am currently working on a research project for a pairs trading strategy and would like to know the correct positions to take when a signal has been triggered. Say we are using this equation to generate signals: \begin{equation} z = y - \beta x \end{equation} $\mu_z$ = 0, $\sigma_z$ = 0.5, and $\beta$ = 1, for simplicity. And our signals to open are: (z >= $\mu_z$+$\sigma_z$ & z <= $\mu_z$-$\sigma_z$) Then a signal will be triggered when : 1) y = 10, x = 9.5 2) y = 10.5, x = 10 3) y = 10, x = 10.5 4) y = 9.5, x = 10 Should the positions taken in these scenarios be different? Should we short 1 share y and go long $\beta$ shares of x for 1 and 2? Should we go long 1 share y and short $\beta$ shares of x for 3 and 4? Or should we actually be calculating pct change in y and $\beta$x and then short which ever had the greatest pct change and go long the other?
## Answer by LazyCat (score 2, accepted)
https://quant.stackexchange.com/a/24818
It should be consistent with the way you calculate $\beta:$ if you use stock returns to compute it, then you should be using returns to compute the spread and your signal, and aim to be cash neutral: N $\it{dollars}$ long of x and $\beta\times N$ $\it{dollars}$ short of y. If you regress the prices of x and y to obtain $\beta,$ then pretty much, what you wrote - N $\it{shares}$ of x and $\beta\times N$ $\it{shares}$ of y.
## Answer by Peter Salomonsen (score 0)
https://quant.stackexchange.com/a/24812
This doesn't answer your question directly, but it may be interesting for you to see a visualization of a pair trading strategy.
I'm the developer of an interactive chart tool for technical analysis that also has a pair strategy function. In my pair trading implementation I'm calculating the mean ratio between the stocks and generating entry signals when the ratio is 2 std. deviations from the mean ratio and exit when 1 stddev. I'm also running cointegration (ADF) and correlation tests that has to pass for the entry signal to be generated.
An "random" example of the strategy is shown in the live interactive chart (link below). The white area shows when a trade is active - and "Algo" shows the return for all trades in total. As shown in the chart for the past 9 months the automated strategy generated 6 trades and all of them gave positive returns including the one that is currently open.
https://bors.e24.no/?qlyze=j5fPryaPUiS1z5pUj1R52yDygE#!/instrument/OSEBX.OSE/analysisShown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.