So I am creating a trading algorithm thats uses cointegration, for a pairs trading strategy. Imagine there is stock A for 100 dollars and stock B for 25 dollars. My questions is when caulcating the spread, should I calculate the spread of the prices which would be $75, or should I use the A:B ratio of 4. Does it matter? Is one better than the other? Whats the difference? Thanks!
I can't help you with any theory since that's above my pay grade. All I can offer is some practical experience from my pairs trading.
In a macro sense, the 1:1 and 4:1 graphs over time will have a somewhat similar shape with peaks and valleys somewhat tending to line up (the granular data will determine that). For discussion, let's assume daily data. However, because the daily ROC of each component is different, the daily volatility and ROC will be different for the respective graphs.
For example, if A at \$25 moves up 1% today and B at \$100 moves up 2% today, the the spread width of the 1:1 increases by \$1.75 whereas the spread width of the 4:1 increases by \$1.00 . If you have some criteria for entry and exit, they should be relevant to the actual position.
My short answer is to suggest that you program the spread that you will be trading not the spread data of another pair combination.