In the finance field, it is quite common to express some measures in relation to some grouping criteria. Some groupings can be temporal (year, month, etc.) and others like greography, asset class (e.g. a financial product), strategy (used in trading), and others.
Which one is the most appropriate preposition to apply in this kind of expression ?
Is there any well defined rule behind the most appropriate use ?
I always use by, because in this context we mean "grouped by"
PnL by trader = PnL results grouped by trader
PnL by day= PnL results grouped by day
VaR by asset = VaR results grouped by asset
VaR by portfolio = VaR results grouped by portfolio
The two are often used differently (though there are many cases where both would work).
The word "per" carries the implication (as in percent) that there is a division going on - so if someone says to me "I'll tell you the number of widgets manufactured per employee" I'm expecting one number - the total number of widgets manufactured divided by the number of employees.
If instead they said "This table gives a breakdown of number of widgets manufactured by employee", I would expect to see a list of employees, and for each one the number of widgets manufactured by that employee.
Of course, in many circumstances both usages could work: a table giving the total profit for each of the past ten years could be "profit per year" (because each row in the table gives the profit/year ratio for that one year), or "profit by year" (because it shows the profit associated with each year).
Per is usually used to mean "for each," especially with units, where it is used to express a rate.
You can make a case for either if the grouping is really a subgrouping. There is not a functional difference between "chickens sold per season" and "chickens sold by season."
More often I notice "by" used in this context, but I imagine it's a matter of local preference.
The word "per" has its roots on Latin language, while "by" has roots on Germanic Languages.
Meaning is also a bit different: "by" usually refers to a person or object. "Per" refers to a category.
Example: You don't say "This work was done per me". You say "This work was done by me".
