Learn English – Which is better equivalent for “in stock”? “At hand”, “on hand”, or “in hand”

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 way these different prepositions are used is all very much idiomatic, so there will be a limit to how far you can "rationalise" why any particular preposition is associated with any particular meaning. Especially in respect of "hand", since most of us always have a couple of those about our person ready to be incorporated into our word choices.

One thing I would say that "in" usually denotes something closer than "on" (which itself is usually closer than "at"), which is why the "nearby" meanings use the latter two.

Note that "in hand" doesn't actually mean having more time at your disposal - it's just that we often say we have "time in hand" (things in hand can be in reserve, spare). Apart from the literal held in the hand, the other common idiomatic usage for this one is that if something is "in hand" it's being actively dealt with (by implication, really close to you), not just sitting on your "to-do" list.

OP doesn't mention to hand, which is actually more common than the others in British English (but seemingly quite rare for Americans). In practice few would choose at hand or on hand on the basis of how physically close/accessible something was - largely pointless anyway, since few others would apprehend any subtle distinction being made. Go British and make life easier for everyone!