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This is something I've been thinking about for a while but I can't reach a clear conclusion. When we calculate, for example, the profit factor for a pairs trading strategy, do we treat each pairs trade as a single result or each of the separate trades on each instrument as a single result? For example, lets say we are trading 2 instruments A and B and we have the following results...

A: -2, 1, 3

B: 1,-2,1

Profit factor for each trade separably -> 5/4

Profit factor for each pair added together -> 4/2

If we treat each pairs trade as a single trade we get a better result, the same would apply when trying to calculate a Sharpe ratio. I guess one could ask the same question of hedged options trades, what do people generally do?

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Of course you get through diversification effects different return variation and thus Sharpe ratios depending on whether you calculate the standard deviation on an individual asset or a portfolio standard deviation on a collection of assets. A pairs trade is a small portfolio so with favorable correlation properties you should generally get a better risk adjusted return on the pair than on each asset individually. Market practice is to treat a pair as a portfolio for risk attribution and performance attribution purposes. The whole point of the pairs trade was exactly that, the attempt at capturing a temporary deviation from a presumed co-integration pattern, correct?

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I think so, I'd managed to roughly convince myself of the same, but it's good to see I'm thinking along the correct lines. –  Craig Nov 22 '12 at 17:02
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