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Assume I have done 8 trades and calculated the profit (or loss) of each trade:

Balance     PnL
100 
102         2.00%
105         2.94%
103         -1.90%
101         -1.94%
98          -2.97%
97          -1.02%
99          2.06%
100         1.01%

As one clearly can see I do not have any profit or loss since my balance is back at my starting point. But if I sum up all the single p/l it looks like I would have gained 0.18% which is not the case. How do I have to sum up all returns correctly? I know I simply could calc the p/l on the first and the last row but I really want to know if there is a way of correctly summing up returns?

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Now that you've read an answer you should be able to answer this question: Suppose you reordered the PnLs and recomputed the balances. Say instead of 2, 2.94, ... 1.01, you had all the losses first and all the gains last. Clearly each balance along the way would be different. Would the final balance be different? –  Eric Lippert Apr 29 at 17:34

1 Answer 1

up vote 9 down vote accepted

Assuming you are putting everything into each trade, then what you'd want to do is multiply your returns together with a 1 added to normalize things.

2.00%, 2.94%, -1.90%, -1.94%, -2.97%, -1.02%, 2.06%, 1.01% are the individual returns.

(1.02)(1.0294)(.981)(.9806)(.9703)(.9898)(1.0206)(1.0101) = 1.00004293936 which rounds off to 1 which is a 0% total return in the end.


An easier example to consider is if you had 2 trades: The first makes 10% and the second makes -10%. While at first glance these should cancel, the reality is that you are down 1% in the end if you look at it with compounding:

$100 at the start goes up to $110 and then down to $99. (1.1)(.90) = .99 and thus it is a 1% loss in the end by the multiplication so to combine the returns is to take a product rather than sum.

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