# How do we correctly sum up returns

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?

• 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 '14 at 17:34