How to compute profit and loss with currency trading?
I will assume that the base currency is C1 since that is the initial balance.

Day 1: 1 C1
Day 2: sell 1 C1 for 10 C2, no change in price, so 0% gain, still 1 C1
Day 3: price falls to 1 C1: 1 C2, so 900% gain, sell 10 C2 for 10 C1
Day 4: sell 10 C1 for 1,000 C2, no change in price, so 0% gain, still 10 C1
Day 5: price rises to 200 C1: 1 C2 from 100 C1: 1 C2, sell 1,000 C2 for 5 C1, so 50% loss, now 5 C1


To sum:

0% gain by 900% gain by 0% gain by 50% loss
= 1 * 10 * 1 * 0.5
= 5
= 400% overall gain


I can provide more detail if needed, but a base currency must be selected.  The price only needs to be taken into account if there is a position still open; in other words, the price should be applied in this case if you still own something other than C1, the base currency.  

If all positions are closed out before accounting for gains, only the trades need to be used to calculate the rate of return.



The simple formula for measuring relative prices is x_final/x_initial, and the change/return/yield is x_final/x_initial-1, with gain >= 0% and loss &lt;= 0%.

Directly applying this formula to the trades, denominated in C1 is:

(10 C2/1 C1) * (10 C1/10 C2) = 10
(1000 C2/10 C1) * (5 C1/1000 C2) = 0.5


The overall relative prices is 5, expressed in percent is 400% because the percentage gain of 5 is (5-1)*100%.



If there is an open position, to account for change:

(# of C1 paid/# of C2 received) * (current price expressed as quotient of C2/C1)




Arithmetic vs geometric returns

I reread the final portion of your question.  First, the calculations are incorrect, so you should follow my example.

Second, one cannot add returns, the total arithmetic return.  They must be calculated geometrically, and that is why the each final/initial should be multiplied.