How to compute profit and loss with currency trading? I can't seem to wrap my head around this.  Let's say we have these fake trades between two currencies

        C1  C2      Rate    dPIP    Trade   Value C1    Value C2
Day 1   1   0       10      0       buy      1          10
Day 2   0   10      10      0       sell     1          10
Day 3   10  0        1     -9       buy     10          10
Day 4   0   1000    100    99       sell    10          1000
Day 5   5   0       200   100       buy      5          1000


Day 2 you decide to short and overnight it crashes to 1 on Day 3.  So you buy.  Your holdings for Currency 1 (C1) go up 10x.  But the value of your holdings doesn't change.  Likewise you decide to short on Day 4 after seeing a 100x jump.  On Day 5 you get cold feet and decide you sold too soon and buy in again at 2x at a loss.

How would you compute the running profits and losses (and which currency should be referenced)?  For Example on Day 3 you made 9 of C1.  Day 4: 990 of C2, Day 5: you lost 5 of C1.  What is the right way to track the P&amp;L because they are relative to each other.  

And what is the overall yield?  In the end of it all you went from C1=1 to C1=5 or in terms of C2...C2=10 to C2=1000.

EDIT:  I've looked that this some more.  If I look the change in C2 values during sales and the change in C1 values during buys I think I get the trade-trade yield.  Does this look correct?  Could then be summed to show the accumulative yield?

Example C1 yield (2nd buy) Yield=((10-1)/1)*100 = 900%

        C1  C2      Rate    dPIP    Trade   Value C1    Value C2    Yield %
Day 1   1   0       10      0       buy      1          10
Day 2   0   10      10      0       sell     1          10            0
Day 3   10  0        1     -9       buy     10          10          900
Day 4   0   1000    100    99       sell    10          1000       9900
Day 5   5   0       200   100       buy      5          1000        -50


So if you add up the yields you get 900+9900-50=10750%, but if you look at the yield on C1 it is 500% vs C2 at 1000%.  Obviously I'm not doing something right.
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.