# 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&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 <= 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.

• I have a few questions, but first how are you computing gain. 1/1*100= 100% not 0%, but 10/1 * 100 = 1000%. Is gain the same as yield? Dec 25, 2013 at 6:26
• @user6972 Sorry, was a little inebriated, and it was late when I wrote it. Please note edit and let me know if you have any more questions.
– user5107
Dec 25, 2013 at 6:55
• Thanks that is very helpful and thanks for redoing your numbers. Now I see what I was doing wrong. I would like to find a way to express the gains made by shorting if the price drops. Is this what you mean by measuring the open position (your last formula)? Dec 25, 2013 at 17:28
• @user6972 Yes, and if that last formula is still a little elusive, add an open short including the initial trade and the present price to your question, and I will use that data with the general formula to give you an explicit example. For any full roundtrip, where you sell `C1` to buy `C2` then sell `C2` to buy `C1`, the above examples should be sufficient.
– user5107
Dec 26, 2013 at 5:33
• I think I understand. I just take the initial purchased share ratio of C1/C2 * (current rate C2/C1) to see how the short is doing. Thanks for walking me through the basics. It's odd that most references I found on trading just say "your trading account will compute this automatically" and skip on along. Dec 26, 2013 at 18:58

The simplest way to track profits and losses from trading is to mark your holdings to market in your local currency each day. That is, each day, value all your holdings in your local currency at their market price and sum them. If that number goes up, you made a profit on your combination of holding and trading currencies. If that number goes down, you took a loss.

There are various benchmarks you can compare that to. One is your total investment, which you should also value at market price as you invest it. So if you put in one Bitcoin when Bitcoins are worth \$750, you add \$750 to your total investment. Another is how much you would have if you had simply held Bitcoins instead of trading. Another possibility is to compare against other types of investments such as stocks or bonds.

Note that holding and trading crypto-currencies can be profitable but is extremely risky.

• I'm really more interested in computing trade to trade P&L. See edit. Dec 19, 2013 at 23:11
• Just mark to market the thing you traded and mark to market the thing you received in trade. That's the trade P&L. This can, however, give a deceptively high value because market makers can easily be forced to hold a currency only when it's dropping, so you can't ignore your currency holding losses. Dec 20, 2013 at 11:11
• My question is specific to how the calculations are done. I understand the concepts however my calculations don't seem to work out quite right. Dec 21, 2013 at 16:58

It really depends on what you call profit. If having more X means you made a profit, denominate in X!

If you want to compare two trades you generally want to see if you ended up with more than you went in with. Did a buy result in a better sale, or vise versa.

X can be loafs of bread, cars or preferably other currency.

Ultimately it is about increasing total wealth (I assume). That means you have to measure wealth. How you do that is up to you!

To be more direct: Pick either of those, or their value to a third currency. In the end what matters is how much you can buy with it, so picking a very stable third item is a smart move. If you care just about boosting these two numbers you can express your total value in one of the two.

• Either way my numbers don't seem to be correct. Dec 22, 2013 at 1:29