# What is meant by “position at a given time” in the context of a series of forex trades?

Suppose you are only talking about a single currency pair, say EUR/USD. Throughout some period of time, you engage in trades with various other parties, sometimes buying, sometimes selling. The rates will be different for each trade, as the rates change in response to market conditions.

An example sequence of trades might look like this:

Time | Amount |   Rate |
t1      100   1.2636
t2    -1000   1.2599
t3      200   1.1612


and so on.

Later on, for a given current rate (say the market midpoint), you could transform all of these previous trades into a profit or loss as implied by that current rate. And you could summarize the whole sequence of trades with a "PnL" number by summing across the profit implied by each trade.

But what is usually meant by "position" after a sequence of such trades?

Does that term just refer to the running sum of the Amount column in my example (so just the pure number of units of the currency pair you've net bought/sold)?

The reason this puzzles me is that the position would lose information about what rate each amount was originally traded for. So, while the sum of the amounts would tell you your current total amount held (net long or net short), you wouldn't be able to work out profit from just snapshot of this total plus a snapshot of the rate.

Of course, this number could be useful for other purposes, like comparing how much relative exposure you have to one currency pair compared with another, outside of the running profit/loss of the trades that got you there.

Is this the correct way to think of "position" (e.g. it's just the running total amount you have net bought/sold, even if that summary number is useless in obtaining the profit at a point in time)?

Or is there something else that's customary for keeping track of position that also combines it with the rate at each trade?

Position here is the residual amount of one or other currency at the end:

You gave us:

Time | Amount |   Rate |
t1      100   1.2636
t2    -1000   1.2599
t3      200   1.1612


Assuming the Amount is amount paid in USD, and the rate is EUR/USD:

Time | Amount |  Rate  |  EUR balance | USD balance
t0                           0             0
t1       100   1.2636       79.139      -100
t2     -1000   1.2599     -714.575       900
t3       200   1.1612     -542.339       700


So this book is now net long of USD, short of EUR, compared to t0. If we calculate our PnL using the current spot rate (1.2762), the EUR side is worth -\$692.13, leaving a net profit of \$7.87.

• The amount describes "amount of the pair", so it is denominated in euros, not USD. But, your description is a good one and this is ultimately the way I represented it within the task I was working on. – ely Oct 17 '14 at 14:19

You aren't including how much of your base currency you have in your portfolio. Once you do that your position can be written as $X$ USD and $Y$ EUR. Beyond doing much of the work for your P&L computation, this is also useful for monitoring your risk to FX changes.

• I'm not sure I understand. Suppose you start out with a zero position. If we think of the position as only existing for the currency pair (so a choice of owning Y EUR is equivalently a choice to sell rate*Y USD, as we can always write everything in USD, using negative number to indicate when we sold the pair and positive when we bought the pair). What am I missing there? – ely Oct 9 '14 at 21:25
• Maybe what you are saying is that if you keep track separately of the long position and short position, then you can do long - rate*short to get your profit at any point in time. This means you would use a tuple (X, Y) to represent your position over time. Is this what is commonly called "your position" during a sequence of trades, a 2-tuple? Is it common to plot two overlapping curves, one for the long position amount and one for the short, if you wanted to look at "the position" during the day? – ely Oct 9 '14 at 21:37
• Yes, I see now that this must have been what you meant. I added a bit to elaborate. – ely Oct 9 '14 at 23:02

Position means inventory. See Survey of market making strategies and research

What you're puzzling about is what would be the value of your inventory in some risk (PnL) currency other than the currency you actually have. That's why you'd have rates from one currency to another. But the current value of your inventory expressed in terms of some other currency is not what matters. If EUR is going down, you sell all the EUR you have, and probably go short. It doesn't matter where your inventory came from, or how much it cost, you have to manage your current inventory according to the market conditions.

• I think the phrase "It doesn't matter where your inventory came from, or how much it cost" is misleading and that's what confused me before. If you keep an inventory expressed as two numbers (say EUR and USD), then each time you update the USD part, you are exactly encoding "how much it cost" (the rate of that trade) and "where it came from" (the corresponding amount of Euros). So it is encoding this as you go. If instead you only keep track of EUR, then for each EUR amount, you also need the rate at that trade, to get over to USD for any given trade and compare with the current rate for PnL. – ely Oct 10 '14 at 12:22
• The inventory approach is clearly a much easier and less confusing way to calculate it, which is what was confusing me about the "process each trade in sequence and compare that trade's original rate to the current rate" method. You do that in an impounded way by keeping track of each currency separately. – ely Oct 10 '14 at 12:24
• @EMS if EUR is going down, what I meant is then it's going down against all other currencies. So if you have an inventory then sell it all off. It doesn't matter what price you bought it. That is my basic position. Obviously EUR can simultaneously rise and fall against different currencies, but I think there's overall a correlation with the majors. – rupweb Oct 14 '14 at 10:24