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

Question

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?

Answer 1

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.

Answer 2

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.

Answer 3

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.