How FX Position Tracks Currency Inventory and P&L
Summary
The document clarifies what a forex position represents after a series of buys and sells. For a currency pair, the running signed trade amounts alone can describe net exposure, but the worked answer tracks the balances of both currencies created by each transaction. Each trade changes the amount held in one currency and the amount owed or held in the other, at that trade’s exchange rate. The resulting inventory is expressed as a balance in each currency, such as euros and dollars for EUR/USD.
To estimate current profit or loss, the currency balances are translated at the current spot rate and combined. The example shows that the residual currency inventory can be valued this way even though the sequence of execution prices is not retained in a single net amount. The answers also frame position as inventory useful for managing exposure to exchange-rate moves; historical cost and current risk are related but distinct tracking concerns. The example depends on a stated interpretation of the trade amount and quote convention, so careful unit and sign conventions are needed when applying the accounting method.
Key ideas
- A forex position can be represented by the residual balances of both currencies in a pair.
- Each trade changes both currency balances according to its exchange rate and transaction direction.
- Current P&L can be estimated by translating inventory at the current spot rate.
- Net currency exposure is useful for assessing risk independently of the trades’ historical rates.
- Clear quote, unit, and sign conventions are needed to maintain correct balances.
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Full text
# What is meant by "position at a given time" in the context of a series of forex trades? # 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? ## Answer by Phil H (score 3, accepted) https://quant.stackexchange.com/a/15070 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 by Degustaf (score 0) https://quant.stackexchange.com/a/14991 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 by rupweb (score 0) https://quant.stackexchange.com/a/14995 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.
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