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How Long Currency Positions Create Gains and Losses

Article Quant Q&A · Author: mjs

Summary

The document asks how a trader whose account is denominated in SEK can profit when the RUB weakens, and whether buying USD/RUB means simply buying USD. The answer models a long USD/RUB position as exposure to 100 USD against a short position of 100 RUB. When the exchange rate moves from parity to 1.1 RUB per USD, closing both legs and converting the result back to SEK produces a profit of 9.09 SEK under the stated assumptions.

The explanation distinguishes holding a currency balance from entering a long position on a quoted pair: buying USD/RUB means being long USD relative to RUB, so the position gains when that quote rises. It also notes that the same exposure translated through USD/SEK gives the same result when that cross rate is flat. The arithmetic assumes zero RUB interest, fixed cross rates, and no transaction costs or other financing effects; actual leveraged forex products may represent positions differently from the simplified balance-sheet illustration.

Key ideas

  • Buying USD/RUB means taking a long USD position against a short RUB position.
  • A rise in the USD/RUB quote benefits a long position in that pair.
  • The stated parity example yields 9.09 SEK after converting the position's gain back to SEK.
  • Holding a currency balance and entering a long position on a currency pair are distinct exposures.
  • The calculation omits interest, transaction costs, and other real-market frictions.

Tags

Full text
# How trading in currency pair works, underlying techniques and mechanisms


# How trading in currency pair works, underlying techniques and mechanisms












I am somewhat experienced in Forex trading, but I have a question which has bothered me for quite some time.

If we for instance go back in time four months, to before the beginning of value loss the RUB(RUBLE).

Say that I wanted to make money on the loss of value of the RUB, with my Forex account being based on SEK.

What I am confused about is this, what is the difference in the amount of money I make, if, we assume that USD/RUB and SEK/RUB will both increase 10% over the next time period, which also means that the USD/SEK will increase/decrease 0% against one and other.

Lets also assume that all currency pairs have an initial 1:1 ratio. 100 SEK = 100 USD = 100 RUB.

Mechanism A)

> If I buy 100 SEK in the USD/RUB currency pair, my prior understanding was that I am actually buying 100 USD. My 100 SEK are therefore first exchanged for 100 USD. When the value of the USD/RUB over the next period goes up 10%. I sell my 100 USD. But what do I then sell it for? 1) Do I get RUB? Ok, my 100 USD now gets me 110 RUB. 2) Do I get SEK? Ok, my 100 USD now gets me 100 SEK, so that scenario is out. Then now, we continue with 1). When my 110 RUB are exchanged back for SEK, I should get 110 RUB/(1.1SEK/1RUB) = 100 SEK. Therefore I did not make any money on the shorting of RUB through USD/RUB. Despite the RUB loosing value against the USD! But this can't be true. So how does the underlying mechanism work? My understanding is, and the above example shows, that it doesn't matter if you buy USD/RUB or USD/SEK currency pairs, since what you are buying is essentially USD in both cases. But I don't believe this scenario is correct. What is then the correct underlying mechanisms to facilitate a transaction where you can make money on shorting the RUB, or as I have been thinking, the increase of value of USD versus the RUB. I used to think that I am buying USD, so it doesn't matter what currency pair, USD/RUB or USD/SEK. But as I write this question now, I am getting a different understanding.

My second possible scenario for how this might go is this:

Mechanism B)

> When I "buy" 100 SEK worth of USD/RUB, I am actually lending 100 RUB from the market, selling it immediately for 100 USD, then when the price of USD/RUB goes up 10%, to 110 RUB I sell my 100 USD getting 110 RUB. I then return the 100 RUB to the lender, keeping 10 RUB. I then sell the 10 RUB for SEK, keeping 10/(1.1SEK/RUB) = 9.09 SEK, for a total profit of 9.09%, despite the USD/RUB, SEK/RUB actually having increased 10%. It would also mean that it is better were you can to trade directly in the currency pair you have, SEK/RUB rather than USD/RUB if your account is in SEK. Then you would have made 10% rather than 9.09% without any additional costs of transactions. ( I find this a bit puzzling though, need to think about this. )

This scenario is kind of strange because you are lending 100 RUB, then selling it for 100 USD, meaning that you could also just be lending 100 USD directly, or buying actual 100 USD, omitting the lender, but then we would end up in Mechanism A) again. The lender is needed, so you are never actually buying any currency. You are lending the other currency pair, and buying USD.

Note that I am kind answering the question as I formulate it, which is something I had difficulties doing for myself earlier. It pays to write questions and try to explain them :)

The second scenario would allow for a profit to be made as we can see, and one that seems to be the way it must be done.

But this also constitutes a difference in how some people normally seem to think of trading in Forex, and how the Forex platform buttons usually say, "Buy" and "Sell".

My original idea is that when you "buy" USD/RUB, it is the same as buying USD currency so it won't matter if it is USD/SEK, or USD/EUR, because it is perceived as the net result is you buying USD. It shouldn't matter what currency pair. You might even save the last exchange cost doing.

This is the way people normally seem to explain it, that you are buying USD. But you are obviously not buying USD when "buying" USD/RUB as if you were "buying" a stock. You are lending RUB, selling it for USD, selling the USD later and returning the original RUB.

When you buy a stock, you are indeed buying it. Possibly not even so in CFD' markets? When you are shorting a stock, you enter the lending mechanisms.

However, in Forex currency pair trading, it must be that you are always in the lending mechanism.

> It would also explain how despite your account being in SEK, you could make money on going long on the SEK/RUB or "buying" SEK with the same amount of SEK as in your account. You are not buying SEK, you are initially lending 100 RUB, selling it for 100 SEK, making it 200 SEK in your account, and then buying 100 RUB for 90.9 SEK later, returning them, keeping (200-90.9)SEK = 109.1 SEK.

Despite the direction, you are always kind of in the mechanisms of shorting/blanking.

Is this the correct understanding?

Sorry for this long post.

## Answer by Phil H (score 1)

https://quant.stackexchange.com/a/15323

Book with counterpart SwedishAlphaBank, with whom you margin in SEK:

```
USD   RUB   SEK   SEKPnL
 0     0     0      0
```

Buy 100 SEK worth of USD/RUB, meaning buy USD and sell RUB.

```
100   -100   0      0
```

With RUB interest rate at 0 (!), USD/RUB moves to 1.1, USD/SEK stays flat at 1

```
100   -100   0    9.09
```

Square up back to SEK on USD and RUB:

```
 0      0    9.09   0
```

You say this is worse than doing it via USD, but USD/SEK is 1:1 for the whole thing, it is exactly the same:

100 USD -(100 RUB/1.1 RUB per USD) = 9.09 USD

Regarding buy/sell: buy means to enter a long position on something. So if I enter a long position on USD/RUB, as USD/RUB goes up (1.0 to 1.1), I win. That can only be the case if I am net positive USD vs RUB. I am not convinced, though, that being 'long Rouble' is the same as having a position in USD over RUB, so there is some care to be had there - certainly 'holding Rouble' is a balance in RUB which would benefit from RUB strengthening (1.0 -> 0.9) rather than weakening (1.0 -> 1.1).

The buy/sell terms are used in other markets where a position is entered rather than an asset explicitly bought. If you buy futures, the same happens; as the future goes up in price, you win, even though the number is just a construct from the exchange. Similarly you can 'buy' an IRS; the buyer pays fixed and receives float. Vanilla IRS are par instruments, so nobody is theoretically paying any money at the outset, but again if the par fix rate goes up, the buyer gains here (the position will be in the money).

If you want to dig deeper, money itself is an asset, which you exchange for a contract or a bill. So even buying a share is exchanging a promissory note from a central bank for a contractual note, certificate or numbers in a database.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.