I am approaching this question from a Computer Science perspective (Developer, Programming etc.), so apologies if the question is trivial. I have been searching the web for a while, but I am afraid I am too unfamiliar with the domain to yield useful answers, so a brief explanation and maybe some references / pointers would be welcome:

Let's say I have currency ABC, DEF and XYZ. (Like USD, EUR, GBP etc.) Now if I want to convert ABC into any of these, I'll end up having something like this, using ABC as the base:

1 ABC = 1.5 DEF
1 ABC = 0.75 XYZ

Now if math holds true, then the if I change the base from ABC to DEF and XYZ, I should see this:

1 DEF = 2/3 ABC
1 DEF = 0.5 XYZ

1 XYZ = 2 DEF
1 XYZ = 4/3 ABC

Now, the questions:

  1. Is this correct? or is it possible that the rates are different? let's say 1 DEF = 0.56 XYZ instead of 0.5, in the above example?
  2. If it's not the case, what is a reliable source to find out the exact rates for different base currencies? (I am looking for a bit more data than a simple google exchange calculator though)
  3. Also, can the difference be so significant that after doing a loop I end up with more money? (e.g 100 ABC --> 150 DEF ==> 80 XYZ --> 106 ABC)


As @DStanley pointed out, reciprocal values are not the same, so let me clarify further.

In other words, where I am going at is something like this: is this 'base currency' a thing in exchange or not really?

  • If you have a 'base' in CAD, the USD --> EUR ratio is 1.27
  • If you have a 'base' in CHF, the USD --> EUR ratio is 1.28
  • If you have a 'base' in USD, the USD --> EUR ratio is 1.30
  • If you have a 'base' in GBP, the USD --> EUR ratio is 1.32

Here's an 'example' maybe this helps to conway what I want to know.

Lets say you have a 130 USD in bank notes and you want to convert it to EUR. You get the EUR sell price, and you'll be able to buy 1 EUR for 1.3 USD, so you'll get 100 EUR. Now, if you want to buy USD with your 100 note, you'll only get 120 USD for the 100 EUR. (so 10 bucks is the profit for the intermidiery. So far so good)

Now what if, you have the same 130 USD in bank notes, you still want EUR but you are from Canada. Is there a mandatory USD --> CAD, CAD --> EUR transition first, or can the canadian institute work with the 1.3 ratio as the US counter-part. Or, and this is the most important bit I guess, can they give an EUR for 1.27, instead of the 1.3 because of some 'magic'?

Apologies I am struggling to formulate the question itself. It really highliths my lack of domain knwoledge and agan, thanks for the help!

  • "Is there a mandatory transition" .. Nope! You walk up to a counter and you say "here's this currency" and you say "I want that currency". It's that simple. The exchange company will have a rate for that particular desire of yours.
    – Fattie
    Apr 1, 2021 at 13:22

2 Answers 2


Is there a mandatory transition first

No, not at all. People can and do directly buy/sell X for Y.

1 ABC = 1.5 DEF

There is really no such figure for any currency pair.

All there is are bids and offers.

(You may be thinking of the "most recent sale price" on an exchange.)

reliable source to find

Consider bids and offers for EUR in USD.

Be aware: there is no "central" or "sole" such exchange.

There are numerous companies (ie, exchanges) worldwide which buy and sell EUR for USD.

(Both at a "wholesale" and "retail" level.)

As I understand it, your investigation relates to tracking bids and offers on some given exchange. It can only be specific to a given exchange. (Or, sure, some sort of average, or "the biggest one".)


is it possible that the rates are different?

It is possible that the reverse is not the exact reciprocal due to bid/ask spreads. In FX markets, like stock markets, there id a difference between the price that you buy and the price that you sell. Since "buying" an FX rate is equivalent to "selling" the inverse rate, the prices are not always exact reciprocals.

In retail markets, where there is just a price (not a bid/ask), then exchangers may charge a "spread" above the market rate in order to cover their expenses and make a profit. Since the spread will be added to both the original rate and its inverse, they will not be the reciprocals of each other.

what is a reliable source to find out the exact rates for different base currencies?

If the exact inverse rate is not published, but you have bid and ask values for the original, then the bid of the inverse should be the reciprocal of the ask, and vice-versa.

Also, can the difference be so significant that after doing a loop I end up with more money?

Only for very short time periods (if at all) - otherwise arbitrageurs would take advantage of this risk-free market by buying and selling the various currencies, which would bring the prices into equilibrium.

  • Thanks for the reply, my interest is a little bit tangent from your answer, so I made some extra notes at the end of the question. I'd appreciate a second glance from you :) What you wrote makes perfect sense though, thanks again
    – Hegi
    Apr 1, 2021 at 2:35
  • 1
    hi @Hegi let me answer your question absolutely clearly: "In other words, where I am going at is something like this: is this 'base currency' a thing in exchange or not really?" NO. There's no such thing. People with currency X make bids to buy currency Y .. that's it.
    – Fattie
    Apr 1, 2021 at 13:20
  • Thanks @Fattie, after spending this much time trying to articulate my question - and failing to an extent - made me wonder if my trouble is partially because of what I am after doesn't really exists. Factoring in all the answers, I rest my case. Much appreciate your help!
    – Hegi
    Apr 1, 2021 at 13:27
  • 1
    right! it does not exist. note that by all means you could nominally make one up. If USDEUR is 2 and USDCHF is 3, and you can't find a EURCHF on that exchange, sure, you could say that the implied EURCHF is "about" .66. Actually on markets "implied" is used a lot! Like every morning you hear that the implied opening (based on futures trading) for xyz stock index is such and such. In a sense what you are asking about is "implied" exchange bids and offers !!!
    – Fattie
    Apr 1, 2021 at 13:46

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