One of my undergrad students just asked why the exchange rate notations that I use in my class are different from what he found in the financial press. I was happy for the question. At least one student who tries to square what he learns in class with what he sees with his eyes!
And I think other professors in economics and finance may be confronted with similar questions, wherefore I share his question and my response:
Good evening, Sir,
Following your last lesson on exchange rates, I would like some clarification. In your lesson, you explain that the exchange rate of the dollar in euros, denoted (€/$), represents the monetary price of the dollar in euros.
When we look at FOREX, currency pairs seem to be quoted in reverse, with EUR/USD representing the price of one euro in terms of dollars. Is there a reason for this reversal? Or have I misunderstood your lecture?
Now my answer:
Dear Sir,
The inversion you have observed is a custom among foreign exchange practitioners. They reason as follows:
If one euro is exchanged for two dollars, then we can write: €1 = $2
By dividing both sides of the equation by ‘€1’, we get: 1 = 2 $/€
By dividing both sides by ‘2’, we get: 1/2 = $/€
Hence, the exchange rate of the dollar in terms of euros is 1/2, but the dimension of this price would be $/€
The error in this construction is the starting point. The expression ‘1€ = 2$’ is literally absurd, that’s like saying “a pen is the same thing as an apple.” For the same reason, it is absurd to write “1/2 = $/€.”
The logically correct construction is as follows:
If one euro is exchanged for two dollars, then we can write:
1€ * euro exchange rate in terms of dollars = 2$
By dividing both sides of the equation by ‘1€’, we obtain:
euro exchange rate in terms of dollars = 2 $/€
Indeed, the euro exchange rate in dollars is 2 dollars per euro.
The same result is obtained if I reformulate my initial equation:
1€ = 2$ * dollar exchange rate in terms of euros.
Then we get: dollar exchange rate in terms of euros = 1/2 €/$
Now you understand that it would be perfectly useless to lecture traders on which notations they should use. But my job is to help my students understand economic principles, and here logical consistency is much more important. So, in the context of my course, please remember my notation and not that of the professionals.
Kind regards,
GH
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