Reading from this and other sources, it appears to me that there are three different ratios between any two currencies, namely
- the bid rate
- the ask rate
- the real rate
My understaning is that the two primal ratios are 1 and 2, while 3 is just a derived quantity, specifically the mid-point between the former two. In other word, I understand that 1 and 2 are the two real, market-driven numbers, and that 3 is just a convenience to know where 1 and 2 roam in that specific historical moment.
Is my understanding correct?
In the following I just report my line of reasoning.
For instance, if I have an amount $A_1$ in one currency and I want to exchange it with another currency, I would receive the amount $A_2$ in this other currency, defined as
$ A_2 = E_{1 \rightarrow 2} A_1$
where $E_{1 \rightarrow 2}$ is the exchange rate.
If I change my mind and decide to convert $A_2$ back to the previous currency, then I will be given the amount $\overline{A_1}$,
$ \overline{A_1} = E_{2 \rightarrow 1} A_2 = E_{2 \rightarrow 1} E_{1 \rightarrow 2} A_1$
I've understood that, if we leave the time elapsed between the two operations aside (or if we do the two exchanges at exactly the same moment), we are sure that $\overline{A_1} < A_1$, because we are sure that in any given moment in time the following holds:
$E_{2 \rightarrow 1} < \displaystyle\frac{1}{E_{1 \rightarrow 2}} \tag{1}$
Is this true?
To me it seems obvious, since if $(1)$ had an equal sign, that would mean that I can freely exchange between currencies at zero cost (hence I could lose or earn money only as a consequence of the change of that unique rate over time due to other factors).