I am not even requiring any proof that they exist. I believe that the dollars only exist:

1.) in our heads

2.) in some position on the balance sheet of the bank

There is usually no “dollar position” - definitely not in a safe and usually not in a forex market (that would be expensive - swap either happens or not, that is not a position. a position would be future, but that has funding cost).

The balances that we see are actually same thing as DAI or LUSD, or Tether. I claim that there is no difference between these forms of dollars and most electronic dollars. Or no substantial difference. The only difference is payment network through which you can send it.

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Discussion

So, what do you think happens when I top up a Revolut account with 100 eur, exchange them for usd, over time the dollar goes up, I swap it back for say 110 eur and then take out my euros? Is Revolut voluntarily losing money?

No, they are not losing money. They might back it with an obligation with another foreign bank that made a usd-denominated loan.

When you change your eur for DAI, is MakerDAO voluntarily losing money? No, the exchange happened, but there is no US dollar. DAI was “printed” into existence by the form of a loan, backed by the obligation of the borrower to repay the loan plus interest to unlock their collateral.

At no point anywhere DAI touches the dollar system, except for the USD value of ETH given by price oracle.

In traditional banking system it is the same. It might be backed by loan obligation in a third party bank and it probably has absolutely nothing to do with FED or american banks. USD-denominated loans are how international trade works, 90% of USD-denominated loans are made this way (outside of the banking system).