>Fungibility is merely how easily the medium is broken into smaller parts that may be exchange for convenience
No, fungibility is whether an asset (ie. individual assets within a particular class of asset) is interchangeable with one another.
It means when you deposit banknotes into your bank, whether the bank has to give you the same banknotes with the same serial number, or whether they can give you equivalent instruments to satisfy their obligation to you. What they owe you aren't the banknotes, but instead the money.
Also note when you deposit money into a bank, it's not treated the same way as if you put banknotes in a safe deposit box. The way you made your argument on stock brokers is as if it is, and fundamentally misrepresents this relationship. They don't owe you 'your' shares, they owe you a number of shares. Your shares become their asset, in exchange for their liability to you. You don't get to control what they do with their assets.
That's also the reason you don't get to control what the bank does with 'your' money you hold with them, because legally, it's their money with an obligation to pay you when requested. Hence the central bank steps in to regulate and guarantee fractional reserve banking in order to prevent bank runs.
> Fungibility is whether an asset (ie. individual assets within a particular class of asset) is interchangeable with one another.
Of course. This is synonymous with my own explanation. However your take is that it means that after you've made it interchangeable, then the bank or exchange somehow automatically gets more rights over it. That just isn't the case. Unless there's an express prior agreement, it's also morally wrong.
No, fungibility is whether an asset (ie. individual assets within a particular class of asset) is interchangeable with one another.
It means when you deposit banknotes into your bank, whether the bank has to give you the same banknotes with the same serial number, or whether they can give you equivalent instruments to satisfy their obligation to you. What they owe you aren't the banknotes, but instead the money.
Also note when you deposit money into a bank, it's not treated the same way as if you put banknotes in a safe deposit box. The way you made your argument on stock brokers is as if it is, and fundamentally misrepresents this relationship. They don't owe you 'your' shares, they owe you a number of shares. Your shares become their asset, in exchange for their liability to you. You don't get to control what they do with their assets.
That's also the reason you don't get to control what the bank does with 'your' money you hold with them, because legally, it's their money with an obligation to pay you when requested. Hence the central bank steps in to regulate and guarantee fractional reserve banking in order to prevent bank runs.