For clarity, a third party can’t act as a custodian for cryptocurrency because by definition cryptocurrency is peer to peer. It’s a transaction that moves from one person to another person without an intermediary. If you have to ask someone to do something before you can move the currency, you don’t have cryptocurrency.
To hold cryptocurrency, you have to be able to transfer the currency yourself without permission from anyone. This is why the cryptocurrency system is called a permissionless system. You don’t have to ask for permission to use it. You don’t have to consult a banker or a financial institution to move your money.
Those individuals and companies that bill themselves as custodial services for cryptocurrency are not holding your cryptocurrency. In fact, sometimes they’re not holding cryptocurrency at all. They’re claiming to hold cryptocurrency.
In any case, imagine that the company that claims to hold cryptocurrency for you is actually storing that specific amount that you purchased at an address on the blockchain for you. You still don’t own any cryptocurrency because you can’t move the money yourself.
In such a situation, you own a contract to receive cryptocurrency in the amount stated in the contract. Until such time that you have the private keys for the addresses on the blockchain containing the amount that you purchased, you don’t own cryptocurrency. In fact, if you’ve invested half a million dollars in Bitcoin under a custodial arrangement, the guy holding $10 of Bitcoin on his Jaxx wallet has more cryptocurrency than you because he has access to the private keys to that $10 and can transfer that money anywhere to anyone at any time without permission.
Custodial arrangements are digital money contracts because there’s an intermediary. Cryptocurrency has no intermediary. This also comes with risk because your Jaxx wallet is connected to the internet and is subject to hacking whereas your custodial service may (or may not) hold the cryptocurrency addresses on devices that are not connected to the internet and not subject to hacking. But these companies can and do go out of business, and then they may or may not fulfill their obligation to you under the contract. It’s all risk of one kind or another.
However, if you’re going to play in the cryptocurrency world, it’s important to understand that it’s not possible for you to own cryptocurrency under a custodial arrangement. You only own cryptocurrency when you, and you alone, have access to your private keys and can transfer the money without consulting anyone anywhere. Until such time, you have digital money because there’s an intermediary involved. You have a contract to receive cryptocurrency which may or may not be fulfilled by the party claiming to hold cryptocurrency on your behalf.
Cryptocurrency means that you can transfer the currency you hold at your address on the blockchain directly to another cryptocurrency address on that blockchain without third-party approval. If there’s an intermediary involved, it’s digital money.