Custody asset
A negotiable instrument of some kind that is capable of being held by another person on its owner’s behalf, and in fact is so held by such a person — being a “custodian”. Typically the custodian will hold legal title to the asset, but it will not form part of its own insolvency estate.
Custody models — being the legal contrivances used to deliver that arrangement — differ in different jurisdictions. Common law jurisdictions tend to use a trust structure whereby the custodian holds legal title on trust for its client. Civil law jurisdictions don’t have a trust concept — well, at any rate, they claim not to, though I would like to understand what a contrat fiduciare is, if it isn't a trust arrangement — so have to do it some other way.
Note: you cannot hold cash in custody. This is an ontological axiom. The person who holds a bank note holds it absolutely, and is be definition a debtor to the person to whom it is owed. Therefore cash that you hold automatically is part of your insolvency estate whether you like it or not.
English law custody model
The standard English law custody model is a trust arrangement. That means legal title to securities is owned by the custodian, but the beneficial interest is held by the client. As against the rest of the world, the custodian owns the assets, but its contract with its client obliges it to follow the client’s instructions when dealing with custody assets.
Because of the trust, the custody assets do not form part of the custodian’s insolvency estate and (subject to any amounts owing to the custodian that secured by lien or security interest over the custody assets) they not available to the custodian’s creditors and are returned to the client. The Lehman insolvency showed that untangling the custodian’s books and records is a trial in itself, and navigating security interests a whole other ball of wax. Hence the CASS cutody rules (CASS 6) have been tightened, and the FCA (and hence, your own firm’s CF10A) takes an extraodinarily dim view of lax book keeping.