Stock trading accounts in the US are backed by the SIPC up to $500k (even for non-US persons). This protects you from an all-out insolvency of the institution, which would happen if somehow they had all their money stolen by hackers.

But it does not protect you from hacking of your individual account. If someone tricks your broker/custodian into selling your stocks and wiring them the money, SIPC (perhaps surprisingly) will not save you.

See: http://www.reuters.com/article/us-investing-hackedaccounts-i...