I also use a broker from a big 4 bank and noticed that they are just a subsidiary of the bank. I would imagine that unless there is a specific written guarantee by the bank for its subsidiary then the normal rules apply, which as I understand matters is that the subsidiary can go bust without anyone having access to its owner's property (ie the subsidiary is a separate person under the law). That is one key reason why subsidiaries are established.
Why not also talk with your broker to clarify this point and any other concerns you may have.
We know that when small brokers go bust there are lots of innocent bystanders. They even sell shares that have been fully paid for by shareholders who do not have a margin loan through the broker.
