You are wrong 
You can not operate a fractional reserve bank using bitcoins, it's impossible by definition because you can lend only the money you actually own and no more. Fractional reserve system works such that you need only 10% reserve of actual money and you can create 90% out of thin air ...
You can not operate a fractional reserve bank using bitcoins, it's impossible by definition because you can lend only the money you actually own and no more. Fractional reserve system works such that you need only 10% reserve of actual money and you can create 90% out of thin air ...
You could, in theory, have fractional reserves of bitcoins, as with dollars. Banks don't create dollars (FDR notes) out of thin air, they create bank account balance out of thin air, and that's is counted as actual dollars in the economy.
Suppose some bank stores bitcoins. People would transfer their bitcoins to the bank and would have an account balance, that they could retrieve when needed. The bank could then lend part of this money without blocking your balance, thus creating fractional reserves.
And just HOW are you going to do that with bitcoins? It's all nice to say "in theory" but in this case the theory has a huge hole so it is like saying "in theory gold is worthless because we could mine all the gold we want from other planets."
So, what is the hole in the fractional reserve bitcoin bank theory?
A "real" bank creates dollars and is allowed by the system to issue those new dollars into circulation.
But you cannot issue more bitcoins into circulation than you have. You can only get bitcoins when they are created in the normal process either by you or transferred to you. Therefore you will not be able to accept bitcoins on deposit and loan bitcoins unless you loan those coins that are on deposit. If you loan them, they will not be on deposit any more and you cannot return them to the depositor.
In a way bitcoins are like gold. If a bank accepted gold on deposit and all loans were made by gold going out of the bank, there would be no fractional reserve banking. The fractions happen if a substitute is allowed to circulate instead of gold. (E.g. warehouse receipts) There are not yet (to my knowledge) any "warehouse receipts" for bitcoins, and hopefully nobody is stupid enough to take a promise for bitcoins in lieu of actual bitcoins.
Do you know of a substitute (a "warehouse receipt") for bitcoins that circulates equivalent to bitcoins? If that substitute can be created more easily than bitcoins then you could have fractional reserve bitcoin banking.