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When a bank extends credit to us, is that the amount of money they currently have at their bank? Say I was given a $5000 credit line. Is it safe to assume that the bank has a float for $5000 in case I file for bankruptcy or something like that?
Banks only are required to hold a percentage (and its a low one) in loan loss reserves to cover defaults. Banks actually create money when they allow you to charge on credit cards or give out other forms of loans.
A good way to think about it is, when you buy something with your CC, do actual paper bills (or gold bars) transfer to the merchant? Nope, just electronic signals that tell the merchant they got $5 for your meal purchase. The merchant then has $5 more "dollars" in their account.
Same when your employer pays you, it is through direct deposit, electronic signals sent to tell your bank that your account now has $XX (or if you're lucky $XX,XXX) more "dollars".
Even at the most basic level, the greenbacks issued by the US Treasury, don't really have any direct gold bullion backing them up. The greenback is a trusted medium of exchange because everyone believes in it, around the world.
So back to the original question, the bank itself really doesn't have any gold bars sitting there as collateral for anything. The bank has share capital that investors put in, takes in deposits from companies and individuals, who want to have a safe place to store their "money" until they need to get their electronic bits out (sometimes converted to greenbacks so they feel better about it), and the bank loans out that money to companies and individuals, including for Credit Cards. The loan on the credit card is that advance to the merchant for $5 on the promise that you will send the bank some electronic signals to "pay" for the $5 at some point later, according to terms of the loan on the credit card.
This requires a high degree of trust, and the consistency that the banks work with, the availability of the "money" when we need it electronically, goes a long way to make people forget that this is all just a bunch of electronic promises floating around. As long as everyone believes in the fiction, it is a reality.
"If men define situations as real, they are real in their consequences".
Most bank held debt, aka loans, are packaged and sold as securitized bonds to the invester market. This is true for mortgages, auto loans and yes credit card debt. We know what happens when there is a major "default" with securitized bonds, such as the mortgage melt down in 2007-2009, if the "debt risk factor" of securitized bonds is over stated, but in general banks only hold a small percentage of cash to loans as required by law.
One of the most profitable and active securitized bond markets right now is the "less than prime" auto loan business. Given the low investment return of Government bonds (generally the safest), investers tend to look for higher yields and bank debt securitized bonds offers higher returns. Banks will continue to charge a percentage to service consumer debt, just like mortgage servicing, but most of the debt is held by investors.
http://www.investinginbonds.com/learnmore.asp?catid=11&subcatid=56&id=130
http://en.wikipedia.org/wiki/Securitization
http://www.imf.org/external/pubs/ft/fandd/2008/09/pdf/basics.pdf