## Tuesday, November 20, 2007

### Two trillion dollars is a catchy number

Banks make money by taking in deposits and lending them out at higher rates than it pays. They don't lend it all out - what they keep is called the capital ratio and it is typically around 10 percent of what they have lent.

For example, say a bank has \$1,000 in outstanding loans. It keeps 10% or \$100 in cash. That's \$100 it won't lend because to do so would put its capital ratio below 10%.

Now say just 1% of the \$1,000 in outstanding loans go bad, which is \$10 of bad loans. The bank has to pay the \$10 out of cash since the loan has to be repaid by someone. Now the bank only has \$90 in cash; the maximum amount it can lend is \$900. But it has \$990 left in outstanding loans. Ooops, the capital ratio just went down to 9.1%.

The bank would need to reduce its lending another \$90 to get back to a 10% capital ratio. That's a total reduction of \$100 in lending: \$10 for the bad loan and \$90 to keep the 10% capital ratio.

The bottom line? A bank needs to reduce its loan balance by \$10 for every \$1 in losses.

Goldman's chief U.S. economist estimates that because of sub-prime mortgage losses, lending may be reduced by as much as \$2 trillion, 7% of US non-financial debt, raising the likelihood of recession.

Now there’s a depressing thought.

JamesD said...

Larry,

Thanks for a fabulous set of posts -- helps make math relavant to all of us!

Just wanted to point out that after paying off the bad loan (\$10), the bank only needs to reduce its lending by about \$8.18 to bring its capital ratio back to 10% (because every dollar pulled out of the lending pool covers another \$10 in current loans). Reducing the loans outstanding has two simultaneous effects---reducing the loan balance while also raising the capital balance (you left out this last bit in the post).

The capital set aside would then be \$98.18 and the loans outstanding \$981.82.

So, really a bank only needs to reduce its loan balance by about \$1.82 for a \$1.00 loss. Depressing? Yes, but not nearly as depressing as \$10 would be!

James

Larry Shiller said...

Hi James,

I agree with your comment: assuming the reduction in outstanding loans is returned to capital your answer is correct.

Thank you for your kind words on the blog and for pointing this out in such a gentle manner, of which I'm 98.2% sure I am not deserving.

Larry