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Really Interesting (Or Nominally Interesting, At Least) December 4, 2012

Posted by tomflesher in Finance, Teaching.
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Interest rates describe how much money you’ll have at the end of a year if you lend to someone. Mostly, you “lend” money to a bank by putting it in a savings account, but you might lend to the government by buying Treasury bonds or to your no-good brother by floating him $100. Currently, my bank pays 0.01%, although some commercial money market accounts pay around 1%; Treasuries pay about 0.18% for one-year bonds; my brother is currently paying me 10% (and the Mets are paying Bobby Bonilla 8%). Why the differences?

Borrowers need to pay the lender for two things: giving up the right to use his money for a year, and the risk that he won’t get his money back. The first element is pretty important for the lender: Patient Patricia will take a lower interest rate because she doesn’t need to buy stuff today – she’s willing to wait, especially if she can make a little money for waiting. On the other hand, Antsy Andrew wants to head right out and buy stuff, so asking him to wait a year for his stuff will cost a lot of money. Plus, I know there’s some inflation most years, so my brother will have to at least cover that.

That explains part of the difference between interest rates. A Treasury bond takes your money and keeps it for a full year, but my bank’s savings account allows me to withdraw my money at will. I’m not giving up much use of my money, so I don’t need to be paid much. When the Mets paid Bobby Bonilla 8% interest, they expected high inflation, when inflation turned out to be low.

It’s also really likely that, when I go to cash in my bond or take out my ATM card, the money’s going to be there. The government’s not going bankrupt1 and my bank deposits are insured. My no-good brother, though, might lose his job tomorrow. He’ll probably have the money to pay me, but he might not. That worries me, and I want him to pay for making me nervous. (In the real world, this also means I’ll get more money up front in an installment payment plan.)

That boils down to an important identity known as the Fisher Effect:

Nominal interest ≈ Real return + Expected inflation

When I expect inflation, that affects how much I’d rather have money now than later. My real return is how much I have to get from my no-good brother to compensate me for the risk that I’ll lose all my money. We can estimate inflation as being nearly zero today, so real returns (compensating for risk) explain almost all of the variation in interest rates.

But what about those banks paying 1%, when other banks (and the government) are paying much less? Banks need to hold reserves. A bank that’s nervous about how much money it has on hand will be willing to pay higher rates in order to get more deposits – in other words, if you need it, you’ll pay for it.

Note:

1 Okay, it might go bankrupt, but it’s reeeeaaaally unlikely to happen this month.

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