Financial Theory: Lecture 18 Transcript
November 5, 2009
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Professor John Geanakoplos:
So weâ€™re talking now about mortgages and how to value them, and if you
remember now a mortgage--so the first mortgages, by the way, that we know of, come from Babylonian
times. It's not like some American invented the mortgage or something.
This was 3,500-3,800 years old and we have on these cuneiform tablets these mortgages. And so the idea of a
mortgage is you make a promise, you back your promise with collateral, so if you don't keep the promise they
can take your house, and there's some way of getting out of the promise because everybody knows the
collateral, you might want to leave the home, and then you have to have some way of dissolving the promise
because the promise involves many payments over time.
So it's making a promise, backing it with collateral, and finding a way to dissolve the promise at prearranged
terms in case you want to end it by prepaying. And that prepaying is called the refinancing option. And
because there's a refinancing option it makes the mortgage a much more complicated thing, and a much more
interesting thing, and something that, for example, a hedge fund could imagine that it could make money
trading. So I just want to give you a slight indication of how that could happen.
So as we said if you have a typical mortgage, say the mortgage rate is 8 percent--maybe this is a different
answer than I did--so here we have an 8 percent mortgage with a 6 percent interest rate to begin with.
Now, if it's an 8 percent mortgage the guy's going to have to pay much more than 8 percent a year because a
mortgage, remember, there are level payments. We're talking about fixed rate mortgages. You pay the same
amount every single year for 30 years, now you're really paying monthly and I've ignored the monthly
business because it's just too many months and there are 360 of them. So I'm thinking of it as an annual
payment. You have to pay, of course, more than 8 dollars a year because if the mortgage rate were 8 percent
and you had a balloon payment on the end, you'd pay 8, 8, 8, 108.
That's the way they used to work, but they were changed. So you could imagine the old fashioned mortgage
would pay 8, 8, 8, 8, 8, 108; if you didn't pay your 8 somewhere along the line they'd confiscate your whole
house and then take what was owed out of it and you could get out of it by paying 100. The new mortgages
instead of paying 8 every year for 30 years you pay 8.88 every year for 30 years because if you discount
payments of 8.8 for 30 years at 8 percent you get 100. So the present value is 100 at the agreed upon
discounting rate or mortgage rate 8 percent. And so you see how important this discount rate is.
And the remaining balance, however, goes down because every time you're paying you're paying more than
the 8 percent interest. You're paying in the first year 8.8 instead of 8 and so that gap of .88 is used to reduce
the balance from 100 to 99.117. And so you see the balance is going down over time and making the lender
safer and safer because the same house is backing it. So it's called an amortizing mortgage.