So, even though I think that my expected profit is positive, because he’s putting up three hundred thousand to make only two hundred when they’re even odds. The fact is it’s such a big number I’m a little worried about that.” So, what do you do? So, what can you do? You’ve got these friends who are willing to bet at even odds. Each game by game, so how much money – presumably the first night you’re going to bet with one of your friends. You take the guy’s bet, the customer, you take his three hundred thousand. You promise to deliver him five hundred back if the Yankees win and to keep it if the Yankees lose. What should you do with your friends?
Should you bet on the Yankees with your friends? Should you bet on the Dodgers with your friends and how much should you bet at even odds the first night? So, the answer is, well, I don’t want to give all the answers now, but so there’s a way of skillfully betting with your friends and not betting two hundred or three hundred thousand the first night with your friends at even odds. You bet some different number than that, which you’ll figure out how much to bet so that if you keep betting through the course of the World Series, you can never lose a penny. How do you know how much that is? Well, that’s the kind of clever thing that these finance guys developed and you’re going to know how to do.
So, let’s do another example like that. I’m running out of time a little bit, but an example. Suppose there’s a deck of cards, twenty six red and twenty six black cards. Somebody offers to play a game with you. They say, “If you want to pick a card and it’s black, I’ll give you a dollar. If it’s red, you give me a dollar.” So, if I’m picking, I’m in the black, I get a dollar, it’s in the red I lose dollar, I have to throw away the card after I pick it. The guy says, “By the way, you can quit whenever you want.” So, should you pick the first card? It looks like an even chance of winning or losing. Let’s say you pick the first card, it’s black, you win a dollar. Now, the guy says, “Do you want to do it again?”
You picked a black one so there’s twenty six red left and twenty five black. So now, the deck is stacked against you. Should you pick another card? Well, it doesn’t sound like you should pick another card. But, you should pick another card and I can even tell you how many cards to pick. Even if you keep getting blacks, you should keep picking and picking. So, how could that be? It sounds kind of shocking. Well, it’s going to turn out to be very simple for you to solve halfway to the course.
So, a more basic question. There are thirty year mortgage now you can get over for five and three quarter percent interest. There are fifteen year mortgages you can get for less, like five point three percent interest. One’s lower than the other. Should you take the fifteen year mortgage or the thirty year mortgage? How do you even think about that? Why do they offer one at a lower price than the other?
One more example, suppose you’re a bank and you hold a bunch of mortgages. That means the people in the houses, you’ve lent them the money and they’re promising to pay you back. And you value all those mortgages at a hundred million dollars. The interest rates go down. The government lowers the interest rates. Half of them take advantage to refinance. They pay you back what they owe and they refinance into a new mortgage. So now, you’ve only got half the people left. Let’s say all the people had the same mortgage and everything. Half the people are left. That shrunken pool, half as big as the original pool, is that worth fifty million, half of what it was before or more than fifty million or less than fifty million? How would you decide that?
Again, this is a question which might be a little puzzling now, but actually you should be able to get the sign of that today even, and we’ll start to analyze it. So, that’s what mortgage traders have to do. They see interest rates went down. A bunch of people acted. The people who are left in the pool are different from the people who started in the pool. Now, we’ve got to revalue everything and rethink it all, so how should we do that?
Finance: Examples of Finance Pt 5
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