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So, let me start with a more modern behavioral

Â economic and talk about prospect theory.

Â So, the term prospect theory was coined by psychologists Daniel Kahneman and

Â Amos Tversky in an economic journal, Econometrica, 1979.

Â A very important paper and, in fact, at least as of some years ago,

Â the most cited paper ever published in Econometrica,

Â which is the top journal for economic mathematical economists.

Â 0:41

What they are criticizing is the core theory of economics,

Â and they're replacing it with a constructive alternative.

Â The core theory being expected utility theory.

Â So, the economic profession

Â tends to used the idea that everyone has a utility function,

Â which depends on the things that they consume and it represents their happiness.

Â You've heard of indifference curves, those are contours of the utility function.

Â And that people in a world with no uncertainty will choose

Â how much to buy at the market prices to maximize their utility function.

Â And then if there's uncertainty,

Â then people use the probabilities of possible events

Â 2:19

that's a plot from their 1979 paper of what the value function might look like.

Â This is based on their experiments, but this is just a hand drawn story.

Â Now, the utility function, if you think of from elementary economics,

Â the utility function exhibits diminishing marginal utility everywhere.

Â And it's concaved down, right, so the upper-right

Â segment of their curve looks like a utility function.

Â You see it's concaved down and it's growing.

Â The axes, okay, the horizontal axis is the amount of money gained or lost.

Â And the vertical axis is their counterpart,

Â their replacement for utility, which they call value.

Â 5:58

So, I'll give you an example, the famous example

Â occurred at lunch at MIT about a half century ago.

Â And Professor Paul Samuelson, who's a famous professor,

Â was seated with E Cary Brown, another professor, not so famous.

Â And Samuelson said, on the spur of the moment at lunch, hey,

Â let's try a little gamble here.

Â Let's flip a coin, and if it come up heads, I will pay you $200,

Â but if it comes up tails, you pay me $100.

Â So he proposed, you see that he's being very generous here because

Â he's giving the other guy $200 as against 100.

Â What's the expected value of that bet?

Â Well, it's 0.5, assuming it's a fair coin with a probability of coming up heads,

Â 0.5 times 200 minus 0.5 times 100, so that's $50.

Â So, Samuelson thought he would immediately take it, but E Cary Brown said,

Â no, I don't, what are you talking about, [LAUGH] I don't want to do that.

Â And he didn't want to do it, and Samuelson said,

Â 7:16

are you sure, I mean, I gave you a positive expected value bet.

Â It's only a couple hundred dollars, right?

Â Well, that sounded like a lot, but back then it was worth more than it is now

Â [LAUGH] sounded like a lot of money, but he just didn't want to do it.

Â So, Samuelson then said to E Cary Brown, okay, how about doing it 100 times?

Â Well, I'll do this, and this is hypothetical, I'm not really offering

Â this, but if I offered to do it 100 times in a row would you do it?

Â And then E Cary Brown said, Gee, I mean, by the law of large numbers,

Â [LAUGH] I'm going to make something like $5,000 practically for sure.

Â So, E Cary Brown said, okay, I would do that.

Â So then Samuelson went back to his office, and

Â wrote out a mathematical proof that E Cary Brown is irrational

Â because if you would take 100 of them, you should take one of them, right?

Â But E Cary Brown was just behaving the way this value function.

Â The kink at the value function means the gains look so much smaller than the loss.

Â So, psychologically, so I don't want that, but if it's 100 of them,

Â then it's just moving him up here for sure, so, of course, he'll do it.

Â But see there's a fundamental human error here, that we focus on little things and

Â we panic at little bets.

Â You should be doing, I don't know if you're ready for it.

Â If I actually offer it, I should have asked for

Â a show of hands, if I offered you a coin toss like that, you'd take it, right?

Â 8:49

I assume, at least if you learn anything from this course about rationality,

Â you should do it.

Â Any time you get a bet like, it's a small bet, you should,

Â with a positive expected value, expected utility theory says you

Â take it because there's not much concavity to the utility function, but people don't.

Â The other thing is that this thing curves up for losses, and

Â what that refers to is a, There's risk preference for losses.

Â People, it's a little bit hard to explain, but the key idea

Â is that people are willing to take big risks to escape loses.

Â 9:34

So, for example, someone at a gambling casino, who's lost a lot of money and

Â now is in the reign of losses, starts to think, maybe,

Â of taking a really big bet that might have the possibility of bringing them away so

Â they could close the day up instead of down.

Â So that people have a tendency to take risks in the domain of

Â losses to try to get them back, so that's the value function.

Â The other thing is the weighting function.

Â Now, on this axis we have the stated probability, now,

Â probabilities range from zero to one, and

Â so that's the actual probability of an event.

Â But on this axis we have the decision weight, which is a transformed,

Â psychologically transformed probability.

Â And you can see that they curve, this is the 45 degree line,

Â if people were completely rational,

Â they would use the actual probabilities in their calculations.

Â But they do not actually behave completely like that,

Â they tend to transform their weighting function, so

Â it looks like a curve with a slope less than one.

Â Also, it doesn't show, for very low probabilities and

Â very high probabilities, the line stops.

Â You notice that it doesn't tell you or,

Â by some versions, it drops to the zero or it jumps up to one.

Â So, what they are referring to,

Â let's talk about the fact that it doesn't go to zero or one.

Â What it means is for very low probabilities you have a tendency to

Â not appreciate them and, actually, often, to drop them to zero.

Â I'm not going to think about that.

Â If it's a probability of 10% of happening, you might worry about it, but

Â if it's 1%, I'm going to round that to 0 and not worry about it.

Â Similarly, on the upper end,

Â if something has a very high probability, people don't accept that hype,

Â they don't take that probability into account, and they round it to one.

Â So, I'll give you an example of the application of the weighting function.

Â And that is, it used to be that when you board an airplane they

Â had vending machines that offered you insurance against dying on this flight.

Â It's one flight, and they would charge you like $1 for an insurance policy.

Â And they would put the machine right there where you're boarding the airplane.

Â A lot of people would buy this because they're boarding an airplane and

Â they just get a little scared about this flight.

Â Well, actually, the probability of this flight crashing, what is it, one flight?

Â It's 1 in 10 million, right, so that $1 insurance should

Â give you a coverage of $10 million, but it [LAUGH] doesn't.

Â It gives you something very remote from that, and

Â people still buy it, why do they buy it?

Â It's because they're nervous.

Â 13:08

So, most people didn't buy it, so those are the people who were down here,

Â they rounded it to zero.

Â But some people are right there,

Â [LAUGH] there's a little bit of fluidity in this theory.

Â And you either exaggerate it or you ignore it, and so

Â there's a whole business exploiting people who exaggerate it.

Â Also, the curve has a slope less than one, and

Â you could caricature this by saying there's three possible

Â weighting values, zero, a half, or one.

Â And so, emotionally,

Â I can't process these numbers, that would be the case if this curve were actually

Â flat through a half, but it's not absolutely flat.

Â 14:13

People are overly focused on little losses, little gains and losses.

Â I can get you worrying about a $2, plus or minus, $2 loss,

Â I can get you overly concerned by that.

Â You should not worry about plus or

Â minus $2, that's nothing, but people do worry about it.

Â You should be worrying about the big things,

Â and that's one mistake that Kahneman and Tversky put in their prospect theory.

Â 15:08

set of knowledge about mistakes that people make.

Â And I think it's good to learn about prospect theory to help

Â yourself from making those mistakes.

Â >> So, it sounds like there's a large intersection between social psychology and

Â finance, and that we've been talking about it in class.

Â And this is more abstract, but, in terms of the chick and the egg,

Â what do think comes first?

Â Do you think that people have biases which are then reflected onto the market and

Â make changes?

Â Or do you think that the market is currently structured in

Â a way that confuses the average investor?

Â >> Well, you said which comes first.

Â I know, chronologically, there were two important revolutions

Â in finance over the last half century or so.

Â First was the efficient markets mathematical finance revolution.

Â The second one was, that started in the 50s, 1950s maybe,

Â it's hard to define exactly when it started, but let's say the 50s.

Â And then there was the behavioral finance revolution which brought psychology in.

Â 16:20

So, I think these two revolutions are kind of incompatible views of the world.

Â But they both offer insights, they're both exciting.

Â And so which one comes first, [LAUGH] I don't know.

Â I think that it's just a matter of models that you have in any science are models

Â that abstract from certain details and offer you insights into what is happening.

Â But then if you are an engineer trying to design,

Â I'm thinking of physics and engineering,

Â an engineer has to have a different way of thinking than a physicist does.

Â He has to say, I want to know all the frictions, all the problems.

Â What if someone tries to use my device in freezing weather [LAUGH] will it still

Â work, it's still things like that.

Â So, financial engineering is an important field

Â these days, not using that term disparagingly.

Â Sometimes people use the word financial engineering to describe

Â manipulative practices.

Â I don't mean it that way, I mean in terms of innovation.

Â Financial engineering takes a somewhat different

Â personality than financial theory.

Â