So, let me start with a more modern behavioral economic and talk about prospect theory. So, the term prospect theory was coined by psychologists Daniel Kahneman and Amos Tversky in an economic journal, Econometrica, 1979. A very important paper and, in fact, at least as of some years ago, the most cited paper ever published in Econometrica, which is the top journal for economic mathematical economists. What they are criticizing is the core theory of economics, and they're replacing it with a constructive alternative. The core theory being expected utility theory. So, the economic profession tends to used the idea that everyone has a utility function, which depends on the things that they consume and it represents their happiness. You've heard of indifference curves, those are contours of the utility function. And that people in a world with no uncertainty will choose how much to buy at the market prices to maximize their utility function. And then if there's uncertainty, then people use the probabilities of possible events to calculate the expected utility and the maximized expected utility. Kahneman and Tversky changed two things in expected utility theory. One, they replaced the utility function with what they called a value function. And two, they replaced the probabilities with subjective probabilities determined by a weighting function in terms of the actual probabilities. So, let me talk about these two elements here. The first thing is the value function, that's a plot from their 1979 paper of what the value function might look like. This is based on their experiments, but this is just a hand drawn story. Now, the utility function, if you think of from elementary economics, the utility function exhibits diminishing marginal utility everywhere. And it's concaved down, right, so the upper-right segment of their curve looks like a utility function. You see it's concaved down and it's growing. The axes, okay, the horizontal axis is the amount of money gained or lost. And the vertical axis is their counterpart, their replacement for utility, which they call value. But if you look at it, there's a funny kink here, at the origin, and then they have it concave upward, not downward for losses. The other thing is, or that I should emphasize, the utility function is not usually put at, in this term, between gains and losses in economic. Your utility is determined by how much you have, and it doesn't apply, it doesn't make a distinction, it doesn't focus on what you have now. What they're talking about here is how you react to an opportunity on any given day. And what they said is that on any given day, you form a reference point for today, and that's this reference point, okay? And the utility depends on, relative to your reference point, what your gains and losses might be. There's a kink at the reference point, okay, which means that, There's something special going on. But this reference point is kind of arbitrary, it's just where you see yourself today. So, that is, now, I'm not going to get into details of this, but this is the idea which they proposed, instead of utility, based on experimental evidence. So let me talk about evidence, quickly through this, the kink, the first thing is that the origin moves through time, you're not consistent through time. If I get more money, then I move my reference point up to more money for the next choice that I make. And if I have less money, I move it back. That doesn't happen with utility. What they're saying is that it's subjective, I'm thinking always relative to where I am now. So, for example, there's a kink in the slope. You see the slope is high here, and then it becomes low at a point, which is today's reference point. And so what it means is that people, one implication of this is people will not take small bets. So, I'll give you an example, the famous example occurred at lunch at MIT about a half century ago. And Professor Paul Samuelson, who's a famous professor, was seated with E Cary Brown, another professor, not so famous. And Samuelson said, on the spur of the moment at lunch, hey, let's try a little gamble here. Let's flip a coin, and if it come up heads, I will pay you $200, but if it comes up tails, you pay me $100. So he proposed, you see that he's being very generous here because he's giving the other guy $200 as against 100. What's the expected value of that bet? Well, it's 0.5, assuming it's a fair coin with a probability of coming up heads, 0.5 times 200 minus 0.5 times 100, so that's $50. So, Samuelson thought he would immediately take it, but E Cary Brown said, no, I don't, what are you talking about, [LAUGH] I don't want to do that. And he didn't want to do it, and Samuelson said, are you sure, I mean, I gave you a positive expected value bet. It's only a couple hundred dollars, right? Well, that sounded like a lot, but back then it was worth more than it is now [LAUGH] sounded like a lot of money, but he just didn't want to do it. So, Samuelson then said to E Cary Brown, okay, how about doing it 100 times? Well, I'll do this, and this is hypothetical, I'm not really offering this, but if I offered to do it 100 times in a row would you do it? And then E Cary Brown said, Gee, I mean, by the law of large numbers, [LAUGH] I'm going to make something like $5,000 practically for sure. So, E Cary Brown said, okay, I would do that. So then Samuelson went back to his office, and wrote out a mathematical proof that E Cary Brown is irrational because if you would take 100 of them, you should take one of them, right? But E Cary Brown was just behaving the way this value function. The kink at the value function means the gains look so much smaller than the loss. So, psychologically, so I don't want that, but if it's 100 of them, then it's just moving him up here for sure, so, of course, he'll do it. But see there's a fundamental human error here, that we focus on little things and we panic at little bets. You should be doing, I don't know if you're ready for it. If I actually offer it, I should have asked for a show of hands, if I offered you a coin toss like that, you'd take it, right? I assume, at least if you learn anything from this course about rationality, you should do it. Any time you get a bet like, it's a small bet, you should, with a positive expected value, expected utility theory says you take it because there's not much concavity to the utility function, but people don't. The other thing is that this thing curves up for losses, and what that refers to is a, There's risk preference for losses. People, it's a little bit hard to explain, but the key idea is that people are willing to take big risks to escape loses. So, for example, someone at a gambling casino, who's lost a lot of money and now is in the reign of losses, starts to think, maybe, of taking a really big bet that might have the possibility of bringing them away so they could close the day up instead of down. So that people have a tendency to take risks in the domain of losses to try to get them back, so that's the value function. The other thing is the weighting function. Now, on this axis we have the stated probability, now, probabilities range from zero to one, and so that's the actual probability of an event. But on this axis we have the decision weight, which is a transformed, psychologically transformed probability. And you can see that they curve, this is the 45 degree line, if people were completely rational, they would use the actual probabilities in their calculations. But they do not actually behave completely like that, they tend to transform their weighting function, so it looks like a curve with a slope less than one. Also, it doesn't show, for very low probabilities and very high probabilities, the line stops. You notice that it doesn't tell you or, by some versions, it drops to the zero or it jumps up to one. So, what they are referring to, let's talk about the fact that it doesn't go to zero or one. What it means is for very low probabilities you have a tendency to not appreciate them and, actually, often, to drop them to zero. I'm not going to think about that. If it's a probability of 10% of happening, you might worry about it, but if it's 1%, I'm going to round that to 0 and not worry about it. Similarly, on the upper end, if something has a very high probability, people don't accept that hype, they don't take that probability into account, and they round it to one. So, I'll give you an example of the application of the weighting function. And that is, it used to be that when you board an airplane they had vending machines that offered you insurance against dying on this flight. It's one flight, and they would charge you like $1 for an insurance policy. And they would put the machine right there where you're boarding the airplane. A lot of people would buy this because they're boarding an airplane and they just get a little scared about this flight. Well, actually, the probability of this flight crashing, what is it, one flight? It's 1 in 10 million, right, so that $1 insurance should give you a coverage of $10 million, but it [LAUGH] doesn't. It gives you something very remote from that, and people still buy it, why do they buy it? It's because they're nervous. You hear about all these plane crashes, you think this could be my last day on earth, I feel like I want to have done something. But, in fact, you see, the probability is exaggerated. So, most people didn't buy it, so those are the people who were down here, they rounded it to zero. But some people are right there, [LAUGH] there's a little bit of fluidity in this theory. And you either exaggerate it or you ignore it, and so there's a whole business exploiting people who exaggerate it. Also, the curve has a slope less than one, and you could caricature this by saying there's three possible weighting values, zero, a half, or one. And so, emotionally, I can't process these numbers, that would be the case if this curve were actually flat through a half, but it's not absolutely flat. But it is true that, in this realm, people don't, they don't take full account of the differences in probabilities of events. They tend to blur them a little bit, so that's prospect theory. People are overly focused on little losses, little gains and losses. I can get you worrying about a $2, plus or minus, $2 loss, I can get you overly concerned by that. You should not worry about plus or minus $2, that's nothing, but people do worry about it. You should be worrying about the big things, and that's one mistake that Kahneman and Tversky put in their prospect theory. Another thing is that people will often try to gamble out of losses. If you went to the casino and you lost money, you think, maybe I should gamble some more, maybe I can get back to where I was. That only makes things worse, but that's what people do, that's also part of prospect theory. So what I think prospect theory is is a experimentally based set of knowledge about mistakes that people make. And I think it's good to learn about prospect theory to help yourself from making those mistakes. >> So, it sounds like there's a large intersection between social psychology and finance, and that we've been talking about it in class. And this is more abstract, but, in terms of the chick and the egg, what do think comes first? Do you think that people have biases which are then reflected onto the market and make changes? Or do you think that the market is currently structured in a way that confuses the average investor? >> Well, you said which comes first. I know, chronologically, there were two important revolutions in finance over the last half century or so. First was the efficient markets mathematical finance revolution. The second one was, that started in the 50s, 1950s maybe, it's hard to define exactly when it started, but let's say the 50s. And then there was the behavioral finance revolution which brought psychology in. So, I think these two revolutions are kind of incompatible views of the world. But they both offer insights, they're both exciting. And so which one comes first, [LAUGH] I don't know. I think that it's just a matter of models that you have in any science are models that abstract from certain details and offer you insights into what is happening. But then if you are an engineer trying to design, I'm thinking of physics and engineering, an engineer has to have a different way of thinking than a physicist does. He has to say, I want to know all the frictions, all the problems. What if someone tries to use my device in freezing weather [LAUGH] will it still work, it's still things like that. So, financial engineering is an important field these days, not using that term disparagingly. Sometimes people use the word financial engineering to describe manipulative practices. I don't mean it that way, I mean in terms of innovation. Financial engineering takes a somewhat different personality than financial theory. Financial theorists like to develop beautiful models, but a financial engineer wants a beautiful device that works in various conditions with real people. And so that requires, I think like engineers will tell you, you can't rely on any one physical model. You have to realize that the world is complicated and funny things happened to machines and they jammed up, or something goes wrong. Same with financial machines.
