Professor Robert Shiller: Today's lecture is about
behavioral finance and this is a term that emerged into public
consciousness around the mid-1990s;
before that it was unknown.
The term "efficient markets" is much older;
I mentioned the idea goes back to the nineteenth century and
the term goes back to the 1960s.
But behavioral finance is a newer revolution in finance and
it's something that I have been very involved with.
I have been organizing workshops in behavioral finance
ever since 1991, working with Professor Richard
Thaler at University of Chicago.
We've been doing that for eighteen years;
amazing, that's a long time for you, right?
When we started we were total outcasts, we thought;
nobody appreciated us.
I had tenure so I could do it but the problem is,
you don't want to do things that are too out of fashion.
Fortunately, we have a system that allows it
to happen and I'm very happy to have that.
What behavioral finance is a reaction against extreme--some
extremes--that we see in efficient markets theory or also
in mathematical finance.
Mathematical finance is a beautiful structure and I admire
what the people have done and I've worked in it myself,
but it has its limits.
Eventually--you know the way a paradigm develops--it goes
through a certain phase.
When mathematical finance was new, say in the 1960s,
it was the exciting thing and nobody wanted to work on
anything else; you wanted to be doing the
exciting thing. As the '70s and '80s wore on,
it got to be a little bit overdone;
people run with it too far, they think that's all we want
to do, and we don't want to think about anything else.
Then they start to get sometimes a little crazy.
Than we had to reflect that, well, things aren't perfect.
The world isn't perfect and we have real people in the world,
so that led to the behavioral finance.
Behavioral finance really means--what does it mean?
It's not like behavioral psychology.
It doesn't mean behavioral psychology applied to finance.
It really means something much more broad than that.
It means all of the other social sciences applied to
finance. The economics department is
just one of many departments in the university that teaches us
something about how people behave,
so if we want to understand how people behave we can't rely only
on the economics department.
I think that it's coming around to a unifying of our
understanding. Since then--since the
beginnings in the '90s, our behavioral finance
workshops have grown and grown and,
of course, so many people are involved in it now;
it's now very well-established.
Before I get into that, I want to give some additional
reflections on the last lecture.
I have this chart, which you saw last
time--actually it's an Excel spreadsheet that--I also put it
up already on the classes V2 website so you can play with it.
I just want to reflect again--I know I'm repeating myself a
little bit, but it's very important.
What we have in this chart is the blue line,
which is the Standard & Poor Composite Stock Price
Index going back to 1871--from 1871 to 2008,
right now--so that's like 130 years of data.
That's the blue line.
You can see the--do you know what that is there?
That's 1929 and that is the Crash of 1929.
Well, actually it extended to 1932 and you can see other
historic movements.
There's the bull market of the 1990s--a very big upswing--and
then there's the crash from 2000 to 2003.
I don't know if you remember these things,
they were big news, not as big as the 1929 crash,
but the upswing was just as big as the 1920s upswing,
wasn't it? Here's the 1920s upswing and
here's the 1990s upswing--huge upswing in stock prices.
This is in logs, by the way, so that means that
everything--the same vertical distance refers to the same
percentage change in the price.
Then I had, as I said last period, I have a random walk
shown--that's the pink line.
The random walk is generated by the random number generator.
I fixed the random number generator, so I made it truly
normal this time.
It slows it down a little bit, but if you press F9 we get
another random walk, but it's always the same stock
price. This is a random walk with a
trend that matches the uptrend of the stock price.
I can press--it kind of looks similar, doesn't it?
It kind of shows that in some basic sense the stock market and
the random walk are the same.
Here we have the crash of--here we have the market peak of 1929
except it turned out in this simulation to have occurred in
1910 or thereabout.
Then we have the--that's The Depression of the '30s except
it's not the '30s.
I can just push a button and we get something else.
I find this amusing.
I don't know. Unfortunately,
we live through only one of these in our lifetime.
There's a TV show about parallel universes,
right? What's the name of that show?
I can't remember it.
Don't you know this show?
Where they go in some kind of time machine and they emerge in
another parallel universe where history took another course.
Well anyway, these are parallel universes
that we see. In some of these universes,
Jeremy Siegel would write his book, Stocks for the Long
Run, and in some of them he would
not because–well, this one he might not because
in this case the stock market was just declining for the
better part of a century.
The thing I don't see in these charts and I think we haven't
captured it perfectly with just the standard random walk is I
don't see any crash as big as the 1929 crash.
It's hard to get them.
I keep pushing F9--this just seems to dominate,
right? There's nothing as big
here--press F9 again--you can keep pushing and pushing,
maybe you'll get one but you have--you get the idea that
there's something anomalous about that crash from the
standpoint of this random walk theory.
I'm not getting one, right?
That's something that we'll talk about.
I would--I'm not--I can push for a long time and I don't
see--well there's a pretty big one.
Isn't that just about as--not quite as sharp as the 1929
crash, but it's hard to get them.
I think that one thing–there are a couple
of things that we'll come back to.
One is--I think I've already mentioned it--fat tales.
Stock price movements have a tendency to show some extreme
outliers that are not represented by the normal
distribution. But also, there are variations
in the variance. So, in this period here--in the
'20s and '30s--the stock market was extremely variable on a
day-to-day basis; it was way beyond anything
we've observed since.
So, that's why it seems to be more volatile in that period
because the accumulation of bigger random shocks.
Anyway, we can play this game for a while but now I want to go
and talk about--remember that the random walk that we see in
stock prices is not the behavior of a drunk,
even though you can describe a random walk as drunken behavior.
The idea in the theory is that these movements only appear
random because they're news and news is always unpredictable.
If the market is doing the best job--this is efficient
markets--in predicting the future,
that means then that any time the stock market moves it's
because something surprising happened.
Like there might be a new breakthrough in science or there
could be war or something outside--this is the
story--outside of the economic system that disrupts things.
The next question then–now,
I've added something--it's on this little tab here--I've added
something, which is a plot of present values.
This is something that I published in 1981.
That's a long time ago, isn't it?
It was my first big success.
Not everyone liked this article, but what I had--I got
into a lot of trouble for it.
I learned some people react with hostility when you offend
their cherished beliefs, so I was on the outs for a
while with this article.
I said, it's kind of interesting to think that all
these apparently random movements are really resulting
in news about something that is fundamental--that's the
efficient markets.
Every time the stock market moves it's because there was
some news about what?
Well, it's about present value.
The efficient markets theory, in its simplest incarnation,
says that the price is the expected present value of future
dividends. What I did, in a paper that I
published in 1981, is I said, well let's just plot
the present value of dividends through time.
That's how I constructed this long time series back to 1871;
nobody else was looking at it.
Typically, researchers want the best data, the high quality
data, and so they would look at recent data,
which was the best data, and they would think going back
to 1871 is crazy because that's so long ago.
We have daily or minute-by-minute data by now,
but we can't get it for that remote period.
On the one hand, as I argued,
the stock market is pricing things that occur over long
periods of time. The present value formula is
pricing dividends into the future, decades into the
future--well, actually to the infinite
future, but most of the weight is on the next few decades.
So, we can't evaluate the theory by just looking at ten
years of data we've got to get a lot of data.
What I did then in that paper was I computed the actual
present value of subsequent dividends for each year--that's
on this tab--and compared it with the stock price;
so that's what I did.
This is an update of a plot that I showed in my 1981
American Economic Review paper.
The blue line--because when I published it I was right here.
It's amazing how time goes by; it was 1979, I was right here.
We had just come off from the big stock market drop of the--it
was the '73-'75 drop and it was a couple of years later,
so we were kind of bumbling around down here.
We didn't have any idea whether this was coming at the time.
What I did was I just, for each year,
computed the present value of the dividend.
I have a dividend series for every year.
In fact, it's right over here.
I have to--this is the data, so I have the--this is the
S&P Price Index monthly, back to 1871,
and here are the dividends they paid per share every year since
1871. I just, for each year,
I took all subsequent dividends and I priced them out at the
present value formula and I used the constant discount rate of 6%
a year. So, you see how we get what the
present value was.
Of course, there's a problem because we don't know dividends
after 2007 because we don't have data on dividends past then.
But, I just made some assumptions, so the value at the
end is maybe a little bit arbitrary.
It could be dragged up or down if I made a different assumption
about dividends at the end.
More or less, this is going to be what
actually the present value of dividends was over this whole
period. Here's the dilemma--this is
what I said in my 1981 article--this is the thing that
is supposed to be forecasted.
That's the present value and the blue line is the forecast of
that thing. Then you ask,
does this look like a good forecast?
Were people doing a good job of forecasting the red line with
the blue line? Now, that may be a loaded
question; but, I think that you get the
impression that there's something possibly wrong here
with efficient markets because the red line is just a smooth
growth path like nothing happens to it and yet the stock market
is going up and down all over the place.
It's a little bit like if you had a weather forecaster and
this morning he says, I predict today that the low
says, I predict that the low today
You would eventually start concluding that this weather
forecaster can't be trusted because we never get to those
temperatures. That's sort of what the stock
market is doing; it's fluctuating much more than
the thing that's forecasted.
You've got to be careful; I ended up with so many critics.
There are lots of issues here that--some people said,
well people don't know where the red line was last period.
And other people said, well you just are showing one
reality for the realization--you're
showing--they kind of get back to this parallel universe story.
There must be another universe where there's another Earth and
where everything looks the same except that the red line did
something very different; that could be.
So, people are saying, you never know,
there could have been a communist revolution in America
in the 1930s and they could have nationalized the whole stock
market and then the red line would be down at zero--they
would have taken the whole thing.
Or there could have been some good news, some great
breakthrough that we haven't discovered yet but in another
reality they could have.
So, all this noise in the stock market could have somehow been
new information about things that didn't happen.
I think we're getting kind of philosophical when we go to
that. The point is that we've never
seen any movement in the present value of dividends that would
justify the movement.
If we knew the future with certainty, according to this
model, then the stock market would behave like the red line,
not like the blue line.
Well, anyway. For example,
let's look at the Great Depression of the 1930s,
at the very least I think this chart will reveal some
misconceptions that some people have.
The Great Depression of the 1930s was awful,
right? I mean you hear these stories;
I assume you hear these stories.
We had 25% unemployment at the peak--it sounds really bad.
We had people selling apples on the street;
you must know these images, right?
It sounds awful, but look what happened to
p* in the Great Depression.
I can hardly see anything.
Well, what actually happened was businesses continued paying
their dividends right through the whole Depression and some of
them cut their dividends, but it was only for a few years.
The present value of--the value of stock depends on what it pays
out over decades not just next year.
The stock market--if people knew the--even if they knew the
depression was coming, they shouldn't have marked down
the stock market so much, according to this simple
efficient markets story--according to the present
value story. At the very least,
I think that this diagram helps you to see what is wrong or what
simple theories are wrong.
So, it must be that if the stock market is reacting to new
information over all this century of history,
it must have been new information about things that
just didn't happen.
It could be that an asteroid almost struck the Earth and then
it just missed and so the stock market crashed.
Then when it missed it came back up again,
so we don't see any interruption in dividends.
But it has to be something like that.
The problem is, I can't think of anything like
that. I don't think that any asteroid
came close to the Earth--not close enough to be worried
about--and I can't think the communist revolution had much
chance of taking place in the United States--but you can
imagine--so we don't know.
Behavioral finance kind of tends to reach the opposite
conclusion: that this volatility in the stock market is the sign
of something else; it's some social force,
some speculative bubbles, some activity that is not
related to anything fundamental.
The reason I got so much hostility when I wrote these
papers is I was striking a nerve,
I guess, because many people have developed these beautiful
mathematical theories that said that the stock market was the
optimal predictor of everything and I was saying the emperor has
no clothes; so there were others like that.
What is happening?
What I'm coming around to think--maybe it's my cynical
view, I've always been a cynic.
I don't know if you are cynics or not, but I think people
convinced themselves of things.
They--people think they understand things better than
they do. You spend your whole life
looking at this one picture of the stock market and you think
you have an explanation for all of it--all rational good--but
it's just over-confidence that's doing that;
it's an illusion.
I want to talk about over-confidence and I thought
I'd try–there's also no eraser.
Can you find another eraser?
There's probably one in this closet.
I wanted to try an experiment of asking you a series of a few
short questions. It's a game we'll play,
which I'll need your cooperation with.
So, these are questions about over-confidence.
Actually, I just want you to try to give me 90% confidence
intervals for the answers to these questions.
Do you know what a 90% confidence interval is?
It's, for example, if I were to ask you what--how
many people are there in New Haven?
I want you to not just give me a number, I want you to give me
a range such that you're 90% sure that you're right.
I could say, well, it's between 90,000 and
100,000 people and I'm 90% sure I'm right.
If you give me a true 90% confidence interval,
then you should be right 90% of the time, right?
What I'm going to do is give you a few questions and ask you
for a 90--ask you to write down--you have a piece of paper
there--a 90% confidence interval.
I have five questions; this is just an experiment.
The first one is about the Statue of Liberty.
What does it weigh in pounds--in tons?
Good, thank you. So, weight.
Incidentally, just to remind you,
a U.S. ton is 2,000 pounds--not a
British pound, which is 2,240 pounds--and a
ton is 907 kilograms.
Can you write down on your paper your 90% confidence
interval? For example,
I won't use realistic numbers.
If you thought it was--you might write down,
it's between one pound and three pounds and that you're 90%
sure it falls in that interval.
I didn't say--its tons, tons.
I'm asking--it's more than a pound--I'll give you a hint,
it's in tons. Let me also say,
we're not weighing the base.
The Statue of Liberty stands on a tall edifice;
we're not counting that but we're counting also the steel
reinforcing that they put in a few years ago.
Remember, the Statue of Liberty was getting weak and they were
worried that something might topple down,
so they reinforced it and we're counting that.
So, it's a copper structure with steel reinforcement.
Can you write down on your notes a range within which
you're 90% sure that the statue weighs, in tons?
If you could do that--I'm going to come back--what I'm going to
do is come back and see how often you are right so we'll go
back through these.
Have you all written down a weight for the Statute of
Liberty?
Population of the country, Turkey.
Since I don't have the current population, I want it in the
year 2000. I didn't get the latest
estimate; so, how many people were there
in Turkey in 2000?
And again, put down a range, a low and a high,
that's 90% sure.
Third, the Sahara Desert.
How many square miles in the Sahara Desert?
Remember that a square mile is 2.6 square kilometers;
just in case you think in terms of kilometers,
you can devise your answer in kilometers and then multiply by
2.6. Again, write down a range.
Enrollment at Yale.
By the way, I should have asked, you have to be honest
with it. You could game me by writing
really wide intervals for nine of ten questions and then an
extremely narrow interval for the tenth.
I'm expecting some sincere cooperation here--then you would
guarantee that you were right exactly 90% of the time,
right? I mean, you could say the
Statute of Liberty weighs between zero and a hundred
quintillion tons and you know you're right.
Then you could deliberately say the population of Turkey is
between one and two people and then you know you're wrong.
You could do--you're not supposed to do that.
I want the enrollment in Yale; I don't have the latest
number--2005. That's the total number of
students at Yale University in 2005, including Yale College and
all the graduate schools.
The fifth question is about the Pulitzer Prize.
Do you know this prize?
It's a prize that journalists win for writing great articles
or books. I want to know,
what is--how much do you get in cash if you win the Pulitzer
Prize? I have it for last year, 2007;
it might be different in 2008, so I'm asking for the 2007,
in dollars.
I hope you were honest in putting confidence intervals.
Have you gotten them?
Now, what I'm going to do, if you've answered all five
questions, I'm going to tell you the answers--the correct
answer--and then ask for a show of hands of how many--please be
honest and don't be embarrassed.
Raise your hand if you were right, meaning that if my answer
falls within your 90% confidence interval, okay?
Let's go to the Statue of Liberty.
The Statue of Liberty weighs 252 tons.
So, can I have a show of hands--how many people here have
252 in the interval?
You're doing fairly well; what fraction–keep your
hands up--looks like it's about, what would you say,
20-25%? Thank you for being honest and
not gaming me. It should have been 90% who
were right. What is the 2000 population of
Turkey? I'll give you the exact number
that I got from their statistic: 65,666,677.
That's a little over sixty-five million.
How many people have that in their interval?
That's better; that's like 40%--40% or 50%.
You're doing better but it's still not 90%.
How many square miles in the Sahara Desert?
3.5 million. Can I get a show of hands--how
many were right on that?
Well, this one really got you, that was like 5%.
Was anyone right on all of them so far?
Nobody. Enrollment in Yale, Fall 2005?
11,483 students. How many were right?
Okay, that's about 40%--right close to 40%,
I'd say. Finally, how much do you win
if--how much do you receive if you win the Pulitzer Prize?
$10,000. Can I have a show of hands?
That was really low, that's like 5%.
I knew that was a trick because you've heard about the Nobel
Prize. Those are both prestigious,
right? Nobel Prize gives you something
on the order of $1,000,000 and the Pulitzer Prize gives you
something like--it only gives you $10,000.
So how can that be?
I sort of picked something that I thought you might be wrong on.
That reveals something about human behavior.
It's a choice in life.
You go into different walks of life.
This is something that's fundamental to economics:
there are just different expectations about how much
money you're going to make.
If you go into the news media--and I think that's a
wonderful career--you're not going to make much money
probably. The whole thing is just scaled
down and I think there's something revealing about this
that we just have social norms for how much someone is to be
paid. If you were to give Stephen
Schwartzman a $10,000 prize, it would be more like an insult
than anything. But if you are working for The
New Haven Register and you get this prize, it's a life-changing
event, not because of the $10,000
maybe--even they get more money than that.
Anyway, the point was that people tend to be overconfident.
Incidentally, it's not just males;
females are well-known to be overconfident too.
There is a thing about macho males--"know it all"--but
experiments prove that women have the same problem.
That's why I think that when we look at charts of the stock
market, we see things that we think we understand,
especially young people.
They get deluded into thinking they understand more than they
really do. I wanted to talk about some
authors that I admire who have written about this.
These are books that I don't have on the reading list,
but they're fun to read.
There's a professor at The Harvard Business School,
Rakesh Khurana; he has a book on the search for
charismatic CEOs.
It's not just overconfidence in yourself;
we tend also to put overconfidence in leaders.
We have a sense that some people are just natural geniuses
and know everything, so we think that they can
transform our lives or our companies.
So, boards of directors are constantly looking for a CEO who
is a genius and they keep getting fooled and disappointed.
They bring someone in and this person often messes things up
more than helps because this person realizes that he or she
has to live up to this genius role,
so they better do something.
So, they do something in a flailing way,
not understanding what they're doing, and they mess up the
whole company. Really, a lot of what
happens--good things that happen in human society--are the result
of lots of people doing their own special things and all
working together.
There's no great genius but there's this idea in our mind
that we are going to be such a thing.
Related to that--and I wanted to mention, it's on the reading
list--an article by one of my students in this class,
who's now at MIT.
He took this class about ten years ago, Fadi Kanaan and
co-authored with another MIT professor,
Dirk Jenter, again looking at overconfidence
in our judgments.
Again, they looked at CEOs, chief executive officers of
companies, and they found that companies in industries that
fail tend to fire their CEOs.
This is unjust; this is an overreaction.
You bring in this CEO who's supposed to be brilliant and
then the business fails, so you fire the guy right after
that. We're kind of manic-depressive
about these guys.
When the business fails, we think we were such a
mistake. This guy had such promise and
he just didn't live up so we get rid of him;
but in fact, they found that the CEO gets
fired even if the whole industry went down.
So, you can't blame the CEO for the fact--if you're one company
in an industry and the whole industry goes down--or the
remaining industry even not including that firm--it's not
the CEO's fault. We tend to be kind of wild and
extreme in our judgments.
You've seen that a lot--a lot of CEOs lost their jobs recently
in the subprime crisis.
Was it their fault?
Probably not, but they get fired anyway.
We go through this manic-depressive--we try to hire
charismatic CEOs, then we get disappointed and we
keep going through musical chairs one after another.
Nassim Taleb, who lives here in Connecticut
and I know him well, has a book called Fooled by
Randomness, which was a best-seller and
it's very fun to read.
It's a story--he's a Wall Street--he had an investment
management firm and he observed a lot of people.
It's a book about how people over interpret--they tend to
blame themselves for failures and congratulate themselves for
successes too much and they don't realize that it's just
random. Some guy who's in a
business--business is succeeding--why is it
succeeding? Because the guy came in,
dumb luck at the right time and everything is supporting that,
concludes that he's a genius.
Then Taleb observes them later, after things don't go so well,
and suddenly they're depressed.
– I talked to stockbrokers before and after
the '87 stock market crash and one of them told me--or maybe
more than one of them told me--I can tell that the crash occurred
from the tone of voice of the people when they call up the
phone. When the market was soaring
just before the '87 peak, he said they would call up and
they were brash and rude to me and they would say,
let's trade this, get this done--kind of just
disparaging subtlety, the stockbroker.
Then after the crash, when these people were sort
of--many of them--wiped out, they'd answer the phone in a
sheepish way. You could just tell in the tone
of their voice that they were crushed.
So, that's what happens.
I also have down on this part of the reading list Irving
Fisher, who was a professor at Yale,
who was a very prominent economist in the first half of
the century. He's another Yale graduate,
Yale Class of 1895, I think.
I'm sure he lectured on this stage because this building
was--his office was in this building, I believe.
He died around the mid-1940s but he's famous for
overconfidence. In 1929, he was interviewed
just before--two weeks before--the 1929 peak and--do
you know what I'm referring to?
He said he thought the stock market was on a permanently high
plateau and he wrote a book in 1929--actually it came out in
1930--with this extremely optimistic outlook for the
market. He had a beautiful mansion;
he was a wealthy man for a while, but he lost everything in
the stock market crash.
In fact he had to--he had borrowed against his home and he
lost his house, so Yale University bought his
house for him and rented it out to him;
otherwise, he would be on the street.
I have an article written by him in 1930--I think it's 1930
or at the end of 1929--discussing the stock
market crash. He still is unrepentant.
This was our most brilliant professor here at Yale,
but he just totally misjudged the market,
He's just totally unrepentant--he just went back
over his book. There are so many good
reasons--the 20s were a spectacular era--so many good
reasons the stock market will keep going up and he just
wouldn't back down.
In fact, what he actually did was he started borrowing from
his relatives--he had wealthy relatives--and he lost all of
it. He just couldn't have imagined
that the stock market would go down--there was just no reason
that he could think of--and that's what he says in the
article. Anyway, I want to talk more
precisely about how people behave;
this is all general about overconfidence,
but there's some other factors that I want to start with.
The most important theory in behavioral finance is the
Kahneman and Tversky Prospect Theory.
Danny Kahneman, who is now a professor of
psychology at Princeton, and Amos Tversky,
who died a few years ago--they wrote, I think,
the most famous article on behavioral economics;
it goes beyond just finance.
The title of the article was Prospect Theory and that
was 1979. This is, I think,
the–actually, I think there was a ranking of
economics articles--scholarly articles--by numbers of
quotations and this was number two out of all articles written
in the last fifty years.
Number one, it was quoted for some other reason--I'm not
sure--it was some statistical method that everyone quoted.
In terms of an intellectual contribution,
this is the most important economics article in the last
fifty years, at least judged by how many
times it's cited.
Kahneman and Tversky are not really talking about
overconfidence but something, well, perhaps related to
it--something more general.
It's how people make choices and there are two elements to
this theory. It replaces expected utility
and it has--what it does, it replaces the utility
function with a value function--with value
function--and replaces the probabilities with,
what they call, weights.
I'm going to explain what that is and we'll move on.
Let me give a little story that leads up to it and it's a story
that Paul Samuelson, who's a professor at MIT,
told. Paul Samuelson was a highly
esteemed--he is--I think he's ninety-two or about ninety-two
years old now and still writing and still working.
He was a--he is a mathematical economist, retired now,
but he told a story that illustrates some of the
beginnings of Prospect--in fact, he kind of anticipated Prospect
Theory. This goes back to an article
that he wrote in 1963.
In 1963, he was having lunch with one of his colleagues,
another economist; he doesn't name this other
person because it would be embarrassing,
but everyone knows it was E.
Cary Brown, a professor at MIT.
Samuelson, in a playful mood--he was always sort of a
playful person--he said at lunch--he said,
hey let's toss a coin.
Let's make a bet just for the fun of it and if it comes up
heads, I'll give you $200, but if it comes up tails,
you give me $100.
He said, let's do it I'm ready.
This kind of took E.
Cary Brown by surprise.
That sounds like a lot of money, especially in 1963;
prices were much lower--that's like $1,000 or $2000.
It was big money.
But of course, these professors could afford
it; it's not that much money.
So, let's just say it's $100 and $200.
Do you feel like--if I were to offer that to you right
now--let's do it because you don't have cash on you now,
but you'd have to promise to pay me if you came out wrong.
Do you feel like doing that?
No, someone is answering me honestly.
Introspect and think about it while this is suddenly thrust on
you. E.
Cary Brown said, come on I don't want to do
this--Samuelson was being annoying by doing this.
Then Samuelson thought--had another idea-he said,
what if I offered--he didn't actually offer this--what if I
offered to--let's do this 100 times.
We'll toss a coin 100 times and each time it comes up heads I
give you $200 and each time it comes up tails you give me $100.
Well, E. Cary Brown, knowing mathematics
of statistics and the law of probabilities,
he said, well, if we do it 100 times,
by the binomial theorem, I'm sure to win.
I couldn't possibly--this is elementary--100 times is a lot
of times. In fact, I'll make thousands of
dollars. So, E.
Cary Brown said, I'll do it.
I would do it, but he didn't actually do it.
Samuelson then said--he went back to his office and he wrote
a paper--that's this 1963 paper--proving that E.
Cary Brown was irrational.
You cannot possibly say, I will take 100 of them but I
won't take one of them.
That's not rational.
That was one of the motivating things in Kahneman and Tversky.
What Kahneman and Tversky said is that people behave--if you
can introspect and imagine why some of you didn't feel like
taking this bet--people behave as if they have a kink in their
utility. This may sound an abstract way
of putting it, but expected utility
theory--the traditional theory says that everybody has a
utility function that they consistently refer to when
making calculations.
I'm going to put Kahneman and Tversky over here and I'm going
to put Expected Utility Theory over here.
Expected Utility Theory says that I want wealth--and I'll
call w wealth--and I get utility from wealth--that's
U. My utility curve--it has maybe
any number of shapes, but its concave downward and
smooth, so you have what's called diminishing marginal
utility;
that's Expected Utility Theory.
What Expected Utility Theory means--the slope is always
decreasing. Every extra dollar of wealth
gives me less happiness but it always give me a little bit
more, so I always want more.
Expected Utility Theory would say that that's a two-for-one
bet that Samuelson is offering and it's small compared to my
lifetime wealth. My utility is essentially
linear over the relevant range, plus $200 or minus $100,
so I don't really concern myself about risk.
I should just take every bet like that all the time.
You should always be looking--if you are behaving
this way--you should always be looking.
Anyone who wants to make a bet with me anytime,
I'll always take it if it's in my advantage--even a little bit
in my advantage. People seem to like to gamble
but they don't like to do it consistently.
They like to go to--they end up going to gambling casinos where
it's stacked against them, not for them,
but it's somehow arranged as an entertainment.
Well, Kahneman and Tversky said that people don't behave this
way and it's as if they have a value function as a function of
their money. Let's put in the middle of the
value function, the reference point.
Reference point means where you are today and your value--that's
V, which is like utility, but now we're talking in
psychological terms, so we give it a different name.
The value function has a kink; it's something like that at the
reference point. I'm trying to draw it--it's not
necessarily--it looks here like two straight lines and that's
not quite the way to do it.
Let me try and do this again--it's curved downward a
little bit, but it becomes much less--I don't--I'm having
trouble drawing this on the board well.
I don't want to ever--kind of going down.
There's a kink here, where the slope--I think I've
got it sort of there.
It's concave down everywhere, just like the utility function
is, but there's a discontinuity of slope right here.
Where is that? That's where I am now.
What it means is that I value losses much more than I value
gains from wherever I am.
There's a big difference between losing and winning,
so when I reflect on this bet I'm thinking of--I could lose
$100 and that scares me.
It feels bad--the idea that--I would just feel bad.
So gaining $200 is positive for me but it doesn't offset the
loss that I might make.
So, if I have equal probabilities,
what you want to do is weight the gains and losses and the
losses tend to dominate, so you don't want to take the
bet. The weighting function
incorporates Samuelson's lunch colleague's problem:
that people don't want to take bets that are to their
advantage. It goes back to a kink in the
utility function.
Now, incidentally, this is fundamentally different
from--in economic theory, economists would say,
well you can put a kink in the utility function.
There could be some wealth level that's special to you.
But a theory economist--that kink has to stay at a certain
wealth level. With Kahneman and Tversky,
this kink moves around with you, so whatever--it's
whatever--you're always at the kink because it's not rational;
this is not rational Expected Utility Theory.
This is--I'm always looking at where I am now and exaggerating
in my mind the importance of deviations from that.
People are very concerned with small losses;
that's what th kink in the value function is.
Now, I want to talk about another Kahneman and Tversky
thing, called the weighting function.
The weighting function refers to the fact that people distort
probabilities in their mind.
It's not that they don't know probabilities but they distort
them in their thinking.
I'll give an example that illustrates the Kahneman-Tversky
weighting function and it goes back years before Kahneman and
Tversky. It's a famous example from a
French economist, Maurice Allais,
and it's called the Allais Paradox.
It illustrates thinking that violates Expected Utility
Theory. I'm going to give you a choice
between two "prospects," as Kahneman and Tversky called
them. Suppose I offered you a 25%
chance to win $3,000 or, alternatively,
a 20% chance to win $4,000.
Maybe I can get a show of hands.
This is like Samuelson's lunch colleague again,
but a little different.
Suppose I'm offering--I'm not offering this,
but suppose I offered this--you have a choice between Prospect
One or Prospect Two.
Prospect One--I'm going to toss a four-sided coin and if it
comes up with a probability of one-fourth, in a certain way,
you will win $3,000.
In Prospect Two, I'm going to give you a chance
of 20% to win $4,000.
Can you tell me which of these you'd pick if you had to pick
only one of these?
Do you understand the question?
How many would pick number One?
It seems like it's about 20%.
How many would pick number Two?
So, most of you would pick number Two.
Now, let's do a variation on this question here--a very
simple variation.
Which would you prefer?
This is the one that you picked--most people picked.
Another prospect--100% chance of winning $3,000--or Two,
that would be an 80% chance of winning $4,000.
Do you see the--if you pick Prospect One,
you're going to just get $3,000 for sure.
If you pick Prospect Two, you'll probably get $4,000 but
an 80% chance of it.
How many would pick One?
That looks like the--how many would pick Two?
Very few of you would pick Two.
Have to reflect--so we picked One this time.
Now, you might want to reflect on that.
Why was it such a different--why did you pick One
in this case and pick Two in this case?
The thing I want to point out is that the number--the cash
amounts are the same in the two examples but the probabilities
are just multiplied by four.
So the expected utility of the two is just four times as great,
no matter what. They're the same--the utilities
are the same, with the same numbers.
All I've done is multiply your expected utility by four in this
case, so you can't make a different choice.
If you picked Two over here when comparing these two
prospects you should also have picked Two when you compared
these two prospects.
Why didn't you? Most of you switched.
Can you tell me why?
Yes. Student: I would prefer
not to gamble, so if I had the chance a--in
the first situation, I would take the chance to make
$4,000. Professor Robert
Shiller: You would choose not to gamble.
Does this mean it's like a moral judgment or--
Student: No, I prefer certainty.
Professor Robert Shiller: Okay,
you got it exactly.
That's yeah--you got--you prefer certainty.
There's some anxiety about maybe--you got it exactly right.
I think people like certainty and ambiguity is difficult for
them to adjust to.
Kahneman and Tversky put it in this following way:
it's a little bit like we're cavemen.
It turns out, we were all taught to count and
to do arithmetic but primitive people actually have difficulty
counting. There's an old story that
cavemen had only three numbers: one, two, and many.
I used to disbelieve this story but I'm not--actually it was a
psychologist at Princeton told me that,
as a matter of fact, it's proven that there are some
people whose languages have only those numbers:
one, two, and many.
For example, they're called--in Laos in
Thailand, there's a very primitive group of people with
primitive technology.
I don't mean that they're primitive people but they only
have one, two, and many;
and there are others that have been discovered.
Emotionally we're like that.
I used to wonder how could they have only those numbers:
one, two, and many.
You ask a mother, how many children do you have?
She couldn't answer; she didn't have the word three,
but as a matter of fact they didn't.
So I guess, if you asked the mother, how many children you
have, she would probably just name them.
She couldn't say, I have three children.
But anyway, we're all kind of like that when we think about
probability; that's Kahneman and Tversky.
Kahneman and Tversky say what we do is that in our minds we
weight the probabilities in a distorted way and this is the
weighting function.
So, we have the weight--that's weight not wealth here--against
the probability and I'm going to exaggerate a little bit.
This is zero and this is one because probabilities range from
zero to one. The weighting function looks
like this--I'm exaggerating a little bit so you can see
but--and then it jumps up or it jumps down here;
this is the idea.
What Kahneman and Tversky said in their original 1979 article
is, we act as--there's a wide range of probabilities here that
are all kind of blurred and put together.
We minimize and–emotionally,
the difference between probabilities--they're all kind
of in the middle.
So, when I said twenty or twenty-five, in your mind you
said, here's twenty and here's twenty-five but I don't think
they're much different to me emotionally.
The money sounds different but the probability sounds the same.
It's like I have only three probabilities:
can't happen, might happen,
and it's certain to happen.
You tend to be totally in to the certainty story,
so you give it much more weight.
The way--what people do then, summing up--in expected utility
theory, you maximize the probability-weighted sum of
utilities.
You maximize the summation of the probability of the
i^(th) outcome times utility in the i^(th)
outcome. But in Prospect Theory,
you maximize the sum of the weights times the value
function--the values.
This is the Kahneman and Tversky variation on Expected
Utility Theory. There's something related to it
that psychologists talk about, it's called Regret Theory.
It's a little bit different but it's essentially the same
as–well, it's consistent with Prospect
Theory. That is, people experience pain
of regret and they do a lot of things to try to avoid the pain
of regret. For example,
when the stock market goes up they try to sell it and lock in
the gain because they are worried that if it goes down
again they will regret not having sold it;
that's not a rational calculation.
If you come to something, you just have it and then it
escapes you, you feel pain.
I guess that's what happened at the Super Bowl last night when
the New England Patriots had a winning streak and they messed
up at the very end--that's exceptionally painful and that's
part of Regret Theory.
I don't know how pained any of you are but it must have been
painful to them anyway.
I just mentioned some other things that are related to
Prospect Theory. There's something called
"mental compartments" that people--Expected Utility Theory
says, your utility depends on your
whole lifetime wealth, so you should be always
thinking that everything that happens today is just part of a
bigger story; I'm always thinking about my
lifetime. I had you do an exercise at the
beginning where I asked you to estimate the present value of
your lifetime income and it probably came out to several
million dollars. So, if you were behaving
rationally you would always be weighing things against that big
sum of several million dollars.
That's why plus $100, minus $200--who cares,
right? That's the way you should be
thinking but you don't think that way because you're human.
People put things in mental compartments,
all different compartments in your mind,
and you have separate values for things depending on which
compartment they're in.
For example, when you go to the gambling
casino, the winnings and losses are completely different.
You just put them in a game compartment and you think,
I can accept these and it doesn't matter.
Investors are that way too, they'll sometimes put part of
their portfolio in "I can play with this" mental compartment
and others in another mental compartment.
Anyway, I just want to come back--I have maybe a little bit
more to say about this, but let me come back and talk
just about the problem set we talked about last period.
Problem Set #3--you've got your second problem set here--Problem
Set #3 is a stock market forecasting exercise and the
spreadsheet that I have up here is one spreadsheet that you
could use to do that.
It's illustrated--I clarified it a little bit in the version I
put up. So, you run a regression like
that to predict the stock market.
This is actually a hands-on experience that's supposed to
help you eliminate your overconfidence by trying to
predict the market.
This is the example where I tried to use time as a predictor
of the stock market and failed pretty decisively to do so.
What I want to say is that I have this spreadsheet up here
that has some data--it has monthly--this is my 130-year
long stock price series, but you could add other data
and whatever--if you can find data series somewhere it would
be more fun to try to predict using other data.
This is just for you to really try to do it.
Some people do sports things, so if somebody wins the Super
Bowl--I don't know what the story is--this is a famous story
actually--the stock market goes up or goes--do you know that.
I don't know this exact repeated story--so you could
create other variables like a dummy variable for winning
the--somebody winning the Super Bowl and put that in.
There's a famous story--it goes back to the 1930s--about skirt
lengths and the stock market.
Do you know this story?
In the 1920s, an unprecedented thing happened
in women's fashion, never been seen before in the
United States, maybe in--women started wearing
short skirts and it was scandalous.
They weren't quite mini skirts, but they were scandalous.
The women's hemlines rose and peaked in 1929 and then the
skirt lengths came down in the 1930s, right with the market;
so that was noticed.
Some people thought there was some euphoria that was driving
women crazy or something about the 1920s--the optimism,
the sense; it sort of happened again in
the '70s. Remember, the mini skirts came
in the 1970s, right?
Then the 1970s--'74 crash didn't exactly--I don't know if
hemlines came down.
But anyway, I had one student who thought, well maybe there
are other fashion things that explain the market and she went
back to microfilm newspapers and measured the width of men's ties
in fashion advertisements.
She thought, wide ties are a sign of--it's
like a short skirt I guess--a sign of optimism and excitement,
so she collected data on widths of ties.
She had a time series--this is a very good answer to a very
good problem set--and she collected fifty years of data on
the width of men's ties and correlated--to see if it
predicted the market.
Unfortunately it did not, but it was a wonderful choice.
I'm hoping that some of you can think of interesting things to
do to try to predict the stock market.
Alright, I'll see you again in two days.