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
today will be -100º
and then two days later he
says,
I predict that the low today
will be +150º.
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.
