00:00:00
- This single equation spawned
00:00:02
four multi-trillion dollar industries
00:00:04
and transformed
everyone's approach to risk.
00:00:07
Do you think that most people
are aware of the size, scale,
00:00:11
utility of derivatives?
00:00:13
- No. No idea.
00:00:15
- But at its core, this
equation comes from physics,
00:00:18
from discovering atoms,
00:00:20
understanding how heat is transferred,
00:00:22
and how to beat the casino at blackjack.
00:00:25
So maybe it shouldn't be surprising
00:00:27
that some of the best
to beat the stock market
00:00:29
were not veteran traders,
00:00:30
but physicists, scientists,
and mathematicians.
00:00:34
In 1988, a mathematics
professor named Jim Simons
00:00:37
set up the Medallion Investment Fund,
00:00:40
and every year for the next 30 years,
00:00:42
the Medallion fund delivered
higher returns
00:00:44
than the market average,
00:00:45
and not just by a little bit,
00:00:47
it returned 66% per year.
00:00:51
At that rate of growth,
00:00:53
$100 invested in 1988 would be worth
00:00:56
$8.4 billion today.
00:01:00
This made Jim Simons easily the richest
00:01:02
mathematician of all time.
00:01:04
But being good at math
00:01:06
doesn't guarantee success
in financial markets.
00:01:09
Just ask Isaac Newton.
00:01:12
In 1720 Newton was 77 years old,
00:01:15
and he was rich.
00:01:17
He had made a lot of money working
00:01:18
as a professor at Cambridge for decades,
00:01:20
and he had a side hustle as
the Master of the Royal Mint.
00:01:24
His net worth was £30,000
00:01:27
the equivalent of $6 million today.
00:01:31
Now, to grow his fortune,
Newton invested in stocks.
00:01:34
One of his big bets was
on the South Sea Company.
00:01:37
Their business was shipping
00:01:38
enslaved Africans across the Atlantic.
00:01:42
Business was booming
00:01:43
and the share price grew rapidly.
00:01:45
By April of 1720, the value of
Newton's shares had doubled.
00:01:49
So he sold his stock.
00:01:51
But the stock price kept going up
00:01:54
and by June, Newton bought back in
00:01:57
and he kept buying shares
even as the price peaked.
00:02:01
When the price started to
fall, Newton didn't sell.
00:02:03
He bought more shares thinking
he was buying the dip.
00:02:07
But there was no rebound,
00:02:09
and ultimately he lost
around a third of his wealth.
00:02:12
When asked why he didn't see
it coming, Newton responded,
00:02:16
"I can calculate the motions
of the heavenly bodies,
00:02:19
but not the madness of people."
00:02:22
So what did Simons get
right that Newton got wrong?
00:02:27
Well, for one thing, Simons was able
00:02:29
to stand on the shoulders of giants.
00:02:33
The pioneer of using math
to model financial markets
00:02:35
was Louis Bachelier, born in 1870.
00:02:39
Both of his parents died when he was 18
00:02:41
and he had to take over
his father's wine business.
00:02:44
He sold the business a few years later
00:02:46
and moved to Paris to study physics,
00:02:48
but he needed a job to
support himself and his family
00:02:51
and he found one at the Bourse,
00:02:52
The Paris Stock Exchange.
00:02:54
And inside was Newton's
"madness of people"
00:02:57
in its rawest form.
00:02:59
Hundreds of traders screaming
prices, making hand signals,
00:03:02
and doing deals.
00:03:04
The thing that captured
Bachelier's interest
00:03:06
were contracts known as options.
00:03:10
The earliest known options
were bought around 600 BC
00:03:13
by the Greek philosopher
Thales of Miletus.
00:03:17
He believed that the coming
summer would yield
00:03:19
a bumper crop of olives.
00:03:20
To make money off this idea,
00:03:22
he could have purchased olive presses,
00:03:24
which if you were right,
would be in great demand,
00:03:27
but he didn't have enough
money to buy the machines.
00:03:29
So instead he went to all the
existing olive press owners
00:03:32
and paid them a little bit
of money to secure the option
00:03:35
to rent their presses in the
summer for a specified price.
00:03:39
When the harvest came,
Thales was right,
00:03:42
there were so many olives
00:03:44
that the price of renting
a press skyrocketed.
00:03:46
Thales paid the press owners
their pre-agreed price,
00:03:49
and then he rented out the
machines at a higher rate
00:03:52
and pocketed the difference.
00:03:54
Thales had executed the
first known call option.
00:03:58
A call option gives you the right,
00:04:00
but not the obligation to buy something
00:04:02
at a later date for a set price
00:04:04
known as the strike price.
00:04:06
You can also buy a put option,
which gives you the right,
00:04:08
but not the obligation
00:04:10
to sell something at a later date
00:04:11
for the strike price.
00:04:13
Put options are useful if you expect
00:04:14
the price to go down.
00:04:16
Call options are useful if
you expect the price to go up.
00:04:20
For example, let's say the current price
00:04:21
of Apple stock is a hundred dollars,
00:04:24
but you expect it to go up.
00:04:26
You could buy a call option for $10
00:04:28
that gives you the right,
but not the obligation
00:04:30
to buy Apple stock in one
year for a hundred dollars.
00:04:34
That is the strike price.
00:04:36
Just a little side note,
00:04:37
American options can be exercised
00:04:39
on any date up to the expiry,
00:04:41
whereas European options
must be exercised on
00:04:43
the expiry date.
00:04:45
To keep things simple, we'll
stick to European options.
00:04:48
So if in a year the price of Apple stock
00:04:51
has gone up to $130,
00:04:52
you can use the option to buy shares
00:04:55
for a hundred dollars and
then immediately sell them
00:04:57
for $130.
00:04:59
After you take into
account the $10 you paid
00:05:01
for the option, you've made a $20 profit.
00:05:04
Alternatively, if in a year
00:05:06
the stock prices dropped to $70,
00:05:08
you just wouldn't use the option
00:05:10
and you've lost the $10 you paid for it.
00:05:13
So the profit and loss
diagram looks like this.
00:05:16
If the stock price ends up
below the strike price,
00:05:18
you lose what you paid for the option.
00:05:20
But if the stock price is
higher than the strike price,
00:05:23
then you earn that difference
minus the cost of the option.
00:05:28
There are at least three
advantages of options.
00:05:32
One is that it limits your downside.
00:05:34
If you had bought the
stock instead of the option
00:05:36
and it went down to $70,
00:05:37
you would've lost $30.
00:05:39
And in theory, you could
have lost a hundred if the
00:05:41
stock went to zero.
00:05:43
The second benefit is
options provide leverage.
00:05:46
If you had bought the stock
00:05:47
and it went up to $130,
00:05:49
then your investment grew by 30%.
00:05:52
But if you had bought
the option, you only had
00:05:54
to put up $10.
00:05:55
So your profit of $20 is actually
00:05:57
a 200% return on investment.
00:06:00
On the downside, if you
had owned the stock,
00:06:03
your investment would've
only dropped by 30%,
00:06:05
whereas with the option you lose all 100%.
00:06:09
So with options trading, there's a chance
00:06:11
to make much larger profits,
00:06:13
but also much bigger losses.
00:06:16
The third benefit is you
can use options as a hedge.
00:06:20
- I think the original
motivation for options
00:06:22
was to figure out a way to reduce risk.
00:06:24
And then of course, once people decided
00:06:26
they wanted to buy insurance,
00:06:28
that meant that there are
other people out there
00:06:30
that wanted to sell it
00:06:32
or a profit, and that's
how markets get created.
00:06:36
- So options can be
00:06:38
an incredibly useful investing tool,
00:06:40
but what Bachelier saw on the
trading floor was chaos,
00:06:43
especially when it came to
the price of stock options.
00:06:47
Even though they had been
around for hundreds of years,
00:06:50
no one had found a good way to price them.
00:06:52
Traders would just bargain
to come to an agreement
00:06:54
about what the price should be.
00:06:56
- Given the option to buy or
sell something in the future,
00:07:00
it seems like a very
amorphous kind of a trade.
00:07:04
And so coming up with prices
00:07:06
for these rather strange
objects has been a challenge
00:07:10
that's plagued a number of economists
00:07:12
and business people for centuries.
00:07:15
- Now, Bachelier, already
interested in probability,
00:07:18
thought there had to be
a mathematical solution
00:07:20
to this problem, and he
proposed this as his PhD topic
00:07:24
to his advisor Henri Poincaré.
00:07:26
Looking into the math of finance
00:07:28
wasn't really something
people did back then,
00:07:30
but to Bachelier's
surprise, Poincaré agreed.
00:07:34
To accurately price an option,
00:07:37
first you need to know what happens
00:07:38
to stock prices over time.
00:07:40
The price of a stock is
basically set by a tug of war
00:07:43
between buyers and sellers.
00:07:45
When more people wanna buy
a stock, the price goes up.
00:07:48
When more people wanna sell
a stock, the price goes down.
00:07:51
But the number of buyers and sellers
00:07:53
can be influenced by almost anything,
00:07:55
like the weather, politics,
00:07:57
new competitors, innovation and so on.
00:08:00
So Bachelier realized that
it's virtually impossible
00:08:03
to predict all these factors accurately.
00:08:05
So the best you can do is assume
00:08:07
that at any point in time the stock price
00:08:10
is just as likely to go up as down
00:08:12
and therefore over the long term,
00:08:14
stock prices follow a
random walk,
00:08:17
moving up and down as if their
next move is determined
00:08:20
by the flip of a coin.
00:08:22
- Randomness is a hallmark
of an efficient market.
00:08:27
By efficient economists typically mean
00:08:29
that you can't make money by trading.
00:08:33
- The idea that you shouldn't
be able to buy an asset
00:08:35
and sell it immediately
for a profit is known
00:08:38
as the Efficient Market Hypothesis.
00:08:40
- The more people try to make money
00:08:42
by predicting the stock market
00:08:44
and then trading on those predictions,
00:08:46
the less predictable those prices are.
00:08:49
If you and I could predict
00:08:51
the stock market tomorrow,
00:08:52
then we would do it.
00:08:54
We would start trading today on stocks
00:08:56
that we thought were gonna go up tomorrow.
00:08:58
Well, if we did that, then
instead of going up tomorrow,
00:09:02
they would go up now
00:09:03
as we bought more and more of the stock.
00:09:05
So the very act of predicting
actually affects the quality
00:09:10
of the future outcomes.
00:09:12
And so in a totally efficient market,
00:09:14
the prices tomorrow
can't possibly have any
00:09:18
predictive power.
00:09:19
If they did, we would've
taken advantage of it today.
00:09:24
- This is a galton board.
00:09:26
It's got rows of pegs
arranged in a triangle
00:09:29
and around 6,000 tiny ball bearings
00:09:31
that I can pour through the pegs.
00:09:33
Now, each time a ball hits a peg,
00:09:34
there's a 50 50 chance it
goes to the left or the right.
00:09:38
So each ball follows a
random walk as it passes
00:09:41
through these pegs,
00:09:42
which makes it basically impossible
00:09:44
to predict the path of
any individual ball.
00:09:47
But if I flip this over,
what you can see
00:09:50
is that all the balls together
00:09:52
always create a predictable pattern.
00:09:54
That is a collection of random walks
00:09:57
creates a normal distribution.
00:09:59
It's centered around the middle
00:10:01
because the number of
paths a ball could take
00:10:03
to get here is the greatest.
00:10:04
And the further out you go,
00:10:05
the fewer the paths a ball
could take to get there.
00:10:08
Like if you want to end up
here, well the ball would have
00:10:10
to go left, left, left,
left all the way down.
00:10:13
So there's only one way to get here,
00:10:15
but to get into the middle,
there are thousands of paths
00:10:18
that a ball could take.
00:10:20
Now, Bachelier believed a stock price is
00:10:22
just like a ball going
through a galton board.
00:10:26
Each additional layer of
pegs represents a time step.
00:10:29
So after a short time, the
stock price could only move
00:10:32
up or down a little,
00:10:33
but after more time, a wider
range of prices is possible.
00:10:37
According to Bachelier the
expected future price
00:10:40
of a stock is described
00:10:41
by a normal distribution,
00:10:43
centered on the current price
00:10:45
which spreads out over time.
00:10:48
Bachelier realized he had rediscovered
00:10:50
the exact equation which describes
00:10:52
how heat radiates from
regions of high temperature
00:10:55
to regions of low temperature.
00:10:58
This was first discovered
00:10:59
by Joseph Fourier back in 1822.
00:11:02
So Bachelier called his discovery
00:11:04
the radiation of probabilities.
00:11:07
Since he was writing about finance,
00:11:09
the physics community
didn't take any notice,
00:11:12
but the mathematics of the
random walk would go on
00:11:14
to solve an almost century
old mystery in physics.
00:11:20
In 1827,
00:11:21
Scottish botanist Robert Brown
was looking at pollen grains
00:11:24
under the microscope,
00:11:25
and he noticed that the particles
00:11:27
suspended in water on the microscope slide
00:11:28
were moving around randomly.
00:11:31
Because he didn't know
whether it was something to do
00:11:33
with the pollen being living material,
00:11:35
He tested non-organic particles
00:11:37
such as dust from lava and meteorite rock.
00:11:41
Again, he saw them moving
around in the same way.
00:11:44
So Brown discovered that any particles,
00:11:47
if they were small enough,
00:11:48
exhibited this random movement,
00:11:50
which came to be known as Brownian motion.
00:11:54
But what caused it remained a mystery.
00:11:58
80 years later in 1905,
00:12:00
Einstein figured out the answer.
00:12:05
Over the previous couple hundred years,
00:12:06
the idea that gases and liquids
00:12:08
were made up of molecules
00:12:09
became more and more popular.
00:12:11
But not everyone was convinced
00:12:12
that molecules were real
in a physical sense.
00:12:15
Just that the theory explained
a lot of observations.
00:12:18
The idea led Einstein to hypothesize
00:12:21
that Brownian motion is caused by
00:12:23
the trillions of molecules
hitting the particle
00:12:25
from every direction, every instant.
00:12:28
Occasionally, more will hit
from one side than the other,
00:12:30
and the particle will momentarily jump.
00:12:33
To derive the mathematics,
00:12:35
Einstein supposed that as
an observer we can't see
00:12:38
or predict these collisions
with any certainty.
00:12:40
So at any time we have to
assume that the particle
00:12:43
is just as likely to move
00:12:44
in one direction as an another.
00:12:47
So just like stock prices,
00:12:49
microscopic particles move
00:12:50
like a ball falling down a galton board,
00:12:52
the expected location of
a particle is described
00:12:55
by a normal distribution,
which broadens with time.
00:12:59
It's why even in completely still water,
00:13:01
microscopic particles spread out.
00:13:04
This is diffusion.
00:13:07
By solving the Brownian motion mystery.
00:13:09
Einstein had found definitive evidence
00:13:11
that atoms and molecules exist.
00:13:13
Of course, he had no idea
00:13:14
that Bachelier had
uncovered the random walk
00:13:17
five years earlier.
00:13:19
By the time Bachelier finished his PhD,
00:13:21
he had finally figured
out a mathematical way
00:13:24
to price an option.
00:13:25
Remember that with a call option,
00:13:27
if the future price of a stock
00:13:29
is less than the strike price,
00:13:30
then you lose the premium
paid for the option.
00:13:33
But if the stock price is
greater than the strike price,
00:13:35
you pocket that difference
00:13:37
and you make a net profit
if the stock has gone up
00:13:39
by more than you paid for the option.
00:13:42
So the probability that an option buyer
00:13:44
makes a profit is the
probability that the price
00:13:46
increases by more than
the price paid for it,
00:13:49
which is the green shaded area.
00:13:51
And the probability that
the seller makes money
00:13:53
is just the probability that
the price stays low enough
00:13:55
that the buyer doesn't earn
more than they paid for it.
00:13:58
This is the red shaded
area.
00:14:01
Multiplying the profit or loss
00:14:02
by the probability of each outcome,
00:14:04
Bachelier calculated the
expected return of an option.
00:14:08
Now how much should it cost?
00:14:11
If the price of an option is too high,
00:14:12
no one will wanna buy it.
00:14:14
Conversely, if the price is too low,
00:14:16
everyone will want to buy it.
00:14:18
Bachelier argued that the fair price
00:14:20
is what makes the expected return
00:14:22
for buyers and sellers equal.
00:14:24
Both parties should stand to
gain or lose the same amount.
00:14:28
That was Bachelier's insight
00:14:29
into how to accurately price an option.
00:14:33
When Bachelier finished his
thesis, he had beaten Einstein
00:14:36
to inventing the random walk
00:14:37
and solved the problem that
had eluded options traders
00:14:40
for hundreds of years.
00:14:42
But no one noticed.
00:14:43
The physicists were uninterested
00:14:45
and traders weren't ready.
00:14:46
The key thing missing was a
way to make a ton of money.
00:14:52
Hey, so I'm not sure how
stock traders sleep at night
00:14:54
with billions of dollars
00:14:56
riding on the madness of people,
00:14:57
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00:15:00
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00:16:03
In the 1950s,
00:16:04
a young physics graduate, Ed
Thorpe,
00:16:06
was doing his PhD in Los Angeles,
00:16:08
but a few hours drive away,
00:16:10
Las Vegas was quickly becoming
00:16:11
the gambling capital of the world,
00:16:13
and Thorpe saw a way to make a fortune.
00:16:16
He headed to Vegas and sat
down at the blackjack table,
00:16:19
back then, the dealer only
used a single deck of cards,
00:16:21
so Thorpe could keep a
mental note of all the cards
00:16:24
that had been played as he saw them.
00:16:27
This allowed him to work out
00:16:28
if he had an advantage.
00:16:30
He would bet a bigger portion of his funds
00:16:32
when the odds were in his favor
00:16:33
and less when they weren't.
00:16:35
He had invented card counting.
00:16:38
This is a remarkable innovation,
00:16:40
considering blackjack had been around
00:16:42
in various forms for hundreds of years,
00:16:45
and for a while this
made him a lot of money.
00:16:48
But the casinos got wise to his strategy
00:16:50
and they added more decks
of cards to the game
00:16:52
to reduce the benefit of card counting.
00:16:55
So Thorpe took his winnings to
00:16:57
what he called the
biggest casino on Earth:
00:17:00
the stock market.
00:17:03
He started a hedge fund that would go on
00:17:05
to make a 20% return every year
00:17:07
for 20 years,
00:17:08
the best performance
ever seen at that time.
00:17:11
And he did it by transferring
the skills he honed
00:17:13
at the blackjack table
to the stock market.
00:17:16
Thorpe pioneered a type of hedging,
00:17:18
a way to protect against
losses with balancing
00:17:20
or compensating transactions.
00:17:22
- Thorpe did it mathematically.
00:17:24
He looked at the odds
of winning and losing
00:17:27
and decided that under certain
conditions you can actually
00:17:30
tilt the odds in your favor
by using certain patterns
00:17:34
to be able to make bets.
00:17:36
- Suppose Bob sells Alice
a call option on a stock,
00:17:40
and let's say the stock has gone up,
00:17:41
so now it's in the money for Alice.
00:17:44
Well now for every additional
$1, the stock price goes up,
00:17:47
Bob will lose $1,
00:17:50
but he can eliminate this risk
by owning one unit of stock.
00:17:54
Then if the price goes up, he
would lose $1 from the option
00:17:58
but gain that dollar back from the stock.
00:18:00
And if the stock drops back
outta the money for Alice,
00:18:03
he sells the stock
00:18:04
so he doesn't risk losing
any money from that either.
00:18:07
This is called dynamic hedging.
00:18:09
It means Bob can make a profit
00:18:11
with minimal risk from
fluctuating stock prices.
00:18:14
A hedge portfolio pi at any one time
00:18:17
will offset the option V
00:18:19
with some amount of stock delta.
00:18:21
- It basically means I
can sell you something
00:18:25
without having to take the
opposite side of the trade.
00:18:28
And the way to think about it is
00:18:30
I have synthetically manufactured
00:18:33
an option for you.
00:18:36
I've created it out of nothing
00:18:37
by doing dynamic trading. Dynamic hedging.
00:18:42
- As we saw with Bob's
example delta,
00:18:44
the amount of stock he has to hold,
00:18:46
changes depending on current prices.
00:18:48
Mathematically, it represents
00:18:50
how much the current option price changes
00:18:52
with a change in the stock price.
00:18:54
But Thorpe wasn't satisfied
with Bachelier's model
00:18:57
for pricing options.
00:18:58
I mean, for one thing, stock
prices aren't entirely random.
00:19:01
They can increase over time
if the business is doing well
00:19:04
or fall if it isn't.
00:19:06
Bachelier's model ignored this.
00:19:08
So Thorpe came up with
a more accurate model
00:19:10
for pricing options, which
took this drift into account.
00:19:14
- I actually figured out
00:19:16
what this model was back in
00:19:19
the middle of 1967,
00:19:22
and I decided that I would
just use it for myself
00:19:26
and then later I kept it
quiet for my own investors.
00:19:30
The idea was to basically make a lot
00:19:32
of money out of it for everybody.
00:19:33
- His strategy was if the
option was going cheap,
00:19:36
according to his model, buy it.
00:19:38
If it was overvalued, short sell it,
00:19:40
that is bet against it.
00:19:41
And that way, more often than not,
00:19:43
he would end up on the
winning side of the trade.
00:19:47
This lasted until 1973.
00:19:50
In that year, Fischer Black
00:19:52
and Myron Scholes came up with an equation
00:19:54
that changed the industry.
00:19:56
Robert Merton independently
published his own version,
00:19:58
which was based on the mathematics
of stochastic calculus,
00:20:01
so he is also credited.
00:20:04
- I thought I'd have the field to myself,
00:20:06
but unfortunately, Fischer Black
00:20:08
and Myron Scholes published the idea
00:20:11
and they did a better job
of the model than I did
00:20:14
because they had very tight mathematics
00:20:16
behind their derivation
00:20:18
- Like Bachelier,
00:20:19
they thought that option
prices should offer a fair bet
00:20:21
to both buyers and sellers,
00:20:23
but their approach was totally new.
00:20:26
They said if it was possible
00:20:28
to construct a risk-free
portfolio of options
00:20:30
and stocks just like Thorpe was doing
00:20:32
with his delta hedging,
then in an efficient market,
00:20:35
a fair market, this portfolio
should return nothing more
00:20:38
than the risk-free rate,
00:20:40
what the same money would earn if invested
00:20:42
in the safest asset, US treasury bonds.
00:20:45
The assumption was that
if you're not taking on
00:20:47
any additional risk, then
it shouldn't be possible
00:20:49
to receive any extra returns.
00:20:53
To describe how stock
prices change over time,
00:20:55
Black, Scholes, and Merton
used an improved version
00:20:58
of Bachelier's model just like Thorpe.
00:21:00
This says that at any time
we expect the stock price
00:21:03
to move randomly,
00:21:04
plus a general trend
up or down, the drift.
00:21:09
By combining these two equations,
Black, Scholes, and Merton
00:21:12
came up with the most
famous equation in finance.
00:21:15
It relates the price of any
kind of contract to any asset,
00:21:19
stocks, bonds, you name it.
00:21:21
The same year they
published this equation,
00:21:23
the Chicago Board Options
Exchange was founded.
00:21:27
Why is that equation so important?
00:21:30
Like for finance, how
did that change the game?
00:21:32
- Well, because when you solve
00:21:34
that partial differential equation,
00:21:36
you get an explicit formula
of the price of the option
00:21:39
as a function of a bunch
of these input parameters.
00:21:42
And for the very first time,
00:21:44
you now have an explicit expression
00:21:46
where you plug in the parameters
00:21:48
and out pops this number
00:21:50
so that people can actually
use it to trade on.
00:21:53
- This led to one of the
fastest adoptions by industry
00:21:55
of an academic idea in all
of the social sciences.
00:21:59
- Within just a couple of years,
00:22:01
the Black Scholes formula was
adopted as the benchmark
00:22:05
for Wall Street for trading options.
00:22:07
The exchange traded
options market has exploded
00:22:11
and it's now a multi-trillion
dollar industry,
00:22:14
the volume in this
market has been doubling
00:22:17
roughly every five years.
00:22:19
So this is the financial
equivalent of Moore's Law.
00:22:21
There are other businesses
00:22:23
that have grown just as quickly,
00:22:26
like credit default swaps market,
00:22:28
the OTC derivatives market,
00:22:30
the securitized debt market.
00:22:32
All of these are multi-trillion
dollar industries
00:22:35
that in one form
00:22:36
or another make use of the idea
00:22:39
of Black Scholes Merton option pricing.
00:22:42
- This opened up a whole new
way to hedge against anything,
00:22:46
and not just for hedge funds.
00:22:48
Nowadays, pretty much every
large company, governments,
00:22:50
and even individual investors use options
00:22:53
to hedge against their own specific risks.
00:22:56
Suppose you're running an airline
00:22:58
and you're worried that an
increase in oil prices
00:23:00
would eat into your profits.
00:23:02
Well, using the Black
Scholes Merton equation,
00:23:04
there's a way to accurately
00:23:06
and efficiently hedge that risk.
00:23:08
You price an option to
buy something that tracks
00:23:10
the price of oil, and
that option will pay off
00:23:13
if oil prices go up,
00:23:15
and that will help compensate
you for the higher cost
00:23:17
of fuel you have to pay.
00:23:19
So Black Scholes Merton
can help reduce risk,
00:23:22
but it can also provide leverage.
00:23:24
- An ongoing battle
between bullish day traders
00:23:27
and hedge fund short sellers
00:23:29
that have bet against the stock,
00:23:31
GameStop shares, have now risen some 700%.
00:23:35
- Well, GameStop is a
really interesting example
00:23:38
for all sorts of reasons,
00:23:39
but options figured
prominently in that example
00:23:41
because a small cadre of users
00:23:44
on this Reddit sub-channel
r/wallstreetbets
00:23:47
decided that the hedge fund managers
00:23:49
that were shorting the stock
00:23:51
and betting that the company
would go out of business
00:23:53
needed to be punished.
00:23:55
And so they bought
shares of GameStop stock
00:23:59
to try to drive up price.
00:24:00
Turns out that buying
the stock was not enough,
00:24:03
because with a dollar's worth of cash,
00:24:06
you can buy a dollar's worth of stock,
00:24:08
but with a dollar's worth
of cash, you can buy options
00:24:11
that affected many more than
a dollar's worth of stock,
00:24:15
perhaps in some cases $10
00:24:17
or $20 worth of stock for a
dollar's worth of options.
00:24:20
And so there's natural leverage embedded
00:24:23
in these securities.
00:24:24
And so the combination
of buying both the stock
00:24:28
and the options caused the
prices to rise very quickly.
00:24:32
And what that did was to cause
these hedge fund managers
00:24:34
to lose a lot of money quickly.
00:24:37
- How big is this market for derivatives?
00:24:39
How big is this whole area that kind of
00:24:42
comes out of Black Scholes Merton?
00:24:45
- There are estimates of how
large derivatives markets are,
00:24:49
and first, let's be clear
what a derivative is.
00:24:51
A derivative is a financial
security whose value derived
00:24:55
from another financial security.
00:24:58
So an option is an
example of a derivative.
00:25:01
In general, the size of
derivative markets globally
00:25:04
is the on the order
00:25:06
of several hundred trillion dollars.
00:25:08
- How does that compare to the size
00:25:10
of the underlying
securities they're based on?
00:25:13
- It's multiples of the
underlying securities.
00:25:17
- I just have to interrupt
because it seems kind of crazy
00:25:20
that you have more money
riding on the things
00:25:23
that are based on the thing
than the thing itself.
00:25:26
- That's right.
00:25:28
- So tell me how that makes any sense.
00:25:30
- Because what options allow you to do is
00:25:33
to take the underlying thing
00:25:36
and turn it into 5, 10, 20, 50 things.
00:25:39
So these pieces of paper
00:25:41
that we call options and derivatives,
00:25:43
they basically allow us to create many,
00:25:45
many different versions of
the underlying asset,
00:25:49
versions that individuals
find more palatable
00:25:53
because of their own
risk reward preferences.
00:25:56
- Does this make the markets
00:25:59
and the global economy more stable,
00:26:02
or less stable, or no effect?
00:26:05
- All three. So it turns out
that during normal times,
00:26:11
these markets are a very
significant source of liquidity
00:26:15
and therefore stability.
00:26:16
During abnormal times,
00:26:19
by that I mean when there are
periods of market stress,
00:26:23
all of these securities
can go in one direction,
00:26:27
typically down,
00:26:28
and when they go down together,
00:26:30
that creates a really big market crash.
00:26:34
So in those circumstances,
00:26:36
derivatives markets can
exacerbate these kinds
00:26:40
of market dislocations.
00:26:43
- In 1997, Merton
00:26:44
and Scholes were awarded the
Nobel Prize in economics.
00:26:47
Black was acknowledged
for his contributions,
00:26:49
but unfortunately he had passed away
00:26:51
just two years earlier.
00:26:53
- We were gonna make a
lot of money in options,
00:26:54
but now Black and Shoals
have told everybody
00:26:56
what the secret is.
00:26:59
- With the option pricing formula now out
00:27:01
for everyone to see
00:27:02
hedge funds would need
to discover better ways
00:27:04
to find market inefficiencies.
00:27:07
Enter Jim Simons.
00:27:09
Before Simons had any
exposure to the stock market,
00:27:12
he was a mathematician.
00:27:14
His work on Riemann geometry
was instrumental in many areas
00:27:17
of mathematics and physics,
including knot theory,
00:27:19
quantum field theory, and
quantum computing
00:27:23
Chern Simon's theory laid the
mathematical foundation
00:27:25
for string theory.
00:27:27
In 1976,
00:27:28
the American Mathematical
Society presented him
00:27:30
with the Oswald Veblen Prize in geometry.
00:27:33
But at the top of his academic
career, Simons went looking
00:27:37
for a new challenge.
00:27:39
When he founded Renaissance
Technologies in 1978,
00:27:42
his strategy was to use machine learning
00:27:44
to find patterns in the stock market.
00:27:46
Patterns provide
opportunities to make money.
00:27:49
- The real thing was to gather
a tremendous amount of data
00:27:52
and we had to get it by
hand in the early days,
00:27:56
we went down to the Federal Reserve
00:27:57
and copied interest rate
histories and stuff like that
00:28:00
'cause it didn't exist on computers.
00:28:03
- His rationale was that the
market is far too complex
00:28:05
for anyone to be able to make
predictions with certainty.
00:28:08
But Simons had worked for
00:28:10
the US Institute for Defense Analysis
00:28:12
during the Cold War,
breaking Russian codes
00:28:14
by extracting patterns
from masses of data.
00:28:18
Simons was convinced
00:28:19
that a similar approach
could beat the market.
00:28:21
He then used his academic
contacts to hire a bunch
00:28:24
of the best scientists he could find.
00:28:26
- What was your employment criteria then?
00:28:28
If they knew nothing about finance,
00:28:30
what were you looking for in them?
00:28:31
Someone with a PhD in physics
and who'd had five years out
00:28:35
and had written a few good papers
00:28:36
and was obviously a
smart guy or in astronomy
00:28:40
or in mathematics or in statistics.
00:28:44
Someone who had done
science and done it well.
00:28:48
- It's not surprising that mathematicians
00:28:50
and physicists are involved in this field.
00:28:53
First of all, finance pays a
lot better than, you know,
00:28:56
being an assistant
professor of mathematics.
00:28:58
And for a number of
mathematicians, the beauty
00:29:02
of option pricing is equally
compelling to anything else
00:29:05
that they're doing in their professions.
00:29:07
- One of these was Leonard Baum, a pioneer
00:29:09
of Hidden Markov models.
00:29:11
Just as Einstein realized that
00:29:13
although we can't directly observe atoms,
00:29:15
we can infer their existence
00:29:16
through their effect on pollen grains,
00:29:18
Hidden Markov models aim to find factors
00:29:21
that are not directly observable,
00:29:23
but do have an effect
on what we can observe.
00:29:25
And soon after that,
00:29:26
Renaissance launched their now-famous
00:29:28
Medallion fund.
00:29:30
Using hidden Markov models
00:29:32
and other data driven strategies,
00:29:33
The Medallion fund became
the highest returning
00:29:36
investment fund of all time.
00:29:38
This led Bradford Cornell
of UCLA, in his paper
00:29:41
Medallion Fund: The
Ultimate Counterexample?
00:29:44
to conclude that maybe the
efficient market hypothesis
00:29:47
itself is wrong.
00:29:49
- In 1988, I published a paper testing it,
00:29:52
the US Stock Market,
00:29:53
and what I found was that
the hypothesis is false.
00:29:58
You can actually reject
the hypothesis in the data.
00:30:01
And so there are predictabilities
00:30:03
in the stock market.
00:30:05
- So it's possible to beat the
market is what you're saying.
00:30:10
- It's possible to beat the
market if you have
00:30:13
the right models, the right training,
00:30:16
the resources, the computational power,
00:30:19
and so on and so forth, yes.
00:30:22
- The people who have found the patterns
00:30:24
in the stock market,
00:30:25
and the randomness for that matter,
00:30:27
have often been physicists
and mathematicians,
00:30:30
but their impact has gone
beyond just making them rich.
00:30:34
By modeling market dynamics,
00:30:35
they've provided new insight into risk
00:30:38
and opened up whole new markets.
00:30:41
They've determined what the accurate price
00:30:43
of derivatives should be,
00:30:45
and in doing so,
00:30:46
they have helped eliminate
market inefficiencies.
00:30:49
Ironically, if we are ever able
00:30:51
to discover all the patterns
in the stock market,
00:30:54
knowing what they are will
allow us to eliminate them.
00:30:57
Then we will finally have
a perfectly efficient market
00:31:01
where all price movements
are truly random.
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