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00:00This single equation spawned four multi-trillion-dollar industries
00:04and transformed everyone's approach to risk.
00:08Do you think that most people are aware of the size, scale, utility of derivatives?
00:13No. No idea.
00:15But at its core, this equation comes from physics,
00:18from discovering atoms, understanding how heat is transferred,
00:22and how to beat the casino at blackjack.
00:25So maybe it shouldn't be surprising that some of the best to beat the stock market
00:29were not veteran traders, but physicists, scientists, and mathematicians.
00:34In 1988, a mathematics professor named Jim Simons set up the Medallion Investment Fund.
00:40And every year for the next 30 years,
00:42the Medallion Fund delivered higher returns than the market average.
00:45And not just by a little bit.
00:48It returned 66% per year.
00:51At that rate of growth, $100 invested in 1988
00:55would be worth $8.4 billion today.
01:00This made Jim Simons easily the richest mathematician of all time.
01:05But being good at math doesn't guarantee success in financial markets.
01:09Just ask Isaac Newton.
01:12In 1720, Newton was 77 years old, and he was rich.
01:16He had made a lot of money working as a professor at Cambridge for decades,
01:20and he had a side hustle as the master of the royal mint.
01:24His net worth was £30,000, the equivalent of $6 million today.
01:31Now to grow his fortune, Newton invested in stocks.
01:34One of his big bets was on the South Sea Company.
01:37Their business was shipping enslaved Africans across the Atlantic.
01:42Business was booming, and the share price grew rapidly.
01:45By April of 1720, the value of Newton's shares had doubled,
01:49so he sold his stock.
01:51But the stock price kept going up.
01:54And by June, Newton bought back in.
01:56And he kept buying shares even as the price peaked.
02:00When the price started to fall, Newton didn't sell.
02:04He bought more shares, thinking he was buying the dip.
02:07But there was no rebound,
02:09and ultimately he lost around a third of his wealth.
02:12When asked why he didn't see it coming,
02:15Newton responded,
02:16I can calculate the motions of the heavenly bodies,
02:19but not the madness of people.
02:22So what did Simons get right that Newton got wrong?
02:27Well, for one thing,
02:28Simons was able to stand on the shoulders of giants.
02:33The pioneer of using math to model financial markets
02:35was Louis Bachelier, born in 1870.
02:39Both of his parents died when he was 18,
02:41and he had to take over his father's wine business.
02:44He sold the business a few years later
02:46and moved to Paris to study physics.
02:48But he needed a job to support himself and his family.
02:51And he found one at the Bourse,
02:53the Paris Stock Exchange.
02:55And inside was Newton's madness of people
02:57in its rawest form.
02:59Hundreds of traders, screaming prices,
03:01making hand signals, and doing deals.
03:04The thing that captured Bachelier's interest
03:06were contracts known as options.
03:10The earliest known options were bought around 600 BC
03:13by the Greek philosopher Thales of Miletus.
03:17He believed that the coming summer
03:18would yield a bumper crop of olives.
03:21To make money off this idea,
03:22he could have purchased olive presses,
03:24which, if he were right, would be in great demand.
03:27But he didn't have enough money to buy the machines.
03:29So instead, he went to all the existing olive press owners
03:32and paid them a little bit of money
03:34to secure the option to rent their presses in the summer
03:37for a specified price.
03:39When the harvest came, Thales was right.
03:42There were so many olives
03:43that the price of renting a press skyrocketed.
03:47Thales paid the press owners their pre-agreed price,
03:49and then he rented out the machines at a higher rate
03:52and pocketed the difference.
03:54Thales had executed the first known call option.
03:58A call option gives you the right,
04:00but not the obligation to buy something at a later date
04:03for a set price, known as the strike price.
04:06You can also buy a put option,
04:08which gives you the right,
04:09but not the obligation to sell something
04:11at a later date for the strike price.
04:13Put options are useful if you expect the price to go down.
04:16Call options are useful if you expect the price to go up.
04:20For example, let's say the current price of Apple stock
04:22is $100, but you expect it to go up.
04:26You could buy a call option for $10
04:28that gives you the right, but not the obligation
04:30to buy Apple stock in one year for $100.
04:34That is the strike price.
04:36Just a little side note,
04:37American options can be exercised on any date
04:39up to the expiry,
04:41whereas European options must be exercised
04:43on the expiry date.
04:45To keep things simple,
04:46we'll stick to European options.
04:48So if in a year,
04:50the price of Apple stock has gone up to $130,
04:53you can use the option to buy shares for $100
04:55and then immediately sell them for $130.
04:59After you take into account the $10 you paid for the option,
05:02you've made a $20 profit.
05:04Alternatively,
05:05if in a year the stock price has dropped to $70,
05:08you just wouldn't use the option
05:10and you've lost the $10 you paid for it.
05:13So the profit and loss diagram looks like this.
05:16If the stock price ends up below the strike price,
05:18you lose what you paid for the option.
05:20But if the stock price is higher than the strike price,
05:23then you earn that difference
05:25minus the cost of the option.
05:28There are at least three advantages of options.
05:32One is that it limits your downside.
05:34If you had bought the stock instead of the option
05:36and it went down to $70,
05:37you would have lost $30
05:38and in theory,
05:40you could have lost $100 if the stock went to $0.
05:43The second benefit is options provide leverage.
05:46If you had bought the stock
05:47and it went up to $130,
05:49then your investment grew by 30%.
05:52But if you had bought the option,
05:53you only had to put up $10.
05:55So your profit of $20
05:56is actually a 200% return on investment.
06:01On the downside,
06:02if you had owned the stock,
06:03your investment would have only dropped by 30%.
06:05Whereas with the option,
06:07you lose all 100%.
06:09So with options trading,
06:11there's a chance to make much larger profits,
06:13but also much bigger losses.
06:15The third benefit is you can use options as a hedge.
06:20I think the original motivation for options
06:22was to figure out a way to reduce risk.
06:24And then of course,
06:25once people decided they wanted to buy insurance,
06:28that meant that there are other people out there
06:30that wanted to sell it for a profit.
06:33And that's how markets get created.
06:36So options can be an incredibly useful investing tool.
06:39But what Bichellier saw on the trading floor was chaos,
06:44especially when it came to the price of stock options.
06:47Even though they had been around for hundreds of years,
06:50no one had found a good way to price them.
06:52Traders would just bargain to come to an agreement
06:54about what the price should be.
06:56Given the option to buy or sell something in the future,
07:00it seems like a very amorphous kind of a trade.
07:03And so coming up with prices for these rather strange objects
07:08has been a challenge that's plagued a number of economists
07:12and business people for centuries.
07:15Now, Bichellier, already interested in probability,
07:18thought there had to be a mathematical solution to this problem.
07:22And he proposed this as his PhD topic to his advisor, Henri Poincaré.
07:26Looking into the math of finance
07:28wasn't really something people did back then.
07:30But to Bichellier's surprise, Poincaré agreed.
07:34To accurately price an option,
07:37first you need to know what happens to stock prices over time.
07:41The price of a stock is basically set by a tug of war
07:43between buyers and sellers.
07:45When more people want to buy a stock, the price goes up.
07:48When more people want to sell a stock, the price goes down.
07:51But the number of buyers and sellers
07:53can be influenced by almost anything,
07:55like the weather, politics, new competitors,
07:58innovation, and so on.
08:00So Bichellier realized that it's virtually impossible
08:03to predict all these factors accurately.
08:06So the best you can do is assume that at any point in time,
08:09the stock price is just as likely to go up as down.
08:12And therefore, over the long term,
08:14stock prices follow a random walk,
08:17moving up and down as if their next move
08:19is determined by the flip of a coin.
08:21Randomness is a hallmark of an efficient market.
08:26By efficient, economists typically mean that
08:29you can't make money by trading.
08:33The idea that you shouldn't be able to buy an asset
08:36and sell it immediately for a profit
08:37is known as the efficient market hypothesis.
08:40The more people try to make money by predicting the stock market
08:44and then trading on those predictions,
08:46the less predictable those prices are.
08:49If you and I could predict the stock market tomorrow,
08:52then we would do it.
08:54We would start trading today on stocks that we thought
08:56were going to go up tomorrow.
08:57Well, if we did that, then instead of going up tomorrow,
09:02they would go up now as we bought more and more of the stock.
09:05So the very act of predicting
09:07actually affects the quality of the future outcomes.
09:12And so in a totally efficient market,
09:15the prices tomorrow can't possibly have any predictive power.
09:20If they did, we would have taken advantage of it today.
09:24This is a Galton board.
09:25It's got rows of pegs arranged in a triangle
09:28and around 6,000 tiny ball bearings
09:31that I can pour through the pegs.
09:33Now, each time a ball hits a peg,
09:35there's a 50-50 chance it goes to the left or the right.
09:38So each ball follows a random walk
09:40as it passes through these pegs,
09:42which makes it basically impossible
09:44to predict the path of any individual ball.
09:47But if I flip this over,
09:49what you can see is that all the balls together
09:51always create a predictable pattern.
09:54That is, a collection of random walks
09:57creates a normal distribution.
09:59It's centered around the middle
10:01because the number of paths a ball could take
10:03to get here is the greatest.
10:04And the further out you go,
10:06the fewer the paths a ball could take to get there.
10:08Like if you want to end up here,
10:10well, the ball would have to go left, left, left, left,
10:12all the way down.
10:13So there's only one way to get here,
10:15but to get into the middle,
10:17there are thousands of paths that a ball could take.
10:19Now, Bachelier believed a stock price
10:22is just like a ball going through a Galton board.
10:26Each additional layer of pegs represents a time step.
10:30So after a short time,
10:31the stock price could only move up or down a little,
10:33but after more time,
10:34a wider range of prices is possible.
10:37According to Bachelier,
10:38the expected future price of a stock
10:40is described by a normal distribution,
10:43centered on the current price,
10:45which spreads out over time.
10:47Bachelier realized he had rediscovered
10:50the exact equation
10:51which describes how heat radiates
10:54from regions of high temperature
10:55to regions of low temperature.
10:58This was first discovered by Joseph Fourier
11:00back in 1822.
11:02So Bachelier called his discovery
11:04the radiation of probabilities.
11:08Since he was writing about finance,
11:09the physics community didn't take any notice.
11:12But the mathematics of the random walk
11:14would go on to solve an almost century-old mystery
11:16in physics.
11:20In 1827, Scottish botanist Robert Brown
11:22was looking at pollen grains under the microscope,
11:25and he noticed that the particles
11:26suspended in water on the microscope slide
11:28were moving around randomly.
11:31Because he didn't know whether it was something to do
11:33with the pollen being living material,
11:35he tested non-organic particles,
11:37such as dust from lava and meteorite rock.
11:41Again, he saw them moving around in the same way.
11:44So Brown discovered that any particles,
11:47if they were small enough,
11:48exhibited this random movement,
11:50which came to be known as Brownian motion.
11:54But what caused it remained a mystery.
11:5880 years later, in 1905,
12:00Einstein figured out the answer.
12:02Over the previous couple hundred years,
12:06the idea that gases and liquids were made up of molecules
12:09became more and more popular.
12:11But not everyone was convinced
12:12that molecules were real in a physical sense,
12:15just that the theory explained a lot of observations.
12:18The idea led Einstein to hypothesize
12:21that Brownian motion is caused
12:23by the trillions of molecules
12:24hitting the particle from every direction,
12:27every instant.
12:28Occasionally, more will hit from one side than the other,
12:31and the particle will momentarily jump.
12:33To derive the mathematics,
12:35Einstein supposed that, as an observer,
12:37we can't see or predict these collisions
12:39with any certainty.
12:40So at any time, we have to assume
12:42that the particle is just as likely to move
12:44in one direction as another.
12:47So just like stock prices,
12:49microscopic particles move like a ball
12:51falling down a galten board.
12:53The expected location of a particle
12:54is described by a normal distribution
12:57which broadens with time.
12:59It's why even in completely still water,
13:01microscopic particles spread out.
13:04This is diffusion.
13:07By solving the Brownian motion mystery,
13:09Einstein had found definitive evidence
13:11that atoms and molecules exist.
13:13Of course, he had no idea
13:15that Bachelier had uncovered
13:16the random walk five years earlier.
13:19By the time Bachelier finished his PhD,
13:21he had finally figured out
13:23a mathematical way to price an option.
13:26Remember that with a call option,
13:28if the future price of a stock
13:29is less than the strike price,
13:30then you lose the premium paid for the option.
13:33But if the stock price is greater
13:35than the strike price,
13:36you pocket that difference,
13:37and you make a net profit
13:38if the stock has gone up by more
13:40than you paid for the option.
13:42So the probability that an option buyer
13:44makes a profit is the probability
13:45that the price increases by more
13:47than the price paid for it,
13:49which is the green shaded area.
13:50And the probability that the seller makes money
13:53is just the probability
13:54that the price stays low enough
13:55that the buyer doesn't earn more
13:57than they paid for it.
13:58This is the red shaded area.
14:01Multiplying the profit or loss
14:02by the probability of each outcome,
14:04Bachelier calculated the expected return
14:07of an option.
14:09Now, how much should it cost?
14:11If the price of an option is too high,
14:13no one will want to buy it.
14:14Conversely, if the price is too low,
14:16everyone will want to buy it.
14:19Bachelier argued that the fair price
14:20is what makes the expected return
14:22for buyers and sellers equal.
14:24Both parties should stand to gain
14:26or lose the same amount.
14:28That was Bachelier's insight
14:29into how to accurately price an option.
14:33When Bachelier finished his thesis,
14:35he had beaten Einstein
14:36to inventing the random walk
14:37and solved a problem
14:38that had eluded options traders
14:40for hundreds of years.
14:42But no one noticed.
14:43The physicists were uninterested
14:44and traders weren't ready.
14:46The key thing missing
14:47was a way to make a ton of money.
14:52Hey, so I'm not sure
14:53how stock traders sleep at night
14:54with billions of dollars
14:55riding on the madness of people,
14:57but I have been sleeping just fine
14:59thanks to the sponsor of this video,
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16:01of the video.
16:01In the 1950s,
16:04a young physics graduate,
16:06Ed Thorpe,
16:06was doing his PhD in Los Angeles.
16:08But a few hours drive away,
16:10Las Vegas was quickly becoming
16:11the gambling capital of the world
16:13and Thorpe saw a way
16:15to make a fortune.
16:16He headed to Vegas
16:17and sat down
16:18at the blackjack table.
16:19Back then,
16:19the dealer only used
16:20a single deck of cards
16:21so Thorpe could keep
16:23a mental note
16:23of all the cards
16:24that had been played
16:25as he saw them.
16:27This allowed him to work out
16:28if he had an advantage.
16:29He would bet a bigger portion
16:31of his funds
16:32when the odds were in his favor
16:33and less when they weren't.
16:35He had invented card counting.
16:38This is a remarkable innovation
16:40considering blackjack
16:41had been around
16:42in various forms
16:43for hundreds of years.
16:45And for a while,
16:46this made him a lot of money.
16:48But the casinos got wise
16:49to his strategy
16:50and they added more decks
16:52of cards to the game
16:52to reduce the benefit
16:54of card counting.
16:55So Thorpe took his winnings
16:57to what he called
16:57the biggest casino on earth,
17:00the stock market.
17:03He started a hedge fund
17:04that would go on
17:05to make a 20% return
17:06every year for 20 years,
17:08the best performance
17:09ever seen at that time.
17:11And he did it
17:12by transferring the skills
17:13he honed at the blackjack table
17:14to the stock market.
17:16Thorpe pioneered
17:17a type of hedging,
17:18a way to protect against losses
17:19with balancing
17:20or compensating transactions.
17:22Thorpe did it mathematically.
17:24He looked at the odds
17:25of winning and losing
17:26and decided that
17:28under certain conditions,
17:29you can actually
17:30tilt the odds
17:31in your favor
17:31by using certain patterns
17:33to be able to make bets.
17:36Suppose Bob sells Alice
17:38a call option on a stock.
17:40And let's say
17:40the stock has gone up,
17:41so now it's
17:42in the money for Alice.
17:44Well now,
17:44for every additional $1
17:46the stock price goes up,
17:47Bob will lose $1.
17:50But he can eliminate this risk
17:52by owning one unit of stock.
17:54Then, if the price goes up,
17:56he would lose $1 from the option
17:58but gain that dollar back
17:59from the stock.
18:00And if the stock drops back
18:01out of the money for Alice,
18:03he sells the stock
18:04so he doesn't risk
18:05losing any money
18:06from that either.
18:07This is called
18:08dynamic hedging.
18:09It means Bob can make a profit
18:11with minimal risk
18:12from fluctuating stock prices.
18:14A hedged portfolio pie
18:16at any one time
18:17will offset the option V
18:19with some amount of stock delta.
18:21It basically means
18:22I can sell you something
18:24without having to take
18:26the opposite side of the trade.
18:28And the way to think about it is
18:30I have synthetically manufactured
18:32an option for you.
18:35I've created it out of nothing
18:37by doing dynamic trading,
18:40dynamic hedging.
18:42As we saw with Bob's example,
18:44delta,
18:44the amount of stock
18:45he has to hold,
18:46changes depending
18:47on current prices.
18:48Mathematically,
18:49it represents how much
18:50the current option price
18:51changes with a change
18:53in the stock price.
18:54But Thorpe wasn't satisfied
18:56with Bichellier's model
18:57for pricing options.
18:58I mean, for one thing,
18:59stock prices
19:00aren't entirely random.
19:01They can increase over time
19:03if the business is doing well
19:04or fall if it isn't.
19:06Bichellier's model
19:07ignored this.
19:08So Thorpe came up
19:09with a more accurate model
19:10for pricing options,
19:11which took this drift
19:13into account.
19:13I actually figured out
19:17what this model was
19:18back in the middle of 1967.
19:22And I decided that I would
19:24just use it for myself.
19:26And then later,
19:28I kept it quiet
19:29for my own investors.
19:30The idea was to basically
19:31make a lot of money
19:32out of it for everybody.
19:33His strategy was,
19:35if the option was going cheap,
19:36according to his model,
19:37buy it.
19:38If it was overvalued,
19:39short sell it.
19:40That is, bet against it.
19:42And that way,
19:42more often than not,
19:43he would end up
19:44on the winning side
19:45of the trade.
19:47This lasted until 1973.
19:50In that year,
19:51Fisher Black and Myron Scholes
19:53came up with an equation
19:54that changed the industry.
19:56Robert Merton
19:56independently published
19:58his own version,
19:59which was based on the mathematics
20:00of stochastic calculus.
20:01So he is also credited.
20:03I thought I'd have
20:04the field to myself.
20:06But unfortunately,
20:07Fisher Black and Myron Scholes
20:09published the idea.
20:11And they did a better job
20:13of the model than I did
20:14because they had
20:15very tight mathematics
20:16behind their derivation.
20:18Like Bichellier,
20:19they thought that option prices
20:20should offer a fair bet
20:22to both buyers and sellers.
20:23But their approach
20:24was totally new.
20:26They said,
20:27if it was possible
20:28to construct a risk-free
20:29portfolio of options
20:30in stocks,
20:31just like Thorpe was doing
20:32with his Delta hedging,
20:33then in an efficient market,
20:35a fair market,
20:36this portfolio should return
20:38nothing more
20:38than the risk-free rate,
20:40what the same money
20:41would earn if invested
20:42in the safest asset,
20:43U.S. Treasury bonds.
20:45The assumption was
20:46that if you're not
20:46taking on any additional risk,
20:48then it shouldn't be possible
20:49to receive any extra returns.
20:52To describe how stock prices
20:54change over time,
20:55Black, Scholes, and Merton
20:56used an improved version
20:58of Bichellier's model,
20:59just like Thorpe.
21:01This says that at any time,
21:02we expect the stock price
21:03to move randomly,
21:04plus a general trend
21:06up or down,
21:07the drift.
21:08By combining these two equations,
21:11Black, Scholes, and Merton
21:12came up with the most
21:12famous equation in finance.
21:15It relates the price
21:17of any kind of contract
21:18to any asset,
21:19stocks, bonds, you name it.
21:21The same year
21:22they published this equation,
21:23the Chicago Board
21:24Options Exchange
21:25was founded.
21:26Why is that equation
21:28so important?
21:30Like for finance,
21:30how did that change the game?
21:32Well, because when you solve
21:34that partial differential equation,
21:35you get an explicit formula
21:37for the price of the option
21:39as a function of a bunch
21:40of these input parameters.
21:42And for the very first time,
21:44you now have an explicit expression
21:46where you plug in the parameters
21:47and out pops this number
21:50so that people can actually use it
21:51to trade on.
21:52This led to one of the fastest
21:54adoptions by industry
21:55of an academic idea
21:56in all of the social sciences.
21:59Within just a couple of years,
22:01the Black-Scholes formula
22:02was adopted as the benchmark
22:05for Wall Street
22:06for trading options.
22:08The exchange-traded options market
22:10has exploded
22:11and it's now
22:12a multi-trillion dollar industry.
22:14The volume in this market
22:16has been doubling
22:17roughly every five years.
22:19So this is the financial equivalent
22:20of Moore's Law.
22:22There are other businesses
22:23that have grown just as quickly
22:25like credit default swaps market,
22:28the OTC derivatives market,
22:30the securitized debt market.
22:32All of these
22:33are multi-trillion dollar industries
22:35that in one form or another
22:37make use of the idea
22:38of Black-Scholes-Merton option pricing.
22:41This opened up a whole new way
22:44to hedge against anything
22:45and not just for hedge funds.
22:48Nowadays,
22:48pretty much every large company,
22:50governments,
22:51and even individual investors
22:52use options to hedge
22:54against their own specific risks.
22:56Suppose you're running an airline
22:58and you're worried
22:59that an increase in oil prices
23:00would eat into your profits.
23:02Well, using the Black-Scholes-Merton equation,
23:05there's a way to accurately
23:06and efficiently hedge that risk.
23:08You price an option
23:09to buy something
23:09that tracks the price of oil
23:11and that option will pay off
23:13if oil prices go up
23:14and that will help compensate you
23:16for the higher cost of fuel
23:17you have to pay.
23:19So Black-Scholes-Merton
23:20can help reduce risk,
23:21but it can also provide leverage.
23:23An ongoing battle
23:25between bullish day traders
23:27and hedge fund short sellers
23:29that have bet against the stock,
23:31GameStock shares,
23:32have now risen some 700%.
23:35Well, GameStop is a really interesting example
23:38for all sorts of reasons,
23:39but options figured prominently
23:40in that example
23:41because a small cadre of users
23:44on this Reddit sub-channel,
23:46WallStreetBets,
23:47decided that the hedge fund managers
23:49that were shorting the stock
23:51and betting that the company
23:52would go out of business
23:53needed to be punished.
23:55And so they bought shares
23:57of GameStop stock
23:59to try to drive up price.
24:00Turns out that buying the stock
24:02was not enough
24:03because with a dollar's worth of cash,
24:06you can buy a dollar's worth of stock.
24:08But with a dollar's worth of cash,
24:10you can buy options
24:11that affected many more
24:13than a dollar's worth of stock.
24:15Perhaps in some cases,
24:1610 or $20 worth of stock
24:18for a dollar's worth of options.
24:20And so there's natural leverage
24:22embedded in these securities.
24:25And so the combination
24:26of buying both the stock
24:28and the options
24:29caused the prices
24:30to rise very quickly.
24:32And what that did
24:33was to cause these hedge fund managers
24:34to lose a lot of money quickly.
24:37How big is this market for derivatives?
24:39How big is this whole area
24:41that kind of comes out
24:43of Black-Scholes-Merton?
24:44There are estimates
24:46of how large derivatives markets are.
24:49And first, let's be clear
24:50what a derivative is.
24:51A derivative is a financial security
24:53whose value derives
24:55from another financial security.
24:58So an option
24:59is an example of a derivative.
25:01In general,
25:02the size of derivative markets globally
25:04is on the order
25:06of several hundred trillion dollars.
25:08How does that compare
25:10to the size
25:10of the underlying securities
25:12they're based on?
25:12It's multiples
25:14of the underlying securities.
25:17I just have to interrupt
25:18because it seems kind of crazy
25:20that you have more money
25:22riding on the things
25:23that are based on the thing
25:24than the thing itself.
25:26That's right.
25:28So tell me how that makes any sense.
25:30Because what options allow you to do
25:33is to take the underlying thing
25:35and turn it into 5, 10, 20, 50 things.
25:39So these pieces of paper
25:41that we call options and derivatives,
25:43they basically allow us
25:44to create many, many different versions
25:46of the underlying asset.
25:49Versions that individuals find
25:51more palatable
25:52because of their own
25:54risk-reward preferences.
25:57Does this make the markets
25:59and the global economy
26:00more stable
26:01or less stable
26:03or no effect?
26:05All three.
26:06So it turns out
26:08that during normal times,
26:10these markets
26:12are a very significant source
26:14of liquidity
26:14and therefore stability.
26:16During abnormal times,
26:19by that I mean
26:20when there are periods
26:21of market stress,
26:23all of these securities
26:24can go in one direction,
26:27typically down.
26:28And when they go down together,
26:30that creates
26:31a really big market crash.
26:33So in those circumstances,
26:36derivatives markets
26:37can exacerbate
26:38these kinds
26:40of market dislocations.
26:42In 1997,
26:44Merton and Scholz
26:45were awarded
26:45the Nobel Prize in Economics.
26:47Black was acknowledged
26:48for his contributions,
26:49but unfortunately,
26:50he had passed away
26:51just two years earlier.
26:52We're going to make
26:53a lot of money in options,
26:54but now Black and Scholz
26:56have told everybody
26:56what the secret is.
26:58With the option pricing formula
27:00now out for everyone to see,
27:02hedge funds would need
27:03to discover better ways
27:04to find market inefficiencies.
27:07Enter Jim Simons.
27:09Before Simons had any exposure
27:11to the stock market,
27:12he was a mathematician.
27:14His work on Riemann geometry
27:15was instrumental
27:16in many areas
27:17of mathematics and physics,
27:18including knot theory,
27:20quantum field theory,
27:21and quantum computing.
27:23Chern-Simons theory
27:24laid the mathematical foundation
27:25for string theory.
27:27In 1976,
27:28the American Mathematical Society
27:29presented him with
27:30the Oswald Veblen Prize
27:32in Geometry.
27:33But at the top
27:34of his academic career,
27:36Simons went looking
27:37for a new challenge.
27:39When he founded
27:39Renaissance Technologies
27:40in 1978,
27:42his strategy was to use
27:43machine learning
27:44to find patterns
27:45in the stock market.
27:46Patterns provide opportunities
27:47to make money.
27:48The real thing
27:50was to gather
27:51a tremendous amount
27:52of data,
27:53and we had to get it
27:54by hand in the early days.
27:56We went down
27:56to the Federal Reserve
27:57and copied interest rate histories
27:59and stuff like that
28:00because it didn't exist
28:01on computers.
28:03His rationale was
28:04that the market
28:04is far too complex
28:05for anyone to be able
28:06to make predictions
28:07with certainty.
28:08But Simons had worked
28:10for the U.S. Institute
28:11for Defense Analysis
28:12during the Cold War,
28:13breaking Russian codes
28:14by extracting patterns
28:16from masses of data.
28:17Simons was convinced
28:19that a similar approach
28:20could beat the market.
28:21He then used
28:22his academic contacts
28:23to hire a bunch
28:24of the best scientists
28:25he could find.
28:26What was your
28:27employment criteria then?
28:28If they knew nothing
28:29about finance,
28:30what were you looking for?
28:31Someone with a PhD
28:32in physics
28:32and who'd had
28:33five years out
28:35and had written
28:36a few good papers
28:36and was obviously
28:37a smart guy.
28:38Or in astronomy,
28:40or in mathematics,
28:42or in statistics.
28:44Someone who had
28:45done science
28:46and done it well.
28:48It's not surprising
28:49that mathematicians
28:50and physicists
28:51are involved
28:52in this field.
28:53First of all,
28:54finance pays a lot better
28:55than being an assistant
28:56professor of mathematics.
28:58And for a number
28:59of mathematicians,
29:00the beauty
29:01of option pricing
29:03is equally compelling
29:04to anything else
29:05that they're doing
29:06in their professions.
29:07One of these
29:08was Leonard Baum,
29:09a pioneer
29:09of hidden Markov models.
29:12Just as Einstein realized
29:13that although we can't
29:14directly observe atoms,
29:15we can infer their existence
29:16through their effect
29:17on pollen grains,
29:19hidden Markov models
29:20aim to find factors
29:21that are not
29:21directly observable
29:22but do have an effect
29:24on what we can observe.
29:26And soon after that,
29:27Renaissance launched
29:27their now famous
29:28Medallion Fund.
29:30Using hidden Markov models
29:32and other data-driven strategies,
29:34the Medallion Fund
29:34became the highest
29:35returning investment fund
29:36of all time.
29:38This led Bradford Cornell
29:40of UCLA
29:40in his paper
29:41Medallion Fund,
29:42the ultimate counter-example,
29:44to conclude
29:45that maybe
29:45the efficient market hypothesis
29:47itself is wrong.
29:49In 1988,
29:50I published a paper
29:51testing it
29:52for the U.S. stock market
29:53and what I found
29:54was that
29:55the hypothesis is false.
29:58You can actually reject
29:59the hypothesis
30:00in the data
30:01and so there are
30:02predictabilities
30:03in the stock market.
30:05So,
30:06it's possible
30:08to beat the market
30:08is what you're saying.
30:10It's possible
30:11to beat the market
30:11if you have
30:13the right models,
30:14the right training,
30:16the resources,
30:18the computational power,
30:19and so on and so forth.
30:20Yes.
30:22The people
30:23who have found
30:23the patterns
30:24in the stock market,
30:25and the randomness
30:26for that matter,
30:27have often been
30:28physicists
30:29and mathematicians.
30:30But their impact
30:31has gone beyond
30:32just making them rich.
30:34By modeling
30:34market dynamics,
30:36they've provided
30:36new insight
30:37into risk
30:38and opened up
30:39whole new markets.
30:41They've determined
30:41what the accurate price
30:43of derivatives
30:43should be.
30:45And in doing so,
30:46they have helped
30:47eliminate market inefficiencies.
30:49Ironically,
30:50if we are ever able
30:51to discover all the patterns
30:53in the stock market,
30:54knowing what they are
30:55will allow us
30:56to eliminate them.
30:57And then,
30:58we will finally have
30:59a perfectly efficient market
31:00where all price movements
31:02are truly random.
31:07treasure
31:08to be watched
31:09in the stock market,
31:10where we don't
31:10To do the perfect
31:11thing.
31:11Again,
31:12guys,
31:13we can keep
31:14take that
31:14because it's
31:15sometimes
31:16useful.
31:16It's
31:18to have the
31:18token
31:19it has been
31:20a better
31:21and thenba
31:22in the store.
31:22And for
31:24them
31:26as
31:27a
31:283000
31:29hundred
31:30fifty
31:30hundred
31:30thousand
31:31twelve
31:33hundred
31:35totally
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