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Mathematical Finance: Securities and Models - Lecture 1 - Alexander Sokol - CompatibL — Transcript

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0:00my name is alexander sokol
0:01and this is the first lecture
0:03of the course
0:05introduction to mathematical finance
0:07there will be four lectures sold at the
0:09same time of day uh tuesday and thursday
0:12of this week and tuesday and thursday of
0:14next week all starting at the same time
0:17so today
0:18we'll talk about securities
0:20and uh before i get started uh just a
0:23few things on uh
0:25you know how we run the lecture so the
0:27lecture is scheduled for one hour and a
0:28half the slides and the presentation
0:31will be in english
0:33uh this will be a lecture on uh
0:37the first of the four lectures uh on
0:39mathematical finance
0:41which is uh focused on financial
0:44products in the aspect of finance
0:47that
0:49applies to trade between corporations
0:51right so banks
0:52corporations
0:54we will not be talking about crypto
0:55today we may in the future so if you're
0:58here to learn about crypto that's not in
1:00this lecture
1:01also uh even though some of the things
1:03that we'll talk about uh
1:05are also applicable to what's called
1:07retail investing namely individuals
1:09investing in things like stocks
1:11bonds you know other financial
1:13instruments
1:14most of the lecture is specifically
1:16about uh
1:18corporate financial products right so
1:20sell side aspects uh you know in this
1:22case means bank so banks sell financial
1:24products to corporations
1:26so uh this is something that uh will
1:29help you
1:30learn about mathematical finance uh it
1:33will we hope
1:34help you determine if uh
1:36uh mathematical finance is something
1:39that you'd like to make part of your
1:40career
1:41however if your objective is to learn
1:44how to invest in stocks as an individual
1:46again so you may learn a little bit and
1:48like with crypto there will be a little
1:50bit in this lecture that perhaps will be
1:51helpful
1:52but that's not what this lectures are
1:54about again so so we may have uh
1:56lectures like that in the future
1:58but that's not this course
2:00uh and uh just before i get started uh i
2:03want to mention for those of you who are
2:05uh software engineers um
2:08we also will have a course on uh
2:12enterprise uh software development in
2:14python which will start after the end of
2:16that course uh and uh if you learn about
2:18this course somewhere on forums you know
2:21there will be information about that of
2:22course as well so i'd like to invite
2:24everyone who is a software developer and
2:26here today also to attend that of course
2:28because mathematical finance is
2:30primarily software development happens
2:32in python
2:33based on the type of python that you
2:35learn
2:36normally in a you know university course
2:38right there's no jupyter notebooks it's
2:40not uh you know single scripts right so
2:42you have to write
2:43enterprise quality and enterprise scale
2:45code and python uh to do what i'll be
2:48talking about today and there will be a
2:49separate course focused on specifically
2:51on software and development for that
2:53all right so now to the lecture uh
2:56please ask all of the questions in chat
2:58uh my colleagues uh here anastasia and
3:00uh and others will help me so they may
3:04answer some questions and shout out to
3:06directly or they may alert me to
3:08questions that require my answer
3:11everyone please mute
3:12unless um specifically pull on someone
3:15to ask the question with ways just
3:16because we have a very large number of
3:19people logged in today
3:20and now let's get started
3:22first of all um
3:24before getting into details of financial
3:26specific financial instruments we'll
3:28learn about the reason why financial
3:29markets exist and their fundamental
3:31structure right so what are financial
3:33markets
3:34so arizona of financial markets is to
3:38provide companies with financing they
3:39need to run their business by matching
3:41them with investors
3:43so outside financial markets capital can
3:45be obtained by uh you know finding
3:47lenders who give you a loan
3:49right so if you're starting a business
3:50you may ask for a loan to finance your
3:53business
3:54or by finding investors who would put
3:55working capital into the company in
3:57exchange for the ownership all right so
3:59in order you can ask for a loan
4:02or you can give part of your business to
4:04share of your business to someone who
4:05will provide capital
4:07so money raised by money raised by
4:09borrowing
4:10by taking loan is called debt
4:12in money raised by selling fractional
4:14ownership is called equity
4:17so financial markets
4:19make raising both debt and equity
4:20financing
4:22easier and less expensive
4:23by standardizing repackaging and
4:25regulating
4:27for the investors
4:28in financial markets also help the
4:30investors manage the risk of the
4:32investments
4:33and reduce the losses in case the
4:34investment doesn't work out right so you
4:36go to you know a market to buy produce
4:38and you know a lot of vendors selling uh
4:41you know peaches right so that's what
4:43financial markets are right you don't
4:45have to look for investors don't have to
4:47look individually for companies by
4:48calling companies in the area and asking
4:51them if they need money
4:54companies don't have to call investors
4:57and ask if they have money
4:59financial markets is where this trade
5:01occurs just like with any type of market
5:04right so over the years financial
5:06markets became extraordinarily
5:07successful in fulfilling the mission and
5:10uh investing you know that used to be
5:12for the selected few people with a lot
5:14of money uh large companies it
5:16represented significant risk before
5:18right and the need to convince investors
5:21to take a major risk made it difficult
5:23and expensive for companies to raise
5:25financing
5:26with the development of financial
5:28markets it became possible for everyone
5:30to invest
5:31and the risk taken by each individual
5:32investor became better understood
5:35and controlled right so the first part
5:38uh is uh that you know if you don't know
5:40the company
5:41uh the company doesn't know the investor
5:44the investor doesn't know the company
5:45there's a lot of risk involved right so
5:47could some people uh could commit fraud
5:50uh some people just have no experience
5:52so financial markets make it
5:55safer
5:56because there are things called
5:57regulations right so the regulations a
5:59set of rules in order to participate in
6:01financial markets you have to meet this
6:02rules for example you need to do
6:04accounting you need to pay taxes right
6:06so financial markets ensure that this
6:08happens
6:09and make it safer for the investors
6:11compared to just
6:12calling someone and agreeing to give
6:14money
6:15also with financial markets it's it
6:18became possible to
6:20invest in smaller scale right so before
6:23uh you know basically you know couple
6:24hundred years ago uh you have to really
6:27you know look for a few investors this
6:30investor would have to put a lot of
6:31money
6:32so if you don't have a huge amount of
6:34money it was impossible to invest
6:36with financial markets you can own a
6:39tiny share of tesla you can own a tiny
6:42share of boeing
6:43so in other words you don't need a lot
6:44of money to
6:46invest right so you can own also a
6:48little piece of a loan made to tesla or
6:50buying
6:51so that made it more democratic and more
6:54people can now participate so the
6:56technology that makes this possible
6:58which is generally good for the humanity
7:00is called financial engineering and the
7:02science that guides it is mathematical
7:03finance
7:05so uh the reason you know it exists is
7:08because it makes it easier
7:10for people to start companies
7:12it makes it easier for people to invest
7:14in companies
7:16all right so financial engineering
7:18fulfills its goals by creating financial
7:20instruments
7:21and a financial instrument is a legal
7:23contract that makes it possible for
7:26financial market participants to jointly
7:28participate in providing financing to
7:30companies
7:31while precisely controlling their
7:32economic objectives and risk
7:35right so some fi some financial
7:36engineering products invented long ago
7:38are still popular today
7:40for example uh you know the the
7:43uh you know the futures right is uh you
7:46know it was not created yesterday it was
7:48not even created in the 21st century of
7:50course right so the question when was it
7:52created right
7:54so let's have a little poll uh so
7:56um uh you know what do you think we're
7:59not going to use the zoom um uh pole
8:01fisher today but uh but i'll just ask
8:04everybody to uh raise a hand basically
8:07there's a in zoom there is a feature
8:08that you can indicate a reaction
8:10right so let's have a little poll uh of
8:14uh when was the first futures exchange
8:16established
8:17right so everybody who thinks it was and
8:20let's start from the end right everybody
8:21who thinks is one in 1969
8:24please raise your hand okay so so let me
8:27just share like a bigger screen for the
8:29chat and see what uh
8:31what we get
8:32second
8:34all right anybody raising hands okay
8:37right we have four
8:38reactions okay anybody
8:41i promise this will not get into if
8:43you're a student this will not get into
8:44your academic records i promise
8:48okay more reactions
8:50okay four actions okay what about 1886
8:53right so this is already the 19th
8:55century
8:58okay more reactions eight reactions at
9:00the moment
9:02okay
9:03okay
9:041769.
9:08okay so whoever voted for 1886 uh you
9:10know that turned off right so you can
9:12see 1769 who thinks is 1769
9:1713 people
9:19okay
9:20and final 1697
9:23that's 15th century by then
9:25all right
9:29no wait it's uh 17th 17th 17th sorry
9:32count to three 17th century
9:35well so basically the winner was
9:381769 at the moment we have just
9:42eight people who voted for 1697.
9:46all right so well let's take a look now
9:48um
9:49oh sorry one second just get rid of the
9:52can you still see can you see the screen
9:53now
9:54yeah we see the answer
9:56okay so in 1697 dojima rice exchange in
10:00osaka was established so that feudal
10:02lords could pay the samurai
10:04everybody knows who samurai are right
10:07by promising rice from future harvest
10:09because if you're a feudal lord
10:11you need an army so you have samurai and
10:14samurai of course have to be paid
10:17so they can buy the weapons uh and
10:19generally you know wait for the world to
10:21break out and the structure of the
10:23futures contract is not that different
10:25from the rice futures
10:27uh traded on the chicago board of trade
10:29exchange today right so in 17th century
10:32uh federal lords
10:34were using these contracts
10:36uh to finance generally you know the
10:38household and
10:40all the expenses because they got fields
10:43and if they needed money today
10:45no they could sell uh you know basically
10:48uh
10:49they could um
10:50in fact it's not even the money today
10:52right it's more that the prices were
10:55fluctuating and the lords knew how much
10:58money they needed right but they're not
11:00sure if the price of rice would go up or
11:02down because it depended on how good the
11:04harvest was
11:05so the futures contract actually and
11:07we'll talk about it later today what
11:09they get is that it give them the
11:11guarantee that they can sell the rice at
11:13the fixed price
11:15so if there was a great harvest and the
11:17price of rice was very low
11:19they still would get enough money to pay
11:21uh you know the expenses
11:23if there was a bad harvest you know
11:25drought or you know or something
11:27happened with the weather it was a very
11:29bad harvest then they would lose money
11:31because you know they would have the
11:32future contracts at the stern price
11:34and if there was a bad harvest that year
11:36let's say two years from now five years
11:38from now they'll actually lose money
11:40because they could have sold
11:41um uh this old uh you know the higher
11:44price but
11:45the most important thing for them was to
11:47make sure that they don't go bankrupt
11:49right so they don't have uh you know
11:50they have enough money to pay the
11:52expenses
11:53so
11:54they traded potential profit
11:58for stability
11:59right so
12:01they could profit a little bit they
12:03could maybe lose money on some other
12:04years
12:05but futures market gave them stability
12:07they gave them assurance that in a bad
12:10year when a good year they could always
12:12sell the rice at the price that they
12:13know in advance
12:14and that's what happened in 17th century
12:17and the contract traded today at the
12:19chicago board of trade exchange on all
12:21kinds of things including rice is
12:24exactly the same contract
12:26so this innovation happened
12:28uh before the invention of the steam
12:31engine
12:32before the invention of automobile
12:34in 1969 of course is when humans landed
12:37on the moon right so that was uh you
12:39know pretty recent uh development so
12:41this thing is earlier than all of this
12:44but you know what is the security right
12:46and this rice contract traded on a
12:48dojima
12:50exchange in the 17th century is
12:52one of the first or the first security
12:54even though you know there are some
12:55essentially actually the first because
12:57um
12:58even in mesopotamia uh
13:01before the birth of christ right you
13:02know there already some contracts that
13:04are very similar to that as well
13:06so
13:07a security is a standardized tradable
13:09financial instrument with public price
13:10history
13:12standardize of fungible means that
13:14individual units of the same security
13:16are interchangeable
13:18so so we can think of quality sorry
13:20quantity total number of shares of
13:22security and not about the specific
13:24unique share with its own identity
13:26right and it does not matter which
13:28specific share of let's say amazon you
13:30own right if you give me 100 shares and
13:33i give you 100 shares a financial
13:34position is the same right so
13:37amazon issues shares
13:39this is uh you know a piece of
13:42ownership in amazon
13:44all shares are the same and they are
13:45functional right it's not i own share
13:47number five and you own sure none but
13:49then and somehow they're different right
13:51so they're different classes of shares
13:53but within each class
13:54it's exactly the same share right so
13:56it's very important if it's not
13:57funchable if it's some sort of a unique
14:00um uh you know individual share that has
14:03a number i know maybe it has a signature
14:05for jeff bezos on it right that will not
14:07be security
14:09now second thing is that tradable right
14:10it has to be tradable
14:12or negotiable right it's negotiable is
14:13the same as tradable it means a security
14:15can be bought or sold by anyone
14:17without asking its issuer or anyone else
14:20for approval of the sale
14:22right and uh the
14:27reason
14:28you know this in you know so for example
14:29i can buy a hundred shares of amazon
14:31stock
14:32i don't need permission from amazon to
14:34buy this local from anyone else
14:36this is actually not the same uh this is
14:38not how this works for the um
14:42this is not how this works for the um uh
14:48you know private companies that just
14:50started right so so the company some
14:52companies they sell fractional ownership
14:55at the very early stage when they just
14:57started and this
14:58ownership comes with restrictions
15:00attached for example
15:02they may restrict selling the shares to
15:04someone else
15:05but
15:06shares in this company at this early
15:09stage when they just started do not
15:11become security yet until they permit
15:13trading by anyone no usually this
15:15happens when they list on exchange right
15:16so when you list your shares when you
15:18sell shares to someone
15:20you may say okay well you know you
15:22cannot uh
15:24sell them this
15:25your shares to anyone else usually the
15:27company says well you know before you
15:29sell them we have the right to buy them
15:31or there's a period before you can sell
15:33right and uh
15:35the
15:36moment that the company comes and has to
15:38be listed on exchange so you can buy the
15:41shares through the exchange
15:43the exchange says hold on a second right
15:45so first of all are they shares standard
15:47right so none of the shares have any
15:49special conditions or jeff business
15:51signatures which are businesses um you
15:53know they assume everybody knows who he
15:55is right he's a
15:57founder and and until recently president
15:59of amazon
16:01right second thing is that are they
16:03negotiable are they tradable right so
16:06do i need your permission to buy or sell
16:08shares
16:09if i do well the exchange will sell will
16:11go back you know and change that right
16:13and then you can come again and list
16:15all right and finally uh and that's
16:17actually the most important thing is
16:19that uh they have to be public price
16:21history right security is a standard
16:23tradable and financial instrument with
16:25the public price history so public price
16:27history means that anyone interested in
16:29buying or selling a security can do this
16:32with confidence without worrying that
16:34they may do so the wrong price right so
16:36you know sometimes uh there is something
16:38that you don't know really how much it's
16:40worth
16:40right like for example
16:42if you're buying an apartment or a house
16:44right you know all been to that from
16:47most of us
16:48right you say well you know basically
16:49some price and say well maybe it's too
16:51much right so maybe you know i'm paying
16:53too much because you know the apartments
16:55think like apartments or houses
16:57they're very individual
16:59and the price
17:00the real estate agents will say well
17:02that's a really good location it's
17:04really good construction it should be
17:05worth a lot
17:07or they may find some problems that say
17:09you should not pay a lot right should
17:10not ask a lot if you're selling
17:12okay well the thing is with the house
17:14sales happen usually in many countries
17:16actually it's public
17:17but it happens so rarely that you don't
17:19really know the price today if the house
17:21was sold last time 10 years ago
17:23we security
17:24is you know liquidity and we talk about
17:26it a bit later means that it's
17:28continuously bought and sold by someone
17:30so you have continuous price history
17:33right so if you're going to buy a share
17:34of amazon
17:36you know that you know basically
17:37thousands of people bought it in the
17:39previous hour
17:40you know at the price that they bought
17:42it
17:42so you have confidence that the price
17:45you're buying is a fair price today
17:48meaning other people also think it's a
17:50good price because they bought at this
17:51price right and other people think they
17:53sold you know the others sold at the
17:55same same price
17:57so these three attributes is what helps
17:59the security achieve the objective of
18:01being liquid easy to buy
18:04and sell
18:05all right so
18:07now what's security exchange
18:09security exchange is an organized safe
18:11and highly regulated marketplace where
18:13securities are both sold
18:15not all securities are traded on
18:17exchanges
18:18but there are other venues where
18:19securities are traded the opera is
18:21similarly enough so we will not discuss
18:23them here so i'll talk about the
18:24exchange
18:25there are also other ways to buy
18:27securities
18:28and uh this is not something that we get
18:31to in this lecture
18:32uh but you know they all work on similar
18:34principles
18:36so when buying or selling securities and
18:38exchange market participants do not
18:40trade with each other and deal only
18:43with the exchange
18:45uh
18:46what does it mean it means that uh
18:49you know if i bought 100 shares of
18:51amazon
18:52right i have no idea uh who sold them to
18:55me right so i'm just saying you know buy
18:57it you know all of it is uh
19:00all of you know is available online now
19:02so i say bye you know i don't know who's
19:04wrong right
19:05so
19:06we deal with the exchange you know if
19:08you're buying you're dealing with the
19:09exchange
19:10if you're selling you're also dealing
19:12with the exchange
19:13and despite being the party that all
19:15market participants trade with the
19:17exchange does not have their own
19:19inventory of securities
19:21right so the exchange or rather it's
19:23representatives called market makers and
19:26sometimes this market maker is a program
19:29and sometimes it's a human right so
19:31sometimes it's um
19:32basically you know someone in uh
19:35uh you know shortened suspenders right
19:37uh screaming uh on the floor of the
19:39exchange
19:40and uh more frequently it's just a you
19:42know software program
19:44that you will uh if you attend the next
19:46course on enterprise python you will
19:47know how to write programs like that
19:49even though you know to be fair this
19:51type of market making programs that i've
19:53written and i see usually just for speed
19:56right but you know it's a program that
19:57uh you may eventually you know if you
20:00choose career might finance right
20:02so this program it matches buyers and
20:04sellers and it chooses the price such
20:08that the number of buyers in the number
20:10of sellers is the same right
20:12so in other words
20:14this program
20:16sets the price if the price is too high
20:19there will be more sellers than buyers
20:21if the price is too low there will be
20:22more buyers and sellers because for each
20:24buyer and for each seller there is the
20:26price at which they are willing to buy
20:27or the price at which they're willing to
20:29sell
20:30this program looks at and you know
20:32people place orders they say i'm gonna
20:34buy or they say well i will buy if the
20:36price drops below a certain
20:38level right it's a limited order so uh
20:40this program
20:42is designed to set the price such that
20:45the number of buyers is equal to the
20:46number of sellers so the exchange owns
20:48the shares only for a very brief period
20:50of time
20:52or not at all when they just match them
20:53directly right and this is called the
20:55market clearing price
20:57uh what is clearing here it's clearing
20:59the orders right so people place buy
21:01orders people place sell orders
21:04right and they buy and sell orders they
21:06place depend on what the price is
21:09either because people say i will buy if
21:12they place the water to buy if the price
21:14drops
21:15or
21:16because they just wait when the price
21:18drops they place the order
21:19so market clearing price is called
21:21clearing price right is simply because
21:24it clears the order book right so it
21:26basically matches all of the buyers with
21:28all of the sellers such that uh all of
21:30the buyers buy all the sellers sell and
21:32the amount of shares traded is the same
21:34but normally it's just called the market
21:36price which is the price right
21:39okay now uh
21:40with that that was check out the basics
21:43on the
21:44financial markets and before we go to
21:47specific two types of securities equity
21:50securities
21:51and fixed income securities
21:53i wanted to stop for a second and
21:56first of all ask that anyone who has
21:58questions please ask them in a chat
22:00and then my colleagues
22:02will alert me if there's something that
22:04they cannot answer directly
22:07and uh second is uh i want to make sure
22:10that the sound is okay and the video is
22:13okay because we have a natural uh you
22:15know break here between the uh sections
22:18i'm just going to move the camera a
22:19little bit so it's more stable
22:21all right sound all right
22:23oh loud not too loud
22:29can you
22:31put it in a private chat if this is
22:32something that requires my response no
22:34questions so far
22:35okay great
22:36all right so equity security so now uh
22:39so we're going to talk about two types
22:40of securities equity and fixed income so
22:42equity is the first type of security
22:45and equity is a type of security that
22:47represents fractional ownership in one
22:49or multiple companies
22:51uh and we'll discuss what does it mean
22:54to you know where the math comes in
22:55right so what does it mean to model this
22:58securities
23:00and these securities
23:02they are called stocks if they are
23:05shares of ownership in a single company
23:07right so a stock
23:08is a single
23:10is a unit of fractional ownership
23:13in a single corporation
23:16owners of stock or stock shares rather
23:19and sometimes they just call stocks
23:22right and uh sometimes on uh forums um
23:26uh by the way don't uh you know don't
23:28trade the
23:29gamestop right uh after this lecture
23:31that's one thing that i hope you will
23:32take away from that
23:34right uh you know so stocks stocks right
23:36as they call it on this uh investment
23:38forms
23:40uh right stock shares right
23:42and uh you know people who trade them uh
23:45sorry people who who uh own them right
23:47are still holders for shareholders
23:50right and
23:51stock
23:52again it's a single name equity security
23:54there's a kind of a you know
23:56mathematical finance name for it meaning
23:58it represents fractional ownership of a
23:59single corporation right there are other
24:02security the securities which are called
24:04index securities which represent
24:06fractional ownership in a group of
24:09corporation
24:10which is selected either by an algorithm
24:12or by a committee for example you can
24:15invest in s p 500
24:18which is fractional ownership in all of
24:20the
24:21companies that were selected 500 um
24:24not necessarily largest but 500 most
24:27investable or desirable companies in the
24:30u.s stock market selected by a committee
24:33based on a set of rules today we'll just
24:35talk about
24:36single stock shares a lot of the things
24:38in you know from a math finance
24:40perspective
24:41it does not actually matter that much
24:43if it's a single stock or multiple but
24:46there are some differences
24:48okay so now the corporation is jointly
24:50owned by shareholders right so you may
24:52share you may own you know
24:540.01 of tesla
24:57and together with all of the people who
24:59own some share of tesla you own the
25:02corporation in fact you can vote
25:04uh on the uh board and then they you
25:06know basically you can you know go go
25:09and vote on the
25:11elections of board directors uh and uh
25:16that basically you know you can feel you
25:18you buy a share of tesla you feel that
25:19you know you're basically one of the
25:21owners together with elon musk
25:23right
25:24now shareholder pay money for this talk
25:27right so why why are people investing in
25:29shares they pay money for the stock and
25:31would like to make profit for that
25:33how did they earn a profit okay so one
25:35way they can earn a profit is by
25:36receiving a dividend
25:38so dividends are by the way i see that
25:40there's a question i'll answer after
25:41this slide
25:42so the first way they can earn a profit
25:44is by receiving a dividend so dividends
25:46are cash payments made periodically
25:48usually once per quarter
25:50by companies to the shareholders
25:52the second way to earn profit is by
25:54stock appreciation or price growth right
25:56so the stock price goes up
25:58shareholders can sell it for a higher
25:59price than they paid for it
26:02so some stocks don't pay dividends at
26:03all right so the only way to make profit
26:05from this growth stocks like all gross
26:07stocks right so so stocks that don't pay
26:09normally don't pay dividends and by the
26:11way most guru stocks eventually start
26:13paying dividends right but a lot of them
26:15don't do it for a very long time
26:18so the only way to make profit from
26:19these gross stocks is to sell them at a
26:21higher price later
26:22there also stocks uh which are basically
26:25called income stocks uh which do the
26:27opposite right so they don't grow much
26:29they you know grow actually usually
26:32but instead of uh keeping the money and
26:34then making people think well the
26:36company now has a lot more money so the
26:39price you know the stock is worth more
26:41uh they instead pay out whatever they
26:44earn in a dividend right so they pay
26:46money to the shareholders but the
26:48shareholder is not like selling
26:49shareholders still keeps their shares
26:51so gross stocks are for aggressive
26:53investors they usually make more money
26:56over the long run
26:57income stocks they reduce risk
27:00and every time and we'll talk about it
27:02later every time you reduce risk you
27:03also reduce your income
27:05and therefore think people for example
27:07who rely on
27:09their daily expenses for this income so
27:11they pay periodic dividends and for
27:14example if somebody is uh retired you
27:16know it basically is uh
27:18you know it's providing uh income
27:20uh that you can use for a living
27:22expenses while they still retain
27:23ownership of the stock so that's the
27:24income stock
27:26all right so let me just look at the
27:27chart and see what the um question is
27:30if the number of sellers and buyers are
27:31different right uh so uh so again yeah
27:34so basically suppose let me just come
27:37back uh again i'm not going to bring
27:39back the slide but this is about the
27:41market clearing price
27:43okay so
27:44people decide to buy or sell depending
27:46on the price suppose that you look at
27:49the uh you know
27:51well used to wall street used to be wall
27:52street journal but now you look at the
27:54financial service
27:55initially oh wow you know tesla price is
27:58one dollar
28:00i don't need the char i don't need the
28:01pull right or asking people to raise
28:04hands like how many of you would buy
28:06tesla share for one dollar if it could
28:08today just happen to be one dollar
28:10everybody right even people who never
28:12invest in stocks actually i don't
28:14uh because uh i work for uh you know as
28:17a consultant for many banks and these
28:19banks trade as well as hedge funds and
28:21they don't want basically people uh uh
28:24you know trading in person and helping
28:25them trade as a company
28:28but you know i would probably go and say
28:29well hey you know that's really like a
28:31you know amazing opportunity you know i
28:33would be very sad i have to pass it up
28:34right
28:35but without any restrictions i would
28:36just run and buy like as many as i can
28:39now imagine that the tesla
28:41price for one share is let's say 10
28:43million dollars
28:45and you have some shares would you sell
28:47a share
28:48you probably would right you know you
28:49would make 10 million dollars
28:51uh you know you bought it probably for a
28:53lot less
28:54so the number of buyers and the number
28:56of sellers depends on the price
28:59if the price is zero there will be a lot
29:01of buyers
29:02is the prices exorbitant
29:04like 10 million dollars per share or
29:06billion will be a lot of sellers
29:08so somewhere in the middle there is a
29:10price at which the number of buyers and
29:12sellers is the same that's the market
29:14clearing price
29:15in the market makers
29:17they basically set the price they see
29:19well there are more buyers and sellers
29:21right because people are continuously
29:22trading
29:23so people basically every minute or
29:25every second people are placing waters
29:26for buyer to sell so market maker
29:28program
29:29and you know it's again it used to be
29:31some basically uh guy and suspenders
29:34you know screaming on the floor of the
29:36exchange right but now of course it's
29:38everything is most too fast for humans
29:40to keep track
29:41uh so it's a program it says well i set
29:44the price to a hundred dollars per share
29:46and over the next minute or actually
29:48more likely like you know seconds or
29:50milliseconds even see well looks like
29:52there are more buyers than sellers okay
29:54so it's too low right they're going to
29:56raise the price still more buyers raise
29:58again okay now more sellers right so
30:01during this milliseconds the exchange
30:03will accumulate a position because they
30:05still have to fulfill the orders right
30:06so during the time that there are more
30:09buyers than sellers i say well let me
30:11just do sellers and buyers because
30:13there is also a way to borrow and sell
30:15the shares you don't have but we didn't
30:17get to it here
30:18so
30:19imagine that the market making program
30:21set the price
30:23too
30:24high and there are more sellers and
30:25buyers the exchange will start
30:27accumulating shares that's not what they
30:29want they want to have no shares that's
30:32not the role to invest right they want
30:34to facilitate trading
30:35so they will keep uh lowering the price
30:38until the buyers come in and buy all
30:40this
30:41you know surplus right and so forth so
30:44now as this program
30:45changes the price continuously such that
30:47the number of buyers the number of
30:49shares equivalents
30:50every time the exchange has a
30:52excess shares like local position
30:55or
30:56has negative position right which means
30:58that basically they sold the shares they
31:00don't have
31:01you can actually do it in financial
31:03markets there are some restrictions
31:05by borrowing it's just for a few seconds
31:07from people who have the shares right
31:09and they can sell it then they have to
31:10give it back to them later
31:12or for the whole day
31:13so uh so that's how it's set right so
31:16it said continuously such that between
31:19zero and infinity such that the number
31:20of buyers number sellers is the same
31:23and it's like a basically like uh trying
31:26to hit a moving target right but in the
31:28end by the end of the day the exchange
31:29wants to you know close out the position
31:31with no shares at all and whatever
31:33mismatch remains at the end of the day
31:36there is something called closing
31:37auction
31:38which basically is designed to take all
31:40of the closing orders right so people
31:42can say well at the end of the day i
31:43want to buy at the end of the day i want
31:45to sell so at the very very end of the
31:47day the price is set such that all of
31:50these closing orders
31:51match up and that's how
31:53the price is set
31:55okay next question
31:56if stars
31:58uh uh is more than uh
32:02second it sells more than more sales and
32:04buyers
32:05sellers more price uh lower and
32:07searching the buyers estate limit uh
32:11yeah so well
32:12i i think i already answered this is the
32:14second question was this about the same
32:16thing yeah so it's essentially
32:18uh
32:19some people place limit orders that
32:21helps the market making program to know
32:23where to put the price
32:25some people just wait until the price
32:28moves and then place the order
32:29in this case it's more difficult for the
32:31market
32:32making program because uh the market
32:34making program has to start from some
32:36price
32:37then waits to see how many shares come
32:39in
32:40orders come in and then they change the
32:41price but it happens so quickly that
32:44normally uh the exchange does not
32:45accumulate a huge position
32:47either way right so
32:49if then there's no limit order
32:51they can just set the price after a few
32:53trades come in they can see that more of
32:54them are buying that selling you know
32:56they just moved it's actually quite um
32:59interesting um
33:00you know it's like a basically optimal
33:02control problem
33:03with some statistics uh and uh you know
33:06this is one of the things that
33:07mathematical finance does
33:09is uh
33:10one of the you know things that people
33:12who learn mathematical finance work on
33:14is market making programs right
33:17and of course investors also have other
33:19programs that try to beat the market
33:21making program and make money from them
33:23all right why grow stocks can increase
33:25the price later well uh imagine that you
33:28have a company like apple right so apple
33:31makes a huge amount of money
33:33and until recently they did not pay a
33:35dividend
33:36so at some point they've been sitting on
33:38tens of billions of dollars of money
33:40right so they're almost like became like
33:42a bank or a hedge fund hedge fund is a
33:44you know as a money manager who
33:47takes money from other people and then
33:49invests
33:50so at one point apple was receiving
33:53billions of dollars every quarter
33:56in accommodating them
33:58okay now suppose that you own
34:00one percent of apple that would make you
34:02very rich but you know that's just for
34:04the calculation right in this quarter
34:07apple made one billion dollars
34:10right that means that your share
34:13of that income is 10 million dollars
34:16so that
34:17holding that you have
34:19over that quarter
34:21was exactly like before right it's the
34:23same company same products
34:25plus
34:26extra cash
34:28so
34:29the price of the stock
34:31all others being equal right should be
34:35increased by the same amount
34:36in reality it's not exactly like that
34:38because uh also uh you know during this
34:41time people think okay well you know
34:43maybe android
34:45is right you know basically taking over
34:47the market taking market share
34:49maybe there are supply chain problems
34:51and they prevent iphones from being
34:52manufactured quickly enough and people
34:54are lining up and you know they cannot
34:55produce them
34:57so
34:58uh
34:59it's not exactly like that but
35:01companies that do not pay dividend but
35:03make money
35:05or companies that do not make money yet
35:07but people think that they will in the
35:09future because amazon was actually until
35:12you know failure recently was just
35:13losing money at a huge rate right but
35:15they became dominant and now they can
35:17basically make money if they want and
35:19they still pretty conservative right so
35:21they still invest uh most of the money
35:23they make they invest in expanding their
35:24business
35:25so
35:26growth talk
35:27go up for two reasons one is that the
35:30company may be earning cash but not
35:31giving it to anyone
35:33so whatever
35:34value of that cash they have is included
35:36in the stock price and gross
35:38or
35:40castles in the air right so you invest
35:42in a little company
35:44and that company becomes meta or you
35:47know formerly facebook right or it
35:49becomes becomes google
35:51or it becomes uh
35:53amazon
35:55and
35:56you don't need dividends you know that
35:58the price will go up because these
35:59companies are the best in what they do
36:02uh you know people want to do business
36:04with them
36:05in the future they will be able to earn
36:07more money than today and you know in
36:08the future the shares will be worth more
36:10than
36:11so essentially grew stocks and i'll talk
36:12about it more so so let me just you know
36:15wrap this up because there's actually a
36:16whole set of slides about how the price
36:18is determined
36:20essentially growth stocks uh
36:22go up because people think that in the
36:24future
36:26they will be worth more because they
36:28will earn cash
36:30or because they just will uh you know
36:32earn cash and keep it
36:34right
36:36or and if you're selling your share
36:38you're essentially selling the ownership
36:39of a pile of cash somewhere
36:41right fractional ownership
36:43or they will earn money invested in a
36:46business
36:47take over other markets like amazon did
36:49right so amazon started from selling
36:51books
36:52then they started selling other stuff
36:54rather than books
36:55then they started selling electronic
36:57books
36:58nowadays starting selling movies right
37:00and now they can practically you know
37:02sell whatever exists you can buy an
37:04amazon
37:05so
37:07they are worth more than they used to
37:09would be worth 10 years ago right that's
37:11a good stock even they do eventually you
37:14know most large companies eventually
37:16they have to start paying dividends
37:18uh but because they really don't know
37:20what to do with the cash right they
37:21cannot so much
37:22large companies they have so much cash
37:24they can't really invest it effectively
37:26so they have to pay it out
37:28but initially a lot of companies don't
37:30but they still go in price
37:32all right so let's just continue right
37:33so
37:34um now
37:36what is a stock price model right and
37:38actually that will be a more extended
37:40answer to this last question which was a
37:42very good question
37:43um
37:45the stock price right the stock rates
37:47model
37:48and the answer for this is not as
37:50obvious as that machine right so and
37:53contrary to what you may think right so
37:55modeling the stock price in mathematical
37:57finance
37:59does not mean calculating what it is
38:01will be it means calculating
38:03probabilities of what it may be
38:06right so when we talk about price and
38:08mathematical finance
38:10we know the price today and we know the
38:12price in the past
38:14in mathematical finance you never say
38:17that you know the price in the future
38:19and
38:20that's what you know we will talk about
38:22why
38:23okay so let's talk about first about
38:24fundamental analysis
38:26so fundamental analysis
38:28is the opposite
38:30of mathematical finance it also actually
38:32involves math or you know some actuarial
38:34analysis some uh you know balance sheet
38:37analysis some
38:39basically accounting
38:40but
38:41fundamental analysis is not
38:44the moral phenomenon analysis model is a
38:47moral and we need this model
38:50but it's not the moral that mathematical
38:52finance
38:54uh you know uh
38:57you know it's mathematical finance model
38:58is not the same as the fundamental
38:59analysis model
39:01because fundamental analysis is a theory
39:03of how to calculate the stock price
39:07in other words what the stock price
39:08should be even if it's different today
39:11or what it will be
39:13based on analyzing company cash revenue
39:16expenses expected future growth
39:18and based on this fundamental analysis
39:20produces the price the stock should have
39:24right
39:24and it is actually
39:26extremely useful as part of the overall
39:28view of the stock market and is actually
39:30routinely employed by stock analyst who
39:32issued this talk by a cell
39:33recommendation
39:35and
39:36in fact without fundamental analysis
39:40no other model can work so it's not the
39:42model in mathematical for final for
39:44mathematical finance
39:46fundamental analysis model
39:49is not d model but it's input to the
39:51model
39:52and
39:54usually it does not produce anything
39:56close to the actual price and the reason
39:58is is uh something that uh burton
40:01malkail
40:02uh who is a princeton economist uh and
40:05the author of the book that i highly
40:07recommend
40:08to read called random walk down wall
40:10street
40:12uh by the way just so you know so people
40:15who work in investment management they
40:18often don't like to mention this book
40:20because this book argues that you cannot
40:22really build an investment strategy
40:25and it's called random walk down wall
40:27street is because basically they argue
40:29that people who build investment
40:30strategies
40:31they're just
40:32doing random things and some of them
40:34just get lucky
40:36that's a very extreme view
40:37i won't actually share this view i've
40:39seen you know how uh machine learning or
40:42even uh you know and before that
40:43traditional
40:44statistics helped build successful
40:46investment strategies that are
40:47absolutely you know clearly
40:49uh you know are not just random
40:52but
40:53a lot of this uh is in fact random a lot
40:57of successful investment managers
40:59make money just by being lucky as
41:01opposed to by knowing something and then
41:03they give interviews
41:04even though if the you know random coin
41:08that was flipped by someone you know in
41:09the stock market stock market in the
41:11universe right went the other way then
41:13they would be you know working
41:15in a restaurant right and somebody else
41:17would be giving interviews about the
41:20brilliant investment strategy so a lot
41:21of it is random so i think that this
41:24book random walk down wall street
41:26is extremely important
41:28in order to
41:29first of all not to get the illusion
41:31that you can predict things
41:33second is that not to get the illusion
41:36that uh investment strategies work or
41:39if someone was successful in the past
41:41investing or
41:43is
41:44proposing a strategy that they see
41:47they argue you know they tested in the
41:49past it's called a back test right they
41:51say well if i was using this strategy to
41:53invest over the past 10 years i would
41:55have made thousand percent return right
41:57it really helps to understand what the
41:59limits are of backtest
42:01and where the limits are of
42:03knowledge and wisdom and investing
42:06compared to just
42:08you know fundamental factors
42:10or
42:12just being lucky
42:14and
42:15it turns out that
42:17a lot of people who invest just get
42:19lucky and sometimes they just run out of
42:21luck
42:23sometimes
42:24people employ strategies
42:26which mathematical finance can help
42:28develop but also help uncover and detect
42:30we'll talk about risk
42:32so sometimes people can use financial
42:33markets to develop a strategy that will
42:35guaranteed make 10 percent per year and
42:37then you lose everything on year 10 at
42:39which point the investment manager
42:41retires and says sorry you know
42:44you know bad year
42:46right and sometimes uh
42:48people like for example warren buffett
42:51who knows about raise your hand if you
42:52know about warren buffett i'm not sure
42:53how famous he is outside the united
42:55states
42:57a lot of people necessarily how many
42:58people are there
43:02okay anyway so warren buffett is 19
43:04people okay so warren buffett is very
43:06famous u.s investor and actually his
43:07amazing track record
43:10okay but and and he's also very famous
43:12at least until uh you know sometime
43:14until recently he was saying
43:16i don't understand options uh what are
43:18these options so you know horrible
43:21things risky right well it turns out
43:23that at least for a period of time he
43:25made a huge percentage of his income
43:29by
43:30being perceived
43:33as completely reliable party to buy
43:35options from
43:37and during this time
43:40because people knew that his companies
43:42are so well capitalized that he'll
43:44definitely pay
43:45he was selling options on s p 500 index
43:49following
43:51and
43:52most other financial market participants
43:53would have to put up capital for that
43:55and that means that they could not use
43:57this capital to invest somewhere else so
43:59they would have to borrow money and pay
44:00interest
44:01by being seen is a very successful
44:04investor
44:05he was able to earn
44:06income
44:07that
44:08is a kind of a self-fulfilling prophecy
44:10once everybody thinks that you're very
44:12successful investor and cannot go
44:14bankrupt
44:15you can actually sell financial
44:16instruments that people would not buy
44:18from others but will buy from you
44:20and that helps you become successful
44:23investors so the circle is closed and
44:24now you know basically
44:26uh people thought that you will have gay
44:28good returns and you do and that was
44:30actually in some years large part of um
44:33uh his success and that's great right
44:35but uh you know i think uh some
44:38some a lot of people think that he's
44:39just wisely picking stocks but in fact
44:42there are a lot of other factors in his
44:44investment success
44:46that have to do just with the lower cost
44:47of borrowing right just because people
44:49think that it's such a low risk to lend
44:52money
44:52or to buy options from someone right so
44:55that helps them actually become more
44:56successful investors so um you know the
45:00random walk down wall street is a whole
45:01book about castles in the air about
45:03perception and how it affects financial
45:05markets that's not what the lecture is
45:06about but i think it's a part of for any
45:09quant who uses math for financial
45:10markets i think it's very important part
45:12of the education
45:14is to also understand
45:16the fundamentals and understand how
45:19prices deviate from the fundamentals and
45:21what makes uh that happen
45:23all right so now
45:25very short summary of the main thing in
45:26the book right so the reason uh prices
45:29of stocks
45:30are not worth fundamental analysis
45:32projects no matter how record
45:34is called castles in the air
45:36so there's a tendency of investors to
45:38mention huge success of the company they
45:39invest in
45:41and uh investors let the imagination
45:44influence how the prices talk right so
45:46they think every technology company will
45:47be like google or amazon or microsoft or
45:50alibaba right
45:52and
45:52investors sometimes also see ruins in
45:55there right so they're unreasonably
45:56pessimistic for example um you know
45:59maybe you remember
46:01uh
46:02there was a financial crisis that
46:04affected uh that happened after the
46:05default of lehman brothers
46:07uh and then for a period of time was
46:09very very difficult to borrow money from
46:11banks uh you know there was a you know
46:14systemic problem with access to credit
46:16so many people thought that other banks
46:18would also default and did not invest in
46:21banks and there were more sellers than
46:23buyers
46:24and you could buy shares of banks at a
46:26very low price and people who did they
46:28made a lot of money right so sometimes
46:30people have unreasonable
46:32um you know what what alan griespan uh
46:35you know former head of the federal
46:37reserve called
46:38called irrational exuberance right well
46:40but he was talking about the entire
46:42market but the same thing can happen
46:43about the stock so somebody
46:46says electronic sets up electronic
46:47storefront and says well i'll be better
46:49than amazon right that's irrational
46:52but uh
46:54you know back in the
46:56uh sometimes it's justified right so
46:58back in uh the dot com in the years of
47:00dot com crash
47:02around the year 2000
47:04um
47:05a stock analyst
47:06whose name is henry blodgett was
47:08actually fired for his unrealistic
47:10prediction for the price of amazon
47:12because he predicted amazon would i
47:15think you know go 10 10 times up the
47:18price
47:20in fact the whole market crashed and he
47:22was fired
47:23right well over time amazon normally
47:25surpassed his tenfold target
47:29it also made another 10-fold gain after
47:31that
47:32and he was quietly hired back well not
47:34the same firm now he's respected expert
47:38because he was one of the first people
47:40who predicted that there's practically
47:42no limit to the price
47:45of successful companies and e-commerce
47:47because they can expand almost
47:49indefinitely of course he also pushed a
47:51lot of uh well which formal reason for
47:53the firing is that he pushed a lot of
47:55companies which were
47:56not uh really great investments and he
47:59emailed about how you know he had to
48:00push this company he didn't really
48:02believe in
48:03but at the time his predictions that the
48:06days after the dot-com crash seemed
48:08totally crazy but of course there are
48:10these few companies that uh exceeded
48:12this world predictions
48:14and for each of these companies there is
48:15100 that crashed and
48:17ran out of money
48:18so
48:19people what people think about the
48:21company collectively right what market
48:23participants collectively not just one
48:25person collectively think about the
48:27company
48:28affects the orders they place and that
48:30affects the market making program in the
48:31maker making program will set the market
48:34clearing price based on what people
48:36think
48:37and
48:38it's at least equal to the importance of
48:41fundamental analysis in a sense that
48:43price stock price can be twice higher
48:46or twice lower than what the company is
48:48worth based on fundamental analysis for
48:51volatile risky i think uh you know
48:53e-commerce uh
48:55uh you think you know companies dealing
48:57with crypto
48:58right so that can be really you know
48:59very widely very compared comparative
49:01fundamental analysis
49:02if this is something like a power
49:04station
49:06that is basically attached to the ground
49:08and all of the customers are customers
49:10who live nearby and get electric power
49:12and the government controls how much
49:14they can charge for power because of
49:16course you know if somebody overcharges
49:17for power they cannot just relocate
49:19right
49:20then fundamental analysis is extremely
49:22precise
49:24because you know everything right you
49:25know who the customers are
49:27uh well you don't know the price of fuel
49:29right that's one variable i guess but uh
49:31but generally you know where the
49:32customers are
49:33you know what the government controls
49:35you know basically dictates about the
49:36prices
49:38so that's why it's accurate when it's
49:40sunny like early days of amazon it's
49:42very very inaccurate
49:44so
49:45mathematical finance is not about
49:47fundamental analysis it's just one input
49:50it helps to
49:51prevent disconnect complete disconnect
49:54or you know disconnect that's really
49:55insane right from between the stock
49:58price and reality like for example if i
50:00say well you know what i'm going to sell
50:02whatever some uh
50:04you know widget and i'm going to make a
50:06trillion dollars from the switch from
50:08the military analysis will tell you that
50:10cannot happen
50:11but
50:13factor of two factor 10 easily right
50:15depending on
50:16how inspiring the companies if the
50:18company is very inspiring
50:20you know they disconnected be huge right
50:21and eventually it comes down to earth
50:24but in some rare cases it's even
50:26exceeded even further
50:28all right
50:29so today's stock price right is um
50:32uh today's stock price
50:34uh is uh you know the way that you can
50:38fundamental analysis not accurate right
50:40so how can you make it more accurate
50:41well the most accurate model for the
50:43stock price is very easy right you go
50:45and find it in the wall street journal
50:47uh well today of course there are you
50:49know financial information services data
50:51fees
50:52but still you go look it up
50:55you don't need any math you don't need
50:57any work
50:59it's simple right people trade they buy
51:01and sell the prices today is whatever
51:03the market decides it is right
51:06so buying and selling on exchange tells
51:08us the price and this whole price
51:09discovery and that's actually other than
51:12making it possible for people to invest
51:14making it safer making it possible to do
51:16it in small
51:18amounts that's another very important
51:20role of the stock exchange is that price
51:22discovery right so they help understand
51:24how much the company is worth that's
51:26critical
51:27uh you know it validates the views of
51:30early investors
51:31so they feel that they now have other
51:34people confirming what they think about
51:35the price
51:37and financial markets
51:39in price discovery is the reason why it
51:42became so much easier to get
51:44funding for a business right so people
51:46you know two two students in a garage
51:48can go and do a startup
51:49now or you know basically like with now
51:51now you know the garage used to be when
51:53they're building hardware right and now
51:54now all you need is a desk and a laptop
51:57so receiving financing is easier than
51:59ever and financial markets make it
52:01happen
52:02the price discovery is only practical
52:04the stock is liquid right so you have to
52:05have people continuously trading if
52:07people trade once a month that's not
52:09going to be good and that's why uh
52:11exchanges
52:12list companies uh only when there is
52:15enough volume of trading if they don't
52:17think there will be volume they will not
52:18list
52:20now what is the price stock price
52:22tomorrow right so well nobody can find
52:24the tomorrow stock price today
52:26uh because it's influenced by the events
52:28not known in advance right so in finance
52:32events that cannot be predicted from
52:34plus data are called market moving news
52:36and sometimes they're really news and
52:37sometimes they're not even you know
52:39their own stories written by journalists
52:41so well one example uh
52:44is uh let's say
52:46elon musk wakes up
52:48and tweets
52:49i think tesla is overpriced
52:52and people say well you know wow you
52:53know the founder of the company thinks
52:55stock is overpriced so price drops
52:58right then few days later they say well
53:00you know elon must really twist a lot of
53:01random things so it goes back up
53:04or
53:05when a lot of people were betting on the
53:07tesla price to fall
53:09he said
53:10company is being taken private
53:12funding secured
53:14right so price immediately dropped but
53:16actually he did not secure the funding
53:18you know he just talked to someone about
53:20it and actually he got fined by the
53:22securities exchange commission because
53:24they decided this tweet was misleading
53:27so there is no mathematical model that
53:29will predict what elon musk will tweet
53:32when we wakes up tomorrow
53:35and
53:37there could be something relevant right
53:38to the company like for example your bus
53:40shares and a leading password management
53:41company
53:42in the morning the company announces
53:44that hackers broke into its system
53:46stole the passwords
53:48deleted the data uh and the stock you
53:51know password management is what you
53:52definitely want to be secure right so
53:54the stock loses 90 of its value
53:57there's no mathematical model that will
53:58tell you that the hackers broke into the
54:00systems
54:02actually
54:03there is right there are operational
54:04risk models
54:06uh they're not perfect right and uh it's
54:08not really you know i wouldn't probably
54:10consider them part of what i uh you know
54:14call mathematical finance
54:16uh there are models that say well uh you
54:17know they have certain
54:19uh security you know systems protection
54:21software right they have endpoint
54:23security uh they have they invested in
54:26uh
54:27i.t security they hired security
54:28analysts right so so there is actually a
54:30way to also model the likelihood of the
54:33hackers breaking into the service of the
54:35company there's no model to find out uh
54:38you know that will tell you that they're
54:39about to do it tomorrow
54:41so you don't know
54:42what the price will be tomorrow because
54:44there are a lot of things that control
54:46this price
54:47that you have no idea today about
54:50whether they are not they will happen
54:52right tweets from elon musk
54:54hackers doing something uh you know
54:56something changing in the world right so
54:58you know anything can happen
55:00so most market moving news are less
55:03dramatic than what i just described
55:05right but they're more frequent
55:06so uh they form a continuous stream of
55:08routine information about the company
55:10competitors economy as a whole
55:13all of which have power to more markets
55:14by convincing the investors to be more
55:17or less enthusiastic about buying
55:18company shares so in ours journalists
55:21write let's say about
55:23meta right all the time some people say
55:25this whole metaverse idea is crazy other
55:28people say no it's brilliant you know
55:30we'll say well maybe it's brilliant but
55:31will not make them any money
55:33so people are reading this news
55:35and each person who reads positive and
55:38negative articles will then be more
55:39likely to buy or sell
55:41so most of the news and not of course
55:43you know the hackers break into the
55:44company that's a huge trump
55:46uh if someone very important
55:49tweets something about the company it's
55:51a jump
55:52but most of the changes they happen like
55:55one investor for some tweet and others
55:56investors or other tweets or some news
55:58stories so all of it you know most of
56:00this happens in a very small increments
56:02right
56:03and in mathematical models of the stock
56:05market
56:06i see there is a question i'll answer in
56:07a second
56:08uh mathematical models in mathematical
56:10models of the stock market market moving
56:12news
56:13are represented as random noise right
56:16and any successful model of
56:18financial markets can be only stochastic
56:22stochastic means a moral difference
56:23random noise
56:24by definition right and non-stochastic
56:27technical analysis based on chart
56:28patterns do not work and it will fail
56:30you right so so i want to be very clear
56:32that uh
56:33that uh you know there's this head and
56:35shoulders and people like look at charts
56:37and they say oh you know it formed a
56:38particular pattern
56:40all of it is wuru
56:42you know it's like uh you know we always
56:44can uh
56:45you know stare at it and think that you
56:47can see some pattern it's just random
56:49right so you can close a coin
56:51draw your outcomes and it will also have
56:54this head and shoulder it will mean
56:55nothing right so so what works
56:58is statistic and modeling statistics and
57:01modeling probabilities
57:02modeling outcomes or predicting outcomes
57:04does not work
57:05because we don't know what the news are
57:08so
57:09uh in a stock market right and uh you
57:12know first of all the first ingredient
57:14of a stochastic model is a daily drift
57:17right
57:18so if you have a stock price
57:20it will be it's the expected daily
57:22change rate of change average over
57:24multiple days
57:25so again so this is not the predicted
57:27change this is the average change
57:29in the stock with positive drift can
57:31still move down the next day right on
57:33average it will move up a little bit
57:35more
57:36so
57:37if the history is of daily moves right
57:39it's drawn in this chart you can see
57:41that the red line right is slightly
57:44so the red line is zero right and you
57:45can see that that this is like slightly
57:48above the average
57:49that's right the average of this uh bars
57:51up and down
57:56sorry the red line is the average of
57:58this blue bars
58:00and it's slightly away from zero but
58:02much less than this the daily move
58:06so the daily move in a stock
58:08is almost always much higher than the
58:10drift
58:11so the second ingredient and more
58:13important ingredient is the daily evolve
58:15of volatility right so financial you
58:17know people might finance and say well
58:19just to
58:20abbreviate
58:21daily volatility right so daily
58:22volatility is the average on every given
58:24day uh the magnitude of change may be
58:27smaller or large again it's not a
58:28gaussian process it's not a you know
58:30winner process
58:32necessarily it's a random process
58:34in a third and final ingredient of a
58:36stochastic model is correlation right
58:37it's a measure of whether different
58:38stocks move mostly together or mostly
58:40independently
58:42this is only required for models with
58:43multiple stocks and it varies from plus
58:46to minus one
58:48uh i will now answer the question is it
58:50possible to predict the stock price in
58:52the very short run
58:53going to zero using time series analysis
58:56okay so again it's not possible to
58:58predict with certain chair you can only
59:01predict the probability distribution
59:03and in some cases it's very wide
59:06in some cases it becomes more narrow
59:08there is something called high frequency
59:10trading
59:11in which the speed of light is actually
59:13something that people talk about as
59:14being a delaying
59:16you know thing that really is very slow
59:19and the
59:20speed of this algorithms is on
59:22microseconds there's a whole area you
59:24know about how to build programs that uh
59:26make decisions on microseconds
59:28in there you can kind of be more certain
59:30about where the price is going right but
59:32also it's very expensive to run these
59:33programs
59:34generally you cannot predict you don't
59:37know what elon musk will tweet tomorrow
59:39or you know what what else will happen
59:40in the world
59:41so you can only predict probabilities
59:44and even that is not completely accurate
59:46you cannot predict the price in the
59:48short run long run doesn't matter
59:50uh and even in high frequency trading
59:53they still work with probabilities
59:55all right so uh now relative size of the
59:58valuable right so uh the more thing to
1:00:00understand is that daily drift is always
1:00:01much already mentioned like much smaller
1:00:03than daily wall right so even if we
1:00:05correctly estimate the drift uh sorry
1:00:08second one my follow-up question
1:00:10uh can we add to the model the
1:00:12correlation with the market role yes so
1:00:14yeah in a lot of cases you actually
1:00:16don't want to model like you stick with
1:00:17each other you model the stock with the
1:00:19market the world and that's called the
1:00:20beta so a very good question actually
1:00:23that's one of the standard ways to
1:00:24measure correlation correlation of the
1:00:26stock the market will beta equal one
1:00:29uh well it's very it's a correction
1:00:31correction it's not um
1:00:33it's not really the correlation
1:00:34correlation is part of it uh but uh
1:00:37and you know i probably should discuss
1:00:39it in the next lecture but it's be more
1:00:41specific to
1:00:42the slides uh but uh yeah so
1:00:45the correlation with the market overall
1:00:47is a good way to measure correlation
1:00:49when you have a lot of stocks
1:00:50and there are too many correlations so
1:00:52which talk with each other so it's a
1:00:53it's the right way it's not exactly the
1:00:56beta but it contributes to beta
1:00:59uh and i'll in one of the next lectures
1:01:02i'll discuss it further
1:01:04the trader who buys a stock uh winners
1:01:06positive drive where's quality of drift
1:01:07and sells the stock when it's negative
1:01:09jet will not see much difference between
1:01:10the strategy of buying and selling
1:01:11randomly
1:01:12right because mostly it's a random part
1:01:15so that's you know how the stock
1:01:17distribution versus drift right so the
1:01:19drift
1:01:20is a red dash line it goes slightly up
1:01:23right but each individual what's called
1:01:25a path when you simulate right the
1:01:26market you simulate
1:01:28uh sometimes the slow goes up sometimes
1:01:30so it goes down or you can think about
1:01:32this as different time intervals so
1:01:34different stocks so uh
1:01:37the random part is much bigger than the
1:01:38systematic part
1:01:41and diversification means splitting your
1:01:43investment across a large number of
1:01:44securities instead of buying one or
1:01:45several
1:01:47and
1:01:48when you do that it protects against
1:01:50what's called concentration risk right
1:01:51so the risk of putting all eggs in one
1:01:53basket
1:01:54because without diversification even the
1:01:56most skilled trader will become a victim
1:01:58of completely unexpected events such as
1:02:00a hurricane
1:02:01terrorist attacker and something like
1:02:02that
1:02:04it's less obvious but being proven with
1:02:06stochastic method properly diversified
1:02:08portfolio will also reduce the
1:02:09randomness in investment strategy
1:02:11performance caused by the level
1:02:13you have to do it properly in fact
1:02:15sometimes you have to buy one smoke and
1:02:17sell the other if they're negatively
1:02:18correlated but diversification with
1:02:22mathematical finance models
1:02:24you know it was not just buying a bunch
1:02:26of stocks and hoping that they will all
1:02:27uh
1:02:29if you just buy basically 10 different
1:02:31stocks it will reduce your risk somewhat
1:02:33but if you use mathematical finance to
1:02:35compute the weights that are optimal you
1:02:37can do it even better
1:02:39in this case you can reduce the random
1:02:41part
1:02:42improve the systematic part
1:02:44and make your investment performance
1:02:46more predictable and less random
1:02:49and uh
1:02:50once the randomness is reduced then the
1:02:52effect of correctly estimating the drift
1:02:54becomes more evident right
1:02:56but in order to do that it also
1:02:58increases transaction cost because every
1:03:00time you buy a stock it costs money
1:03:03and if you buy and sell a lot of stocks
1:03:05in order to diversify it costs even more
1:03:07money
1:03:08and
1:03:09if you are professional
1:03:11you actually pay a lot less than if
1:03:13you're a retail investor so a lot of the
1:03:15strategies that i'm talking about if
1:03:17you're a bank or an investment manager
1:03:19you can do it because once you trade in
1:03:21large enough volume
1:03:23the brokers and banks you know they
1:03:26they will
1:03:27not charge you a lot for buying and
1:03:28selling and your performance will not be
1:03:31affected by this if you're an individual
1:03:33investor you pay more even on an
1:03:35electronic
1:03:37platform
1:03:38and a lot of the strategies will simply
1:03:39not work just because you'll spend all
1:03:41the money on fees for buying and selling
1:03:45all right so now uh
1:03:48fixed income securities so we have uh 20
1:03:50minutes in our schedule
1:03:52talk
1:03:53and during this time uh we'll talk about
1:03:55the other part of securities rights uh
1:03:58you know if you invest in stock
1:04:00or rather if you would like to
1:04:02financially participate in a company you
1:04:04can lend money
1:04:06to the company or you can take
1:04:07fractional ownership
1:04:09fractional ownership is similar to
1:04:11stocks but stocks are standardized
1:04:14fixed income securities or debt
1:04:16is similar to fractional ownership of a
1:04:19loan to the company
1:04:21right so
1:04:23first part is introduction to bonds
1:04:25right so bonds are future payments
1:04:28promised by two market participants who
1:04:31invest in bonds or bondholders
1:04:34so bonds of financial instruments
1:04:35providing fractional ownership with the
1:04:36company public debt
1:04:38so garb corporational government becomes
1:04:40a debt issuer by borrowing from a debt
1:04:42investor and promising to repay the
1:04:44money in cash with interest
1:04:47unlike stock shares fractional ownership
1:04:48of debt does not give any economic
1:04:50rights with respect to the company
1:04:51itself right so you cannot make money
1:04:54when the company is sold
1:04:56you cannot vote for the board of
1:04:57directors
1:04:58only it gives you only the right to be
1:05:00repaid
1:05:01in public that means that this
1:05:03fractional ownership price can be bought
1:05:05or sold without the approval of the
1:05:07depth issue with public records sales
1:05:08prices
1:05:10so and that's what makes them publicly
1:05:11traded securities in our public debt
1:05:14means it's
1:05:16fundable
1:05:17it's negotiable right so
1:05:19each bond is the same as any other
1:05:21negotiable meaning uh
1:05:23you know you don't need permission to
1:05:25buy or sell uh you can sell by insult to
1:05:27anyone
1:05:28and there is a price record
1:05:30and that makes it different from loans
1:05:31right so loans are
1:05:33typically have a whole ownership of a
1:05:36particular loan
1:05:37sometimes it's fractional but it's more
1:05:39air
1:05:40and loan terms are private when bonus
1:05:42terms are public rights and you don't
1:05:43trade loan on exchange even though again
1:05:45so sometimes there are some indirect
1:05:46ways to do that but
1:05:49is outside this uh scope of the lecture
1:05:52right now the bond types uh first of all
1:05:55uh you know there's a principle of phase
1:05:56value of the bond right which is the
1:05:58amount of money obtained by the issue
1:06:00when the bond is first created
1:06:02a bond makes regular interest payments
1:06:04until and including the maturity date
1:06:07and maturity the principal is returned
1:06:09to the bondholder along with the last
1:06:11interest payment
1:06:13for a fixed rate bond
1:06:14the amounts of periodic interest
1:06:16payments are set were fixed in advance
1:06:18and now illegal
1:06:20for floating rate bond the amounts of
1:06:22periodic interest payments are
1:06:23calculated closer to the time the
1:06:25payment is made
1:06:27based on prices of other securities
1:06:29right so nowadays
1:06:31rate bond you say for the next 30 years
1:06:33i will be receiving five percent of the
1:06:35amount i i lent per year
1:06:39floating rate bonds it says that
1:06:41whatever the uh
1:06:43interest rates are
1:06:45at the time
1:06:47i will be receiving that interest rate
1:06:48plus a spread
1:06:50right let's say one percent
1:06:53the spread is because
1:06:54you know if we comparing to government
1:06:56securities
1:06:57lending to cooperation
1:06:59is more risky they may go bankrupt and
1:07:01not pay back
1:07:03so normally people ask for a spread over
1:07:06the government rate at the time but
1:07:08floating rate bond you don't know the
1:07:09percentage until it's later
1:07:12quick question this one actually was one
1:07:14of the formal polls but what do you
1:07:16think is more risky to invest in fixed
1:07:18rate bond to floating rate bond
1:07:20anybody who thinks in a fixed rate bond
1:07:22is more risky raise your hand
1:07:26nicer how many
1:07:29uh just two three two three okay who
1:07:32thinks floating is more risky
1:07:38more yeah a lot more yeah like 12 13
1:07:41okay well it's the other way around okay
1:07:43it's very interesting thing right
1:07:45uh or rather it depends what you compare
1:07:46to right floating floating rate is less
1:07:49risky because you're not making any bet
1:07:52for 30 years ahead if it's a 30-year
1:07:54bond
1:07:55in other words you have money you can
1:07:57always invest it in the market and
1:07:59whatever the percentage you can put it
1:08:00in bank and we'll pay a percentage right
1:08:02you can buy some short-term securities
1:08:04for paying a percentage
1:08:05if you're agreeing to investing in a
1:08:07floating rate bond that pays you the
1:08:09rate in the market every month plus a
1:08:12spread
1:08:14you only you're not taking much risk
1:08:16compared to
1:08:17not doing the investment right if you
1:08:18did the investment you're getting
1:08:19floating rate plus spread
1:08:21if you didn't
1:08:23you would get floating rate itself or
1:08:26maybe another company floating around
1:08:27press spread right or
1:08:29you can you know sell this bond buy
1:08:31another bond so floating rate bond
1:08:34changes price a lot less and is less
1:08:36risky compared to just investing the
1:08:38money in the market
1:08:40whereas fixed rate bond is hugely risky
1:08:42because for example a couple years ago
1:08:44interest rates were almost zero in
1:08:47dollar and euro
1:08:48so you could actually buy a bond that
1:08:51will pay you people are buying bonds
1:08:53that would pay them tiny tiny interest
1:08:55rates like fractional percent
1:08:57now inflation is here
1:08:59uh wonderful central bankers printed too
1:09:02much money
1:09:03and interest rates are going up so now
1:09:05of course you don't want to buy the bond
1:09:07to this euro right you can just go to a
1:09:09bank and get more interest or
1:09:11invest in an open market
1:09:13so someone who two years ago bought this
1:09:15bond
1:09:16at almost your interest rate lost a lot
1:09:19of money because this bond is now worth
1:09:21a lot less than its price right you know
1:09:23because it's no longer a good investment
1:09:25so actually fixed rate bond is
1:09:26interestingly enough is more risky right
1:09:28floating
1:09:29is less right just because you can what
1:09:31you're comparing to
1:09:33what you're comparing to right here
1:10:03did i get disconnected earlier
1:10:06yes
1:10:07for like four seconds
1:10:09okay good yeah so i hope you didn't miss
1:10:10anything uh
1:10:12apologize for that right so let me share
1:10:14the screen again
1:10:16uh okay
1:10:18i'm not sure just uh
1:10:20i hope the internet
1:10:23doesn't fail us anymore right so um okay
1:10:26so
1:10:27now they consider a fixed-rate bond with
1:10:29one year maturity a hundred dollar
1:10:31principal and quarterly coupons of one
1:10:33percent each
1:10:35to become a bondholder
1:10:37uh the buyer pays the issuer 100
1:10:40dollar principle
1:10:42issuer then pays the bondholder one
1:10:44percent of a hundred dollars
1:10:45one dollar each quarter
1:10:47so the last payment to the bondholder is
1:10:50combined with a hundred dollar principal
1:10:52repayment and unlike a stock
1:10:55after maturity the bond is
1:10:57distinguished disappears right so stock
1:10:59does not
1:11:00get don't disappear
1:11:02but the bond uh does right it has a
1:11:05maturity there are some actually
1:11:07perpetual bonds
1:11:08called the console straight but
1:11:10not a lot of time exist
1:11:12so
1:11:13uh
1:11:14the first payment goes
1:11:16from bondholder to issue
1:11:18here green era
1:11:20all of the other small payments interest
1:11:22go to the bondholder
1:11:24and then at the end the bonehold gets
1:11:26the money back plus the last interest
1:11:28payment
1:11:30accrued interest
1:11:32uh so bondholder accumulates interest
1:11:34continuously but resist receives
1:11:36payments periodically
1:11:38so if a crude interest was not
1:11:39considered when the bond is sold
1:11:41the price of the bond would drop by one
1:11:43dollar after each interest payment
1:11:46but because such price drops could lead
1:11:48investors to think something bad
1:11:49happened to the issuance that they
1:11:51accumulated uh or crude interest but not
1:11:54yet paid interest is subtracted from the
1:11:56bond price when the bond is sold right
1:11:58just so the price is more continuous
1:11:59otherwise you continuously have to look
1:12:01at well the price jump
1:12:03you jump because of the payment or
1:12:04because something happened right so it's
1:12:06much easier if it doesn't jump because
1:12:08of the payment in this case the price
1:12:10does not jump on interest payment dates
1:12:13and price pay movements are easier to
1:12:15analyze in ours when you sell the
1:12:17company one day before the payment
1:12:19you receive almost all of them so you
1:12:22know if you sell it between the two
1:12:23payments
1:12:24the buyer gets half of the accrued
1:12:26interest
1:12:27the seller gets the other half
1:12:29if you sell one day before the payment
1:12:32the seller gets
1:12:33all of this interest except one day one
1:12:36day after the payment
1:12:38all of the interest including the
1:12:39payment right which means that there's
1:12:41no jump
1:12:43so what are the bond price models right
1:12:45so first of all is the bond price today
1:12:47the sum of future bond payments well no
1:12:50right first of all um
1:12:52dollar in your pocket today is worth
1:12:54more than a dollar that you'll receive
1:12:55one year from now right so it's discount
1:12:59second reason is that company or
1:13:01government may go bankrupt
1:13:03and not pay back to the bondholder this
1:13:05is called credit risk
1:13:08when there is a buyer concern that the
1:13:10you know the buyer may need to sell the
1:13:12bond before maturity
1:13:14the price may be lower because traders
1:13:16prefer certainty to uncertainty right so
1:13:18this is called the market price of risk
1:13:20so again
1:13:22why is the bond price not the same less
1:13:25than the sum of future payments
1:13:27first of all because dollar today is
1:13:29worth more than dollar in the future
1:13:32dollar
1:13:33an infinite amount of time in the future
1:13:34is worth zero right because you never
1:13:36see it
1:13:37second you may not get get paid create
1:13:39risk
1:13:40third thing is very important to
1:13:42emphasize right it's not the same as the
1:13:44other two right so sometimes it's
1:13:45confused it's not the same
1:13:47it's another reason the price is reduced
1:13:49because of uncertainty right so
1:13:52if
1:13:53you invest in bond the price of bond is
1:13:55not equal to the sum of the future
1:13:57payments
1:13:58may go up or down
1:14:00and just because it may go up or down
1:14:02that already makes it price less than
1:14:04the amount of money you expect to get
1:14:07and this is called the market price of
1:14:09risk
1:14:10the riskier it is unless you're a
1:14:12gambler in a casino right
1:14:14you don't want risk
1:14:16in fact
1:14:17people in investing in markets on
1:14:19average are risk adverse they don't like
1:14:20risk they have to be paid for risk right
1:14:22if something is risky they pay less
1:14:24money for it
1:14:25in a casino it's exact opposite right so
1:14:27basically you take your certain money
1:14:29and
1:14:29you know
1:14:31hope for a small probability of a huge
1:14:33one
1:14:35price discovery in markets is collective
1:14:37right so when market clearing price when
1:14:39buyers
1:14:40match sellers right same number people
1:14:42want to buy and sell at that price
1:14:44on average traders are risk averse
1:14:47some people are crazy
1:14:49and they're risk-seeking
1:14:51right or pricing one quote right so
1:14:52there is seeking most people are risk
1:14:54averse and what matters in the market
1:14:56for price setting is the average
1:14:58right
1:14:59and uh the um um uh and the
1:15:05sorry one second um am i still online
1:15:07four all good yeah okay
1:15:10yeah so um uh so uh
1:15:13uh so uh
1:15:15on average market participants prefer a
1:15:18certain dollar
1:15:21to a certain let's say dollar and one
1:15:23cent right so somewhere there there's a
1:15:24balance of how much extra money they
1:15:26would be willing to take for risk so
1:15:28that's a separate
1:15:30thing from the other three
1:15:31and finally there is a lost thing right
1:15:33like four reasons why you know the price
1:15:35of bond is reduced right liquidity risk
1:15:37and the reason is that even if there is
1:15:39uh you're selling at the price that
1:15:41fairly takes into account discounting
1:15:43credit risk in market price of risk
1:15:46if
1:15:47buyers don't show up every day it's a
1:15:49you know it's a bond that maybe uh you
1:15:50know not a lot of people know about the
1:15:52company
1:15:54and let's say buyers maybe show up and
1:15:56want to buy once a month
1:15:59this actually reduces the price because
1:16:00what if you need money suddenly right
1:16:02what if you need money today
1:16:03and you have to wait for a month to find
1:16:05a buyer
1:16:06that's called liquidity risk or
1:16:07sometimes
1:16:09there are buyers but if you invest in a
1:16:11billion dollars of that bond right you
1:16:13may not find enough buyers right you you
1:16:16you it may take you a long time to sell
1:16:18your position
1:16:19but
1:16:20if another investment offers you the
1:16:22ability to get the money immediately you
1:16:24will pay more for this other investment
1:16:26so there are four things that reduce the
1:16:27bond price compared to
1:16:29uh compared to we changed upon price
1:16:31rather so you know compared to
1:16:34uh the sum of names right so we'll study
1:16:37the first tool
1:16:38uh
1:16:39in the first in this lecture
1:16:42uh the next in in the following lectures
1:16:45okay so now let's look we have to do it
1:16:47quickly because i still have six slides
1:16:49left and i have seven minutes
1:16:51so when is the bond price equal to its
1:16:53principle right
1:16:55so principle is this hundred dollars
1:16:58answer number one
1:17:01never
1:17:02answer number two so let's do it never
1:17:05let's just raise the hands ready raise
1:17:07your hands who think just never
1:17:10just two people
1:17:12two people
1:17:13first only once on the day the bond is
1:17:15issued
1:17:18just one
1:17:19one on the day the bonus matures
1:17:25four
1:17:26five okay
1:17:27right on both of these days but not the
1:17:29rest of the time
1:17:32three
1:17:33three okay and all the time
1:17:37no
1:17:38three four
1:17:40someone is hesitating
1:17:42come on guys
1:17:43the previous slide was specifically
1:17:45about five not being the answer
1:17:48so okay so four reasons right
1:17:50why the price is not the sum of future
1:17:52bond papers
1:17:53so
1:17:54five is definitely not the thing here
1:17:58one two three or four
1:18:00okay
1:18:01the answer is
1:18:04four
1:18:06so a bond price is like a broken clock
1:18:08that shows correct time twice a day
1:18:10right so the bond price is equal to the
1:18:12principal twice
1:18:13first on the issue date and actually
1:18:16that's kind of it was not a very fair
1:18:17question because uh
1:18:20it was clear from the previous
1:18:21explanation that on the maturity data
1:18:24will be equal to um to the principle
1:18:26right
1:18:27but on the first date that's because the
1:18:29bond
1:18:30percentage right so in a normal bond the
1:18:33company will uh set the percentage rate
1:18:36such that the market clearing price
1:18:40for the bond only start date is equal to
1:18:43the principal
1:18:44so in other words if the bond is selling
1:18:46uh you know companies selling a bond
1:18:47today they will say you know we will pay
1:18:49three percent
1:18:50and
1:18:51you buy the bond at the principal
1:18:53hundred dollars and the company says the
1:18:55percentage such that this hundred
1:18:57dollars equal to the principal is the
1:18:58market clearing price so on the issue
1:19:00date is by choice of the issuer so the
1:19:03the company by convention they could
1:19:05actually do something else right but
1:19:06companies by convention sell they bond
1:19:09on the first day at the at the nominal
1:19:11amount 100 dollars they said the
1:19:13interest rate such that the nominal is
1:19:15the market clearing price
1:19:17so it's not
1:19:18it's the is the choice right as opposed
1:19:20to something that happens automatically
1:19:22now on maturity date that's actually not
1:19:24the choice because it will always happen
1:19:26when one day before maturity the crude
1:19:28interest goes with the old holder
1:19:32so if you sell the bond price on the day
1:19:34before maturity
1:19:35you only get the principal there is this
1:19:38last interest payment remember right uh
1:19:40where's it
1:19:41um
1:19:43okay well i don't want to look for the
1:19:44slide
1:19:45so um uh so
1:19:48there was this uh you know drawing in
1:19:50the beginning where you saw like the
1:19:51principle on the last day and the
1:19:52interest thing is uh if you wait until
1:19:55the last day all of this interest will
1:19:56be accrued to the seller
1:19:58so if you are buying the bond
1:20:01one day before the principal or on the
1:20:03day of the maturity
1:20:05the interest last interest payment will
1:20:07go to the seller right unless you you
1:20:08will not buy it with the bond rate it
1:20:10will be left for the seller you're only
1:20:12buying the principal
1:20:14so in maturity is by
1:20:16design of the bond
1:20:19at issue
1:20:20by choice that's how companies set the
1:20:22interest rate so the market printing
1:20:23price is the principal so it's like a
1:20:24broken call basically you know the bond
1:20:26price is equal to principal twice
1:20:29of course it may randomly like cross the
1:20:31you know the 100 line right so it may
1:20:33randomly you know just uh
1:20:35happen but normally it kind of goes up
1:20:37and then comes down and goes down comes
1:20:38up right so if the interest rates go up
1:20:40bond price
1:20:42goes down
1:20:44because
1:20:44there is a better investment opportunity
1:20:46in the future so the less incentive to
1:20:48buy the bond
1:20:50uh and vice versa right so that's how it
1:20:52looks
1:20:54all right so now what are discounted
1:20:56survival curves
1:20:57i will probably run by about five
1:20:59minutes
1:21:01but probably not more than that
1:21:03so
1:21:04uh discount curve
1:21:07is mathematical representation of the
1:21:09time value of money so that's the first
1:21:11thing about dollar today being worth
1:21:14more than a dollar in the future
1:21:16so dollar today is worth less uh sorry
1:21:19the rule of one year from now is worth
1:21:20less than dollar today because during
1:21:21this year you can invest you can do
1:21:23something with a dollar right you would
1:21:24rather have dollar today than one year
1:21:26from now
1:21:27you could use the dollar during the year
1:21:29right
1:21:30the amount is worth today the amount one
1:21:32dollar
1:21:34the amount if you 100 sure somebody will
1:21:36give you a dollar one year from now
1:21:38the amount is worth to you today is
1:21:40called the discount factor
1:21:42would you rather have a dollar in a in a
1:21:44year from now or 90 cents today
1:21:47if they are the same to you
1:21:49discount factor is 0.9
1:21:52and that's again is the collective view
1:21:54of the market on a time value of money
1:21:57if investors see castles in the air they
1:22:00think that there are a lot of investment
1:22:01opportunities then discount factor is
1:22:03very small right if they think that they
1:22:05basically banks bank you know 10
1:22:08interest
1:22:09tons of future amazons around investor
1:22:12if people are pessimistic about
1:22:15investment apprentice ranges
1:22:17then this contract is about one that's
1:22:19why interest rates were actually
1:22:22zero or even negative
1:22:24um uh you know in the recent past
1:22:26because um the
1:22:28people were pessimistic about the
1:22:30economy and the central banks were
1:22:31trying to make them optimistic but they
1:22:33were what others were trying to
1:22:35say correction trying trying to match
1:22:38what people think rather
1:22:40all right so now survival probability
1:22:42right so
1:22:43a payment a year from now that may not
1:22:45happen if the company goes bankrupt is
1:22:47worth smaller
1:22:48than the amount that's guaranteed
1:22:50right so again so we're talking about
1:22:52two amounts a year from now otherwise
1:22:54for the discount factor
1:22:56one payment heat
1:22:58and other payment that will not happen
1:23:00the company goes bank
1:23:02now the question
1:23:04if the company let's say uh has some you
1:23:07know around 10 probability of default of
1:23:09not being around um you know a year from
1:23:12now
1:23:13then a guaranteed sorry then a dollar
1:23:16from that company one year from now will
1:23:19be worth the same as 90 cents
1:23:21that you know you will get but also a
1:23:23year from now
1:23:25so we're not mixing the two right so
1:23:27we're not changing the times here which
1:23:29is changing the certainty
1:23:31so
1:23:32market implies survival probability of
1:23:34the company is 90
1:23:37if you would rather have or if if 90
1:23:40cents guaranteed is equal to you in
1:23:42value to
1:23:45a dollar from that company
1:23:46both one year from now but one will not
1:23:49happen if the company is bankrupt and
1:23:51other will happen anyway
1:23:54in market implied means it's based on
1:23:56investor news not the actual probability
1:23:57of company survival right
1:23:59so we'll use survival probability here
1:24:01but again so market implied just is too
1:24:03long to pronounce so in math finance
1:24:05people admit it but it's really always
1:24:07been implied
1:24:09the
1:24:10market implies overall probability that
1:24:12you measure like right you compare
1:24:14basically you determine
1:24:16price
1:24:17uh for this dollar that may not happen
1:24:20compared to the dollar that will happen
1:24:22with certain
1:24:24it's actually
1:24:25a lot
1:24:27uh okay
1:24:28now it's uh complaining
1:24:30connection again hopefully it'll work so
1:24:33the
1:24:34price
1:24:35is a lot less
1:24:37than the actual probability of default
1:24:39said third thing market price of
1:24:42risk right so now it's when we're
1:24:45bankrupt
1:24:46people who are risk at work not only
1:24:49they take into account the actual
1:24:51probability of going bankrupt
1:24:53but also
1:24:54they're so afraid to look
1:24:56even more they're so conservative they
1:24:58can uh you know make mark probability
1:25:01higher
1:25:02um
1:25:04market applied probability of
1:25:06kite and dashboards or survival lesson
1:25:08naturally is
1:25:09so it's not just the it's basically it's
1:25:11like the wolf is right and the fear is
1:25:13like that big
1:25:15secret survival probability is a lot
1:25:17less
1:25:18than actual
1:25:20probability of default right
1:25:22if people are pessimistic it's very
1:25:24small if people optimistic it's almost
1:25:26one right
1:25:28it can never be more than one because
1:25:29you know basically
1:25:31you know companies either bankrupt or
1:25:32not so there is no think uh such thing
1:25:34as unbankrupt right
1:25:36okay unless it was already in the
1:25:38beginning uh in background should come
1:25:39out anyway this will be on the scope of
1:25:42this lecture all right so a couple more
1:25:43slides uh so uh
1:25:46both of these curves depend on time
1:25:48right
1:25:49because discount factor time value of
1:25:52money the longer in the future the less
1:25:54value it is today
1:25:56right so it's decreasing function of
1:25:57time
1:25:59so well probability the longer in the
1:26:01future
1:26:02the more likely it will go bankrupt
1:26:04right so even the best company can
1:26:05eventually go bankrupt you know the
1:26:07company making buggy whips
1:26:09using the example from a great movie
1:26:11called other people's money
1:26:14right and uh you know that that by the
1:26:16way is a movie about someone who was in
1:26:17this engagement fundamental analysis i
1:26:20highly recommend this movie uh you know
1:26:22if you want to learn about fundamental
1:26:24analysis
1:26:25so in this movie the company was worth
1:26:28on the market less
1:26:30than the
1:26:32value of land on which the factory was
1:26:34so he wanted to buy the company and just
1:26:36raise the factory and sell the land
1:26:38so that's just shows what fundamental
1:26:40analysis way fundamental analysis is
1:26:41still useful right
1:26:43so uh
1:26:45a company making buggy whips
1:26:47may look good today if you're in the
1:26:4919th century
1:26:51but you'll say well you know what maybe
1:26:53somebody will invent automobile or maybe
1:26:55a dirigible or some other form of travel
1:26:58and i don't know if 200 years from now
1:27:01the company making buggy whips will be
1:27:02doing well and of course it won't
1:27:05uh well you know if it became louis
1:27:07vuitton right started making uh you know
1:27:10suitcases for coaches right and now they
1:27:12sell luxury because they still did well
1:27:13but most of the companies uh selling
1:27:15things around horses went out of
1:27:17business
1:27:18so
1:27:19the longer in the future the more likely
1:27:21it is that the company will not make it
1:27:24so surreal probability also reduces a
1:27:26function of time so that's how they look
1:27:27right so and they're different right
1:27:29these are two different things
1:27:31so price discovery for bonds versus
1:27:33stocks right so stocks are independent
1:27:34from each other because they're issued
1:27:35by different companies
1:27:38a single company of government usually
1:27:39would take multiple bonds traded at the
1:27:41same time so they sell some debt
1:27:4410 years from now before nine years
1:27:46before eight years before all of these
1:27:48bonds are different bonds they have
1:27:50different percentage rate
1:27:51they have different time to maturity
1:27:53because the for example if the issue
1:27:55born for 30 years
1:27:57if the issue 10 years ago it has 20 to
1:27:59go
1:28:00if they issued eight years ago it has um
1:28:03you know 20 22 years to go
1:28:05so all of these bonds have different
1:28:07maturities and percentage rates but they
1:28:09share the same discount factor and soil
1:28:10probability
1:28:12so mathematical finance tells us the
1:28:14relationship of the prices with each
1:28:15other
1:28:16in the next lecture
1:28:18we will study how to find relationships
1:28:20between bond prices
1:28:21based on this curve
1:28:23okay so this concludes the lecture uh as
1:28:26i predicted we're all run by exactly
1:28:28five minutes that's actually the same
1:28:29five minutes that we spent in the
1:28:30beginning um
1:28:32uh you know waiting for people to train
1:28:34so i would like to ask uh for just a
1:28:37quick question so please type in a chat
1:28:39uh
1:28:40and my colleagues will um
1:28:43answer or tell me about the questions
1:28:45let's spend a couple of minutes
1:28:46and then we will uh
1:28:49disconnect until the next lecture
1:28:52uh at the same time on thursday of this
1:28:54week any final questions and of course
1:28:57just a question about the movie
1:29:00okay same movie you mentioned
1:29:02they need the vito other people's money
1:29:05uh by the way
1:29:07i don't condone what condone what he was
1:29:09doing he was basically taking a company
1:29:11and uh
1:29:12uh trying to uh sell it you know and um
1:29:15and uh this is uh from from another
1:29:18movie actually there's a great phrase
1:29:19you know basically like uh
1:29:21there is a there's
1:29:22a pretty woman movie with richard gere
1:29:25right and um julia roberts
1:29:27so he explained what he was doing and
1:29:29she said ah you're like the guy who is
1:29:31stealing cars and selling them for parts
1:29:32which is the same thing as the guy danny
1:29:34devito and other people's money was
1:29:36doing
1:29:37so uh
1:29:39there are a lot of people who
1:29:41see castles in the air
1:29:43and they make money by
1:29:45puncturing them right
1:29:47so they say well you know what i mean
1:29:49this is not realistic so so a lot of
1:29:51people who use fundamental analysis
1:29:54in order to um
1:29:56in order to
1:29:57make you know make money by basically
1:30:00exploiting the disconnect between the
1:30:01reality
1:30:02and what people think something is worth
1:30:05and sometimes the illusion lasts so long
1:30:07that they lose money
1:30:08and sometimes this is proven wrong
1:30:10because the company becomes uh amazon uh
1:30:13and nobody thinks they would or you know
1:30:14like apple right so apple almost went
1:30:16back from then they brought steve jobs
1:30:17back and he invented the iphone with a
1:30:19smart demon smartphone
1:30:21so uh it's also very good movie you know
1:30:24just generally and uh it tells you about
1:30:26how fundamental analyst analysis works
1:30:29and
1:30:29uh no spoilers but it all works out in
1:30:32the end so
1:30:33so uh you know we should uh watch it uh
1:30:36and uh learn about fundamental analysis
1:30:38uh in the in a very enjoyable way all
1:30:41right so uh
1:30:42if no other questions uh let's wrap up
1:30:44today
1:30:45uh
1:30:46next lecture on thursday
1:30:48and
1:30:49the following week the same time tuesday
1:30:50and thursday so four lectures in total
1:30:53one down three to go thank you

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This page contains the full transcript of Mathematical Finance: Securities and Models - Lecture 1 - Alexander Sokol - CompatibL by CompatibL, generated from the public captions YouTube serves with the video. The transcript has 15,756 words across 2,757 segments, with the original timestamps preserved so you can click any line to jump to that moment in the embedded player.

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