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visit MIT OpenCourseWare at ocw.mit.edu. JAKE XIA: This is the second
time we are having this class. We had it last year
in a smaller version. That was for six
units of a credit, and we had it once a week. And mostly practitioners
from the industry, from Morgan Stanley,
talking about examples how math is applied
in modern finance. And so we got some good
response last year. So, with the support
of the math department, we decided to expand this
class to be 12 units of credit and have twice a week. So, we have every Tuesday
and Thursday afternoon from 2:30 to 4:00, as you
know, in this classroom. So last year, Dr. Vasily
Strela and I-- by the way, I'm Jake Xia and
that's Dr. Vasily, and we were the main
instructors last year. Now we doubled it up to
four main instructors. That's Dr. Peter Kempthorne
and Dr. Choongbum Lee. The reason we doubled
up the main instructors is we have newly added math
lectures, mostly focusing from linear algebra,
probability to statistics, and some stochastic calculus
to give you the foundation to understand the
math will be used in those examples in the lecture
taught by the practitioners from the industry. And the purpose of
this course is really to give you a sampling menu to
see how mathematics is applied in modern finance and help you
to decide if this is a field that you would be-- RECORDED VOICE: Thank
you, for using WebEx. Please visit our website
at www.webex.com. JAKE XIA: OK, you heard that. And so hopefully, this will
give you enough information to decide this is a field
you would like to pursue in your future career. In fact, last year when
we finished the class, we had a few students coming
to work in the industry. Some work at Morgan Stanley,
some work at elsewhere. So that's really the goal. And at the same
time, obviously, you will further solidify
your math knowledge and learn new content. And we put the prerequisite
about the math part a bit later. So I will use today's
first lecture's time to give you an
introduction, really, to prepare you some basic
background knowledge about the financial markets. Some terminologies
will be used, which you may not have heard before. So before I get into
the introduction, I always like to know who are
actually in the classroom, so let me ask you
a few questions. You just need to
raise your hands so I know roughly what kind of
background and where you are. So how many undergraduate
students are here? So I would say 80% percent. How many graduate students
are here, just to verify? Yep, that's about right, 20%. And how many students are in
finance and business major? Just one. And how many of you
are a math major? Most of you. How many of you are
engineering majors? A few. How many of you actually
are from other universities? Great, because last
year we had quite a few, so I want to
specifically tell you that you're very welcome
to attend the classes here. So it's open door. And last year I remember
we had a couple of students from Harvard. That's where I actually
work right now. I forgot to mention
that, but I'm affiliated with both the math
department and the Sloan school here. So anyway, thanks for that. We will be doing a bit
more polling along the way, mainly to get feedback of
how you feel about the class. Last year we had it
online, so if you feel the class is
going too fast, or the math part
is going too slow, or the finance part
is a bit confusing, the easiest way is
really just to send us emails, which you will find
from the class website. So anyway, today-- VASILY STRELA: And all
of us got MIT emails. JAKE XIA: Yes. We all have MIT emails, which
are listed on the website. VASILY STRELA: [INAUDIBLE]. JAKE XIA: And obviously,
we have offices here. You can easily stop by Peter
and Choongbum's offices. And Vasily and I probably
will be less often on campus, but we'll be here quite often
and definitely love to be more. So anyway, I will start
today's lecture with a story, and a quiz at the end. Don't worry, it's
not a real quiz. Just going to ask
you some questions you can raise your hand
and give your answer. But let me start with my story. This is actually
my personal story. I want to tell you why
I tell the story later. But the story actually
was in the mid '90s. I just left Salomon Brothers
-- that was my first financial industry job -- to go to Morgan
Stanley in New York to join the options trading desk. So the first day, I sat down,
I opened the trading book, I found something was missing. So, I turned around,
I asked my desk quant. I said, where is
the vega report? So, let me show you. So that's the story. So I'm obviously not going
to tell you the story of Pi or "Life of Pi." That's not a financial story. The rest of the story,
alpha, beta, delta, gamma, theta, which you will learn
from Peter and Choongbum and Vasily's classes. So I'm going to talk about vega. So by the way, before
I tell you the story, what's unique about
vega on this list? AUDIENCE: It's not
a Greek letter. JAKE XIA: It's not
a Greek letter. That's right. So I turned around and
asked my desk quant, I said, where's the vega report? But how many of you actually
know what a vega is? OK, lot of people know. So anyway, I'm not
going to-- just for the people who haven't
heard about it before, it's a measurement about
a book or portfolio or position's sensitivity
to volatility. So, what is volatility? Which again, you will learn
more in rigorous terms how it's defined in mathematics. But the meaning of it is really
a measurement or indication of how volatile, or what's the
standard deviation of a price can change over time. That's all you need
to know right now. I'm not going to ask
you questions later. So my desk quant
look at me, said-- this is supposed to
be options trading desk, so he look at me puzzled. So instead of
answering my question, he handed over me
a training manual for new employees
and new analysts. So I opened the training
manual and looked it through. I actually found my answer. So actually, at Morgan Stanley
this is not called vega, it's called kappa. So now, I remember
to call it kappa. Kappa is actually
a Greek letter. So further, I look
on the same page there was actually a
footnote, which I copied down. So the footnote about why it's
called kappa at Morgan Stanley. Kappa is also called vega
by some uneducated traders at the Salomon Brothers. That's where I came from. I just joined. They have mistaken
vega as a Greek letter after gambling at Vegas. So anyway, so that
was my first day. So obviously, I learned
how to call kappa very quickly, because I
came from Salomon Brothers. And I called it kappa
in the last 17 years, but you will hear
people calling it vega. Obviously, I have probably more
people calling it the vega. But anyway, so that's my
first day at Morgan Stanley. But why did I tell
you the story? What point I try to make? So this story is actually--
when you think about it, mathematical or quantitative
finance is a rather new field. A lot of these terms
were newly introduced. And the pricing model
of options, as you know, was introduced in the
Black-Scholes in the '70s, or some of the ground work
may be done a bit earlier. But it's not like finance
was a quantitative profession to start with. So what we witness
in the last 30 years was really a transformation of
the trading profession coming from mostly
under-educated traders. Some of them typically joined
the firms in the mail room and became trader later on. That's typical career path. And to nowadays, if you
walk on the trading floor, you talk to the traders, most
of them have advanced degrees and quite a few of them
have very high training in mathematics and
computer science. So what has changed over
the last 20 or 30 years? I myself, personally, was
probably one of the data point experiencing this change. And I certainly
didn't expect I would be doing this when
I was at MIT, but I did that in the last 20 years. So the point I'm
trying to tell you is, before you dive into
any details of mathematics or any concept in finance in
this class, just bear in mind, this is a field developed in the
last mostly 30 years, or even shorter. And what you really
need to ask questions is-- it's not really is it
right or wrong in mathematics, is it right or wrong in physics? So, how the concepts
are established and defined and verified. Because this is a field--
the transformation about the participants,
products, models, methodology, everything are
changing very rapidly. Even nowadays, they're
still changing. So with that, I will
give you some background on how the financial
markets actually started, and that's really the history
part of this industry. So, when we talk about
markets, we know in early days people need to exchange goods. You have something
I don't have, I have something you don't
have, so there's exchanges. Then it becomes centralized. There are stock exchanges,
futures exchanges all over the world where
these products will be listed as securities
on these exchanges. That's one way of trading,
which is centralized. Obviously, in the
last 10, 15 years, now we have ECNs,
electronic platforms. Trade over-- you know, even
larger volume of those trades. So, financial products is
really just one form of trading. There are many other ways of
trading aside from exchanges. One of them, which
is called OTC, is over-the-counter, meaning
two counterparties agree to do a trade without really
subject to the exchange rules, or the underlying trading
agreement does not have to be a securitized
product, or standardized, or whatever ways you define it. And the different regions
have different exchanges and markets, as well. And they typically specialize
in local products, local company stocks, local bonds,
and local currencies. So, there are many
different forms. So again, what's in common? That's the question
you need to ask. Also, you don't
know the specifics. And the currencies, money
itself, are also traded. And that's where
different currencies issued by different countries. So, when we talk
about trading stocks-- there are also people
trade baskets of stocks, trade groups of stocks
together, and that's stock index or indices. So, there are
different products. How the stock get listed
on the stock exchange? It goes through IPO-- Initial
Public Offering process. So, when a company changes
from private to public, it goes through
this IPO process. It's called primary
market, primary listing. And once the stock is
listed on the exchange and it becomes
traded in the market, we call it secondary trading. So, that's after
the primary market. And equity or stock
is one form of trading or one form of
financial products. What are other forms? Loans. Actually, debt products are more
generic than equity products. When you started
thinking about it, what is really finance is about? It's really about someone
has money, someone doesn't. Someone has money to lend out,
someone needs to borrow money. So, that's loan. Loan is really a
private agreement between two counterparties
or multiple counterparties. When you securitize
them, they become bonds. And when you look at
bonds, every government will issue large sovereign debt. So, US government has large
outstanding US Treasury debt-- bonds, notes, bills. And corporates have issued a
lot of debt product, as well. They borrow money when they
need to build a new factory or expand. Universities borrow money. When MIT needs to build a new
building, some of the money will come from the
endowment support, some will come from some
other form of research budget, or some will come
from debt financing. Just borrow from the
public-- local governments, states, counties, even. So, they have various forms. So, that's debt product. Commodities, actually, you know. Metal, energy,
agriculture products are traded, mostly
in the futures format and some in
physical format, meaning you take deliveries. When you actually
buying and sell, you build a warehouse
to take them. You ship a tank to
store above the ocean. And the real estate, you're
buying and sell houses. 2008 financial crisis,
if you read about it, this has a lot to do
with the real estate market, the mortgages, and
asset-backed securities. So, I'm not trying to give
you all the definition, dumping the information on you. But I like you at least
hearing it once today, and then you have more interest,
you can read on the side. So asset-backed securities
is when you have an asset, you basically issue a debt
with the asset backing it. And how do you rate
the asset's risk level and what's the income
stream, cash flow? And before 2008
financial crisis, as you heard, large amount
of CMBS-- basically, it's a commercial
real estate backed securities, mortgage securities,
and the residential, as well. And further of all of these,
you heard probably a lot about the derivative products. So, that started
with swaps, options. And the structure
of the products, it become more tailor-made for
either investors or borrowers to structure the products in
a way to suit their needs. And some of the complexity
of those structured products become quite high,
and the mathematics involved in pricing them
and the risk management become rather challenging. So coming back to the
players in the market, one large type of
player is really bank. Essentially, after 1933
Glass-Steagall legislation, there were two main
types of banks. One is called commercial bank,
the other is investment bank. Commercial bank is
supposedly, you're taking deposits and
lend out the money, and doing more
commercial services. Investment bank supposed to
focus on the capital markets, raising capital, trading,
and asset management. But obviously, after 1999, the
Glass-Steagall was repealed. There's no longer that. Some people blame
that, and probably for a very good reason, for the
cause of 2008 financial crisis. But I want to tell you how
currently investment banks are organized. Vasily just mentioned he
works in the fixed income. So banks typically organized
by institutional business and asset management. So, within the institutional
client business, it has typically
three main parts. Fixed income, which
trade the debt and the derivative products. Equity, trade stocks and
the derivative products. And IBD, stands for
Investment Banking Division, which really covers
corporate finance, raising capital, listing
a stock, IPO, and merger and acquisition, and advisory. So that's how banks
are organized. Outside banks, other players,
basically, the asset managers, are obviously a very big force
in the financial markets. So the question a
lot of people ask is, is this a zero sum game? I'm sure you've heard
this many times. So, in the financial
markets, some people win, some people lose. A lot of times, it depends
on the specific products you trade, the market you're in. It is, lot of times,
pretty net zero. But why do we need
financial markets? This comes back to what
I described before. Because something
existed-- actually, there's a need for it. It's really the need to
bridge between the lenders and the borrowers. That's really coming down to
the essential relationship. So, investors who
have money need to have better yield or better
return, better interest. In the current environment,
when you have a savings account, you don't really
earn much at all. And so you would have to take
more risk to generate more return, or you
have longer horizon CDs, other type of products,
or trade the stocks. So, when somebody has money,
when you trade stocks, you're essentially--
you're buying a stock, you give the money somewhere. Supposedly, it will
go to the company. Company use the money to
generate a better return. And for the borrowers,
whoever needs money, they need to have
access to the capital. So obviously, different
borrowers have different risks. Some people borrow
money, never return. So, never generate any
returns, or never even return the principal. And so the trade between
lenders and the borrowers, is again, essentially
the main driver of the financial markets. So, a few more words about
the market participants. So, banks and so-called dealers
play the role of market making. What is market making? So, when you or some end
user go to the market, wants to buy or sell,
typically, if there's no market, you don't really find the match. And some of the products
you want to buy or sell may not necessarily be liquid. So, the dealers step in the
middle, make you a price. Say, OK, you want
to buy or sell. I can tell you-- this
stock, I make you price. $0.99, and that's my bid.
$0.95, that's my offer. So, that's the price I'm
willing to buy or sell. But what the result of
the trade-- the dealer actually takes the other
side of your trade. So, they take principal
risk, in this case. So, that's the difference
between dealers and the brokers. So, brokers don't really
take principal risks. If you want to buy
something or sell something, if I'm a broker, I
don't make you a price. I go to the market makers. I actually put two
people together, matchmaking, make
that trade happen. So, I earn the commission. So, that's a broker's role. So obviously, there are
individual investors, retail investors, same meaning. Mutual funds, who actually
manage public investors' money, typically in the
long-only format. Long means you buy something. So, you don't really short
sell a particular security. Insurance companies
has large asset. They need to generate a
return, generate cash flow to meet their liability needs. So, they need to invest. And the pension
funds, same thing. As inflation goes
higher, they need to pay out more to the retirees,
so where do you get the return? Sovereign wealth fund,
similarly, endowment funds-- they all have
this same situation, have capital and needs to deploy
and to make better return. So this other type of
players, hedge funds. So, how many of you
have heard hedge funds? OK, good. Almost everyone. And Peter mentioned that he
used to work at a hedge fund. And so, there are
different types of strategies, which I
will dive into a bit more, but hedge fund play the role
in the market-- they basically find opportunities to profit
from inefficient market positioning or pricing, so
they have different strategies. And the private equity is
different type of funds. They basically look
to invest in companies and either take them private or
invest in a private equity form to hopefully improve the
company's profitability, and then catch up. And governments obviously have
a huge impact on the market. So, we know in the financial
crisis, government intervened. And not only that, at the
normal market condition, government always have a very
large impact on the market, because they are
the policymakers. They decide the interest
rate and interest rate curve. And the different policies
they push out, obviously, will generate different
outlook for the future markets, therefore, profitability. Then the corporate hedges
and the liabilities. When corporates borrow
money, they create some risk, so they need to be sensitive
to the market, it changes. So, to summarize the
types of trading. The first type is
really just hedging. That means you're
not proactively adding risk to what you have. You already have some exposure. Just give you an example. Let's say you borrow
money, you bought a house, so you have mortgage. So, let's say it's a floating
rate mortgage payments. And you're worried about
interest rates going higher, so you can lock that rate in
into the fixed rate format. Or you can find ways
to hedge your exposure. Or your corporate has a large
income coming from Europe. So, you have euros coming
in, but you're not sure if euro would trade stronger
to the US dollar in the future, or trade weaker. If you think it will be
stronger, you just leave it. But if you think it
will trade weaker, so you may want to
hedge it, meaning you want to sell euro
and buy US dollars. And so that's the hedging type. The second type, as I
mentioned, is a market maker. So, market maker also
takes principal risk, but the main source of profit
is really to earn the bid offer. I gave you the example
$0.90 bid, $0.95 offer. So, that's what the market
maker is trying to profit from. But obviously, they
have residual risks sitting on the book. Not every trade is matched. So, how to optimize
those group of trades, that's what market
maker is doing. Most of the bank's
dealers are market makers. In the new regulation,
obviously, proprietary trading is banned, right? And so the third type is
really the proprietary trader, the risk taker. So, these are the hedge funds
or some portfolio managers. They need to focus on generating
return and control the risk. So, that's where the beta and
alpha, the concept comes in. So, if you're a portfolio
manager, some people say, don't worry. Don't go pick any stocks. Just buy S&P 500 index fund. Very cheap. You can pay very
little cost to do it. That's true. But if you want to
beat the S&P 500 index-- let's assume we call
S&P 500 index fund is asset b. So, the return of that, R(b). That's a return of that index. Now, you have a portfolio a. Your time series of
return of your asset a, obviously, you can
do linear regression. A lot of you are
math major here, and you can find a correlation
between those two time series. So, how the two returns are
related in a simplified form. So you can say, this
actually-- somehow it came out. It's supposed to
be alpha and beta, but it turned out
to be the letters. So, in a short description,
beta is really-- just think as correlated move
with the other asset. Alpha is really the
difference in the return. It's a format. You want to beat S&P 500,
so you want to basically have certain tracking
of this index, but you want to return
more on top of that. So let me just go
in bit of details of how each type of
trade actually occurs. So, when we talk
about hedging, I mentioned the currency example. Let me give you another example. There are a lot of people
issue bonds, or issue debt. So this example I'm
going to give you is, let's think about
Australian corporate. Because interest
rate in Australia is higher than in
Japan, so typically, people like to borrow
money in Japan, because you pay smaller interest. And they invest it in Australia. You earn higher interest rate. So let me ask you a question. Who can tell me,
why don't people just do that all day long,
just borrow from Japan and invest it in Australia? Then that interest
rate, I'm giving you example of a difference is about
3.5% for the roughly 10 year swap rates. Yeah, go ahead. AUDIENCE: [INAUDIBLE]. JAKE XIA: Right. Because you invest
in the Australia Ozzie, Australian dollar. The Australian dollar may
become weaker to the yen. You may lose all your
profit, or even more. And further, if everybody
plays the same game, then when you try to exit, you
have the adverse impact of your trade. So, let's say you think that's
the right time to do it, but then at one
time, you wake up, you said, huh, I think too
many people are doing this. I want to hedge myself. So, what do you do? AUDIENCE: [INAUDIBLE]? JAKE XIA: Yep. So, you try to lock in, right? So basically, you sell
the Australian dollars, buy the Japanese yen. Or on the interest
rate terms, you say you'll basically pay the
Australian dollar in the swap leg, and receive yen. This involves foreign exchange
trade, interest rate swap, and the cross-currency swap. So, your answer about currency
forward is roughly right, but obviously involves a bit
more in actual execution. So that's just to
give you example. Even if you are
not a finance guy, you work in a corporate, you
just do you import, export, or building a factory, you
have to know, actually, what the exposure is. So, risk management, nowadays,
becomes pretty widespread responsibility. It's not just the corporate
treasury's responsibility. So, that's on the hedging side. Obviously, if you are
Intel, for example, you sell a lot of
chips overseas. And your income--
actually, Intel does have lot of overseas income
sitting outside the States. So, the exposure to them is if
the exchange rate fluctuates, dollar becomes a lot stronger,
they actually lose money. So, they need to think about how
to hedge the revenue produced overseas. And obviously, for
import-exporters, that's even more apparent. And if you're entering
in a merger deal, and one company
is buying another, you need to hedge your
potential currency exposure and your
interest rate exposure. And whatever is on the
assets, or the liability, or the balance sheet, you
need to hedge your exposure. So we talked about
hedging activity. Let's talk about market making. So if it's a simple
transparent product, everybody pretty much
knows where the price is. So, if you buy Apple stock,
I think a lot of people know pretty much where it is. You may even have it
on your cellphone, know where that stock is. But if it's not transparent,
so what do you do? So, if instead of asking
you where Apple is, probably you're going
to tell me $495 today. AUDIENCE: I don't really know. JAKE XIA: OK. But if I asked you instead,
what is the call option on Apple stock in
two month's time? I'll give you a
strike, let's say, 500. So you're probably
less transparent. So that market maker comes
in to provide that liquidity, and then takes the risk. They manage the book by
balancing those Greeks, which I mentioned earlier. Delta, which describes the
[INAUDIBLE] relationship of this whole book to the
underlying stock, or underlying whatever currency. That's called delta. Gamma is really the
change of the portfolio. Take the derivative
to the delta, or to the underlying spot. So, that's second-order
derivative. Delta is the first order. So gamma, now you have curvature
or convexity coming in. And theta is really-- nothing
changes in the market. Nothing changes
in your position. How your trading book is
carrying or bleeding away money. And we talk about the
volatility exposure was vega. And on top of that,
what are the tail risks? What are the events can actually
get you into big trouble? So people use value at risk. So you will hear
this "VaR" concept in some of the lectures,
which is also, obviously, a very important concept. I think Peter will-- or
Choongbum will-- probably Peter will teach. Then capital. How much capital are you using? It becomes a very
important issue nowadays. And balance sheet. Again, you have asset,
you have liability. How do you leverage? How much leverage you have? Before the crisis, for example,
lot of the banks leverage up 40 times, meaning when you
have $1, you had $40 exposure. So when the market moves
little, you get wiped out. That's really what amplified
in the 2008 financial crisis. And how do you measure
the asset in balance sheet when you have derivatives
rather than a straightforward notional? So lot of quantitative
type of people like to focus a bit more
on the risk taking side, because people heard stories
about successful cases of some hedge funds
using high math. They generated very
impressive returns and they seem to have an edge. So now, people focus
on trading strategies. So that falls into the category
of proprietary trading or risk taking. So that you can just simply
doing directional trading strategies. Just go long or short the stock. That's very simple. Those so-called the gut
traders, gut feeling. Go with your gut. You don't even think. You say, I'm eating curry
today, so I go long. I'm eating rice
tomorrow, so I go short. So, this arbitrage. Arbitrage is really to find the
relationships between prices, and try to profit from those
relationship mispricing. This is actually
very interesting. Not many people
focus on arbitrage, because lot of people
are gut traders. You essentially just
watch your own market. You don't really
care what's going on. If you trade gold in the
States, the gold price happen in Asia and in
Europe matters, right, because you're trading
the same thing. If they are not
priced the same way, you can profit from
the difference. And that's just
a simple example. But a spot price versus
forward price, that's a deterministic relationship. It's a mathematical
relationship. If that relationship breaks
down, you can also profit. So there are many examples
mathematical relationship which gives you the
arbitrage opportunity. The other type is called a
value trader, or relative value strategies. Think there's a deterministic,
temporary mathematical relationship. You look at the longer
term in horizon, trying to determine what
is really the underlying value of a particular
instrument, then trade on the
relative value. Obviously, there are successful
value investors out there. And the systematic trader
builds computer models. One example is trend following,
so just follow the price trend. That used to be an effective
strategy for some time, but when lot of people
doing the same thing, that becomes much less effective. Or momentum, same thing. Stat arb, finding
statistical relationship among large number
of stocks, then trade at the higher frequency. And fundamental
analysis, you're really trying to understand what's
going on in the world. What is the trade balance? What is the earning
potential of a company? What's the trade
balance of a country? What is a policy change? What does it mean
when Federal Reserve announce they're going to
taper the quantitative easing? Why the stock market is sold
off in the last couple months, especially why stocks in
India, Brazil, Indonesia, sold out more. Why is that? So it goes through those
fundamental analysis. And there are
special situations. Some companies are going
through particular difficulties, assets are priced very cheaply. So, there are firms out there --
you probably heard Bain Capital and many others -- where they
focus on these private equity and special situation
opportunities. So what have all of these
to do with mathematics? Where does math come in? How do you use math? So, I want to give you
some aspects of that. So from my personal experience,
I joined the market, really start to working
on pricing models. So, that's the first area. So, math is very
effective, because when you, your bank,
your corporate, you want to buy some
financial instruments, you have to know
where is the price. It's easy to observe
a stock in the market, but when it comes to
more complex products, they just take one step
forward on the complexity, which is the option. You have to know how
to price an option. So, that's where
the math comes in. You actually have to be able
to solve differential equations to get a model price,
then you obviously adjust to your assumptions
to fit into the market. So, pricing model, which Vasily
and many of his colleagues can tell you more--
which is very much a very interesting
and challenging area. How do you price all
these instruments? And when I say pricing, it's
not in the narrow definition of just coming up
with the price. When you build a
pricing model, you also generate the risk parameters
of these instruments, and how do you risk manage them. So, that comes to
the second part. So math is very useful
in risk management, which I will give you
some -- not quiz -- questions after this slide. You can see that risk management
itself is very challenging. It's not a purely
mathematical question, but yet, math plays
a very important role to quantify how much
exposure you have. Then, the third is
trading strategies. Again, I think a lot of
people with math background, or in general,
people are looking for the so-called holy
grail trading strategies. It's almost like perpetual
motion machines people looking for 100 years ago. You just turn it on. It makes money by itself. You go to sleep, you go on
vacation, you come back, you'll have more in
your bank account. Obviously, that's
not going to happen. The robotrader, a robotic
trader, is a dream. It has its place or its use,
but it's a fast evolving market. You have to constantly
either upgrade your research and adjust your strategies. There's no such thing you
can build and leave it alone, it runs for itself forever. But I just want to
mention that because maybe towards the end of the
term you will feel, hmm, I came up with this
brilliant trading strategy. I think it's going to
make money forever. Please let me know first. AUDIENCE: And me second. PROFESSOR: So, I want to
leave some time to Vasily. Actually, he can give
you some examples of projects of last
year's students who actually came to this class
and did some real application at Morgan Stanley. But before I hand
it over to Vasily, let me ask you some questions. I just want to-- not really
to quiz you, just give you the sense how math and
intuition and judgment can come into the same place. So, let me first give you an
example I call risk aversion. So, you are facing two choices,
choice A and a choice B. Choice A being you have 80
chance to lose $500. You have 20% chance to win $500. That's pretty clear, right? That's choice A. Or
choice B, you basically just lock in you have
100% chance to lose $280. Let me ask you, for whoever
likes to choose choice A, please raise your hand. One, two, three, four. About six out of say,
let's call it 50. So, can I ask you why you
think choice A makes sense? AUDIENCE: So, I know it's
a lower expected value, but I enjoy gambling and I would
rather take the chance of-- JAKE XIA: Right, because you
don't want to lock in that $280 loss, right? That, or you still
have 20% chance to win. For the ones raised
their hand for choice A, are there any other reasons? Same reason. AUDIENCE: [INAUDIBLE] JAKE XIA: I assume
the rest of you would choose choice B,
unless you-- Neither? How many of you choose choice B? Choice B. And are there
anybody think neither is right? You have to choose. No, you have to choose. So, either choice A or choice B. So, let me just talk a
little bit about this. Again, I'm not trying to
tell you which one is right, but I just share my thoughts
how we look at these. Why it called risk aversion? So, this is very
common human behavior. When you go to the
market, you buy a stock. When the stock goes
up, makes bit of money, the natural tendency -- for
especially someone is new to the market -- is
to let's take profit. Let's sell. Oh, I made $1000. I made $500. Let's go have a nice
meal or whatever. Buy an iPad. But when the stock loses money,
what's the natural tendency? AUDIENCE: [INAUDIBLE] JAKE XIA: That's-- AUDIENCE: [INAUDIBLE] JAKE XIA: I think natural
tendency, lot of people will keep it. I think if you have the
discipline to get out, that's great. Trading is really all about
how do you risk manage, have the discipline, and
how to manage your losses. The natural tendency
of a lot of people is, well, I think there's
a 20% chance to come back, and I'm going to make $500 more. Why do I want to lock in
to stop myself out at 280? So even though the expected
value-- I think lot of people said, you lose expected value,
which is $300 in choice A, but you would still
not to choose choice B, because you don't want
to lock in the $280 loss. Again, I'm not trying to inject
the idea to you of which one is right or wrong,
but think about it. So, that's really the common
behavior, which mathematically may not make sense, but lot of
people still would like to do. And also, really, when
you think about it, depends on your situation. And let's say, you
think the market-- I'm giving you the
stock example again. If you're not purely following
the discipline of stop loss, but you just think the
fundamental picture has changed. You really don't think the
stock should go up anymore. Obviously, at whatever level
you should get out, regardless how much loss you lock in. But if you think the fundamental
story is still very sound, you should think about as if
you don't have a position, what you want to do next. But anyway,
mathematically, I just want to see-- I
guess this is MIT, so many people
think mathematically where you would actually
choose choice B, because that's low expectation,
which makes sense. But I think if you
ask a larger audience, I think a lot of people don't
really want to choose choice B, because they don't want
to lock in the loss. Now, let me change the
question a little bit. So, choice A becomes instead
of the 80% chance to lose, now you have 80% chance
to win $500 and 20% chance to lose $500. Choice B, you have 100%
chance to win $280. Who would choose choice A? Again, minority
of this audience. Let's say less than 10%. Who would choose choice B? The rest of you. All right. Can someone choose choice A give
me an argument why would you? AUDIENCE: [INAUDIBLE] JAKE XIA: Yep. Anyone want to give me
a reason for choice B? AUDIENCE: Higher Sharpe. JAKE XIA: Higher Sharpe? Mm-hm. Yup. Well, let me just leave it here. Again, I think we can talk a
bit more along in the class. I mean, the last
day of the class, hopefully we'll have much
deeper discussion on this. It's not unique. The answer, I think it can go
you either way, as you said. If your bank account
balance is-- let's say you are a freshman student. Your bank account is $800. Your choice will be very
different from someone has $100,000 in his bank account. And also, your risk tolerance,
how much you can tolerate. I'm not going to give you
say, this is right or wrong. But with that, let me move on
and give you some homework. So, before I give
you the homework, I want to make a
few more comments. Do people always learn
from their experiences? In science, we collect
evidence, we build models. We first understand the physics. We build mathematical models,
then we verify in physics, doing experiments. But is that the same
investigation process in finance? Market cycles are
typically very long, but people tend to
have short memories. So, how do people really
learn from their experiences? A very interesting question. And very natural tendency
is to extrapolate historical experience. What happened in 2008? People still remember. What happened in 1970s? Maybe some people
still remember. What happened 100 years ago? So, people tend to extrapolate,
drawing conclusions from very recent experience. And deterministic relationship
versus statistical relationship is very interesting, as well. When you try to trade on those,
how do you really build models? Is the market really efficient? What part is efficient? How do you really
apply those theories in your day-to-day risk
management or trading activities? And sometimes, people
tend to oversimplify. Just say, oh, I can model this. This is one important parameter. I just take that. So I just give you
all the warnings that the-- again,
very young, new field and largely, often, this
is art, than science. So keep that in mind,
even though we're talking about mathematics in finance. Math is very powerful
and useful in finance. So learn the math,
learn the finance first, but keep those
questions along the way when you are learning
during this class. So suggested homework, optional. I mentioned a lot of
terminologies today. Go to the course website,
read what we have put up for the financial glossary. So if you still have things
you don't understand, compile your own list of
financial concepts, which you can search on the
web or even ask us. But I encourage you to do that. It will prepare you well. So, that's really-- and
read other materials on the course work. So we got maybe--
how about this? We still got about 15
minutes or 12 minutes left, so I'll pass it to
Vasily, then maybe we can leave five minutes
for some questions. VASILY STRELA: Yeah. JAKE XIA: Yeah, OK. VASILY STRELA:
[INAUDIBLE] mentioned that, Apple trades, that now
it's $494.4 Yeah, just a couple of [INAUDIBLE]. Well, first of all, no offense
to people who were [INAUDIBLE], but I just wanted to give
an example of [INAUDIBLE]. AUDIENCE: [INAUDIBLE]. VASILY STRELA: --because he
was working in our group, and it just will give you a
little bit of an idea what we will be talking about
and what actually we do in the daily life, or what
an intern or somebody who comes to work in this
industry could do. And one project is
[INAUDIBLE] worked was on estimating
the noisy derivative. Derivative is called delta. Delta is usually the first
derivative to a function. And as we will see in the class,
quite often, to obtain a price, you do it through Monte Carlo,
meaning running a lot of paths and then averaging along them. So, it's a statistical method. So obviously, there is a noise
to your answer every time. So, if you want to
differentiate this functions and get a derivative, then this
derivative will be quite noisy. And so, instead of getting
the true derivative, you might obtain something quite
different from true derivative just because there
is a confidence interval around any point. And obviously, there is a
trade off here, as well, because you can run more paths,
throw more computational power, which will reduce your
confidence interval. You will know better where
you are, more precise. Or the other solution
could be, if you know that your function is
not too concave and reasonably flat, you might do the
numerical differentiation on wider interval. Basically, reducing the
significance of the error, and you will hope to arrive
to a better approximation. So obviously, there is somewhere
balance, and the question was, is there an optimal shift
size to get the derivative? And that's what-- uh oh,
the slide got corrupted. So, there was quite
a bit of mathematics involved and minimization
and optimization. There was an answer. And that's actually what
we finally arrived at. And that's some toy
example, but still, it shows you that if
you use constant size and not optimal size, that would
be your numerical derivative of this blue function. While if you use
an optimal shift size, which
[INAUDIBLE] computed, it would be much
smoother and much better. So, that's one of example,
and that's what he did. And we actually are implementing
it in our systems and plan to use it in practice. Another project was
actually quite different. And it was about
electronic trading and basically how to better
predict prices of currencies and exchange rate. And funny enough, it
was on ruble/US dollar, because it was actually
aimed for our Moscow office. And basically, what we had,
we had the noisy observation of broker data and
it was coming out at different non-uniform times. Basically, at random times. So, we decided to
use Kalman filter and to study how it can predict. And that's one of the
nice graphs [INAUDIBLE] produced, which again,
we will use this strategy and the Kalman filters
which he constructed in our e-trading
platform in Moscow. So, that's just a
couple of examples, which I wanted to give you
as a preview of what we will be talking in the class. Just to remind, the website
is fully functional. We put syllabus there, a
short list of literature. We will be posting a
lot of materials there. Probably most lectures
will be published there. Jake's slides are there already. So, any questions? JAKE XIA: Please hand
back the sign up sheets. We like to get your
emails so we can put you on the website for
further announcements, but you can also add
yourselves. [INAUDIBLE]. But it's probably easier
if you put your email on the sign up sheet,
so we can [INAUDIBLE]. VASILY STRELA: Yeah,
but please visit and sign up here,
because there will be announcements to the class. Thank you very much.
