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00:04
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00:10
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00:21
JAKE XIA: This is the second
time we are having this class.
JAKE XIA：這是我們第二次開設這門課。
00:25
We had it last year
in a smaller version.
我們去年曾開過一次，規模較小。
00:28
That was for six
units of a credit, and we had it once a week.
當時是 6 個學分，每週上一次課。
00:32
And mostly practitioners
from the industry, from Morgan Stanley,
talking about examples how math is applied
in modern finance.
主要是業界實務人士，像是摩根史坦利的人，來分享數學在現代金融應用的實例。
00:48
And so we got some good
response last year.
所以我們去年獲得了不錯的迴響。
00:50
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.
因此，在數學系的支持下，我們決定將這門課擴充為 12 個學分，每週上兩次。
00:59
So, we have every Tuesday
and Thursday afternoon from 2:30 to 4:00, as you
know, in this classroom.
所以，如各位所知，我們每週二和週四下午 2:30 到 4:00 在這間教室上課。
01:08
So last year, Dr.
去年，Vasily Strela 博士和我——
01:09
Vasily
Strela and I-- by the way, I'm Jake Xia and
that's Dr.
順帶一提，我是 Jake Xia，這位是 Vasily 博士——我們是去年的主要講師。
01:14
Vasily, and we were the main
instructors last year.
現在我們增加到四位主要講師。
01:18
Now we doubled it up to
four main instructors.
分別是 Peter Kempthorne 博士和 Choongbum Lee 博士。
01:22
That's Dr.
我們增加主要講師的原因是，我們新增了數學講座，
01:23
Peter Kempthorne
and Dr.
主要涵蓋線性代數、機率到統計，以及一些隨機微積分，
01:25
Choongbum Lee.
為各位奠定基礎，以便理解後續將會用到的數學，
01:26
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
這些數學將應用在那些由業界實務人士教授的課程範例中。
01:45
in those examples in the lecture
taught by the practitioners from the industry.
這門課的目的，是提供一份精選菜單，
01:52
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.
And so hopefully, this will
give you enough information to decide this is a field
you would like to pursue in your future career.
因此希望這能提供你們足夠的資訊，來決定這是否為你們未來職涯
02:25
In fact, last year when
we finished the class, we had a few students coming
to work in the industry.
事實上，去年當我們
02:32
Some work at Morgan Stanley,
some work at elsewhere.
有些在摩根史坦利工作，
02:38
So that's really the goal.
這確實是我們的目標。
02:40
And at the same
time, obviously, you will further solidify
your math knowledge and learn new content.
同時，顯然地，你們將會進一步鞏固
02:49
And we put the prerequisite
about the math part a bit later.
我們將關於數學部分的
02:54
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.
所以我將利用今天
03:07
Some terminologies
will be used, which you may not have heard before.
會使用一些術語，
03:12
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.
所以在我開始介紹之前，我總是想知道
03:23
You just need to
raise your hands so I know roughly what kind of
background and where you are.
你們只需要舉手，
03:30
So how many undergraduate
students are here?
所以這裡有多少大學生？
03:33
So I would say 80% percent.
我想大概佔 80%。
03:38
How many graduate students
are here, just to verify?
這裡有多少研究生，
03:43
Yep, that's about right, 20%.
是的，差不多，20%。
03:45
And how many students are in
finance and business major?
那有多少學生是
03:50
Just one.
只有一位。
03:51
And how many of you
are a math major?
那你們之中有多少人
03:55
Most of you.
大部分都是。
03:56
How many of you are
engineering majors?
你們當中有多少人是工程系的？
03:59
A few.
少數。
04:00
How many of you actually
are from other universities?
你們當中有多少人實際上是來自其他大學的？
04:04
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.
太好了，因為去年我們有不少這樣的人，所以我想特別告訴你們，非常歡迎你們來這裡旁聽課程。
04:16
So it's open door.
所以是開放政策。
04:19
And last year I remember
we had a couple of students from Harvard.
而且我記得去年我們有幾位哈佛的學生。
04:23
That's where I actually
work right now.
那其實就是我現在工作的地方。
04:29
I forgot to mention
that, but I'm affiliated with both the math
department and the Sloan school here.
我忘了提這一點，但我同時隸屬於這裡的數學系和史隆商學院。
04:36
So anyway, thanks for that.
總之，謝謝你們。
04:38
We will be doing a bit
more polling along the way, mainly to get feedback of
how you feel about the class.
我們在課程中會做幾次投票，主要是想了解你們對這門課的感受。
04:45
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 by the way, before
I tell you the story, what's unique about
vega on this list?
順便一提，在我講故事之前，Vega 在這份名單上有什麼獨特之處？
06:56
AUDIENCE: It's not
a Greek letter.
觀眾：它不是希臘字母。
06:58
JAKE XIA: It's not
a Greek letter.
JAKE XIA：它不是希臘字母。
07:00
That's right.
沒錯。
07:00
So I turned around and
asked my desk quant, I said, where's the vega report?
所以我轉過身問我的部門量化分析師，我說，Vega 報告在哪裡？
07:06
But how many of you actually
know what a vega is?
但你們有多少人真正知道 Vega 是什麼？
07:09
OK, lot of people know.
好，很多人都知道。
07:11
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.
Which again, you will learn
more in rigorous terms how it's defined in mathematics.
關於這點，你之後會學到更多關於它在數學上如何定義的嚴謹術語。
07:31
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.
但它的意義其實是一種衡量或指標，用來顯示價格隨時間變化的波動程度，或其標準差是多少。
07:42
That's all you need
to know right now.
這是目前你只需要知道的。
07:45
I'm not going to ask
you questions later.
之後我不會考你。
07:48
So my desk quant
look at me, said-- this is supposed to
be options trading desk, so he look at me puzzled.
所以我的量化交易員看著我，說——這應該是期權交易部門，所以他困惑地看著我。
07:56
So instead of
answering my question, he handed over me
a training manual for new employees
and new analysts.
於是他沒有回答我的問題，而是遞給我一本給新員工和新分析師的培訓手冊。
08:05
So I opened the training
manual and looked it through.
所以我打開培訓手冊並仔細看了一遍。
08:09
I actually found my answer.
我其實找到了我的答案。
08:11
So actually, at Morgan Stanley
this is not called vega, it's called kappa.
所以事實上，在摩根士丹利，這不叫 vega，而是叫 kappa。
08:17
So now, I remember
to call it kappa.
所以現在，我記得要稱它為 kappa。
08:20
Kappa is actually
a Greek letter.
Kappa 其實是一個希臘字母。
08:23
So further, I look
on the same page there was actually a
footnote, which I copied down.
再進一步，我在同一頁看到一個註腳，我把它抄了下來。
08:30
So the footnote about why it's
called kappa at Morgan Stanley.
所以這個註腳是關於為什麼在摩根士丹利它被稱為 kappa。
08:36
Kappa is also called vega
by some uneducated traders at the Salomon Brothers.
在所羅門兄弟公司，一些沒受過什麼教育的交易員也把 kappa 稱為 vega。
08:42
That's where I came from.
那就是我之前待的地方。
08:44
I just joined.
我剛加入。
08:45
They have mistaken
vega as a Greek letter after gambling at Vegas.
他們在拉斯維加斯賭博後，誤以為 vega 是一個希臘字母。
08:55
So anyway, so that
was my first day.
總之，這就是我的第一天。
08:58
So obviously, I learned
how to call kappa very quickly, because I
came from Salomon Brothers.
所以很明顯地，我很快就學會了如何稱呼 kappa，因為我來自所羅門兄弟公司。
09:05
And I called it kappa
in the last 17 years, but you will hear
people calling it vega.
在過去的 17 年裡我都稱之為 kappa，但你會聽到有人稱之為 vega。
09:11
Obviously, I have probably more
people calling it the vega.
顯然，可能有更多人稱之為 vega。
09:16
But anyway, so that's my
first day at Morgan Stanley.
總之，這就是我在摩根士丹利的第一天。
09:20
But why did I tell
you the story?
但我為什麼要告訴你這個故事？
09:22
What point I try to make?
我想表達什麼觀點？
09:24
So this story is actually--
when you think about it, mathematical or quantitative
finance is a rather new field.
這個故事其實是——當你仔細想想，數學或量化金融是一個相對新興的領域。
09:34
A lot of these terms
were newly introduced.
這些術語中有許多都是新引入的。
09:38
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.
如你所知，期權的定價模型是在 70 年代由布萊克-休斯提出的，或者有些基礎工作可能做得更早一點。
09:51
But it's not like finance
was a quantitative profession to start with.
但金融業一開始並不是一個量化的專業。
09:57
So what we witness
in the last 30 years was really a transformation of
the trading profession coming from mostly
under-educated traders.
所以我們在過去 30 年所見證的，確實是交易行業的轉型，從大多數教育程度不高的交易員轉變而來。
10:09
Some of them typically joined
the firms in the mail room and became trader later on.
他們中的一些人通常從公司的收發室加入公司，後來才成為交易員。
10:16
That's typical career path.
這是典型的職業路徑。
10:18
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.
I myself, personally, was
probably one of the data point experiencing this change.
我自己個人，可能就是經歷這種變化的數據點之一。
10:45
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.
當我在麻省理工學院時，我當然沒預料到自己會從事這個行業，但我在過去 20 年確實這麼做了。
10:55
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?
你們真正需要問的問題是——這並不是關於數學上的對錯，也不是物理學上的對錯？
11:28
So, how the concepts
are established and defined and verified.
所以，這些概念是如何被建立、定義和驗證的。
11:35
Because this is a field--
the transformation about the participants,
products, models, methodology, everything are
changing very rapidly.
因為這是一個領域——參與者、產品、模型、方法論的轉變，一切都在快速變化。
11:46
Even nowadays, they're
still changing.
即使在今天，它們仍在改變。
11:49
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.
因此，我將為您提供一些關於金融市場如何真正開始的背景知識，這也是該行業的歷史部分。
12:01
So, when we talk about
markets, we know in early days people need to exchange goods.
所以，當我們談到市場時，我們知道在早期人們需要交換商品。
12:08
You have something
I don't have, I have something you don't
have, so there's exchanges.
你有我沒有的東西，我有你沒有的東西，因此有了交換。
12:15
Then it becomes centralized.
然後它變得中心化。
12:17
There are stock exchanges,
futures exchanges all over the world where
these products will be listed as securities
on these exchanges.
全世界都有證券交易所、期貨交易所，這些產品會在這些交易所上市為證券。
12:28
That's one way of trading,
which is centralized.
這是一種交易方式，即中心化交易。
12:32
Obviously, in the
last 10, 15 years, now we have ECNs,
electronic platforms.
顯然，在過去的 10、15 年裡，現在我們有了 ECN，即電子平台。
12:38
Trade over-- you know, even
larger volume of those trades.
交易量甚至更大。
12:43
So, financial products is
really just one form of trading.
所以，金融產品只是交易的一種形式。
12:47
There are many other ways of
trading aside from exchanges.
除了交易所之外，還有許多其他交易方式。
12:52
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.
不同的地區也有不同的交易所和市場。
13:22
And they typically specialize
in local products, local company stocks, local bonds,
and local currencies.
它們通常專注於本地產品、本地公司股票、本地債券和本地貨幣。
13:32
So, there are many
different forms.
所以，有許多不同的形式。
13:35
So again, what's in common?
那麼，共同點是什麼？
13:37
That's the question
you need to ask.
這是您需要提出的問題。
13:40
Also, you don't
know the specifics.
此外，您不知道具體細節。
13:42
And the currencies, money
itself, are also traded.
貨幣本身也是可以交易的。
13:46
And that's where
different currencies issued by different countries.
這指的是不同國家發行的不同貨幣。
13:51
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.
所以，當我們談論股票交易時，也有人交易一籃子股票，將股票群組一起交易，那就是股票指數。
14:02
So, there are
different products.
所以，有許多不同的產品。
14:05
How the stock get listed
on the stock exchange?
股票是如何在證券交易所上市的？
14:08
It goes through IPO-- Initial
Public Offering process.
它是透過 IPO（首次公開發行）的過程。
14:13
So, when a company changes
from private to public, it goes through
this IPO process.
當一家公司從私有轉為公開時，它會經歷這個 IPO 過程。
14:20
It's called primary
market, primary listing.
這稱為初級市場或初次上市。
14:24
And once the stock is
listed on the exchange and it becomes
traded in the market, we call it secondary trading.
一旦股票在交易所上市並在市場上進行交易，我們稱之為次級交易。
14:34
So, that's after
the primary market.
這是發生在初級市場之後。
14:37
And equity or stock
is one form of trading or one form of
financial products.
股權或股票是交易的一種形式，也是金融產品的一種形式。
14:44
What are other forms?
還有哪些其他形式？
14:45
Loans.
貸款。
14:46
Actually, debt products are more
generic than equity products.
事實上，債務產品比股權產品更為普遍。
14:51
When you started
thinking about it, what is really finance is about?
當你開始思考時，金融的本質究竟是什麼？
14:58
It's really about someone
has money, someone doesn't.
其實就是關於有些人有錢，有些人沒有。
15:02
Someone has money to lend out,
someone needs to borrow money.
有些人有錢可以借出，有些人需要借錢。
15:06
So, that's loan.
這就是貸款。
15:07
Loan is really a
private agreement between two counterparties
or multiple counterparties.
貸款其實是兩個或多個交易對手之間的私人協議。
15:14
When you securitize
them, they become bonds.
當你將它證券化時，它們就變成了債券。
15:17
And when you look at
bonds, every government will issue large sovereign debt.
當你觀察債券市場時，每個政府都會發行大量主權債務。
15:23
So, US government has large
outstanding US Treasury debt-- bonds notes bills.
因此，美國政府有龐大的未償還美國國債——包括債券、中期票據和短期國庫券。
15:29
And corporates have issued a
lot of debt product, as well.
企業也發行了大量的債務產品。
15:34
They borrow money when they
need to build a new factory or expand.
當他們需要建造新工廠或擴張時，就會借錢。
15:39
Universities borrow money.
大學也會借錢。
15:41
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.
securities, mortgage securities,
and the residential, as well.
證券、抵押證券，
17:34
And further of all of these,
you heard probably a lot about the derivative products.
而在所有這些產品中，
17:40
So, that started
with swaps, options.
所以，這一切是從
17:43
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.
而這些產品的結構，
17:54
And some of the complexity
of those structured products become quite high,
and the mathematics involved in pricing them
and the risk management
其中一些結構型產品的複雜度
18:05
become rather challenging.
也變得頗具挑戰性。
18:14
So coming back to the
players in the market, one large type of
player is really bank.
那麼回到市場的參與者，
18:29
Essentially, after 1933
Glass-Steagall legislation, there were two main
types of banks.
本質上，在 1933 年
18:36
One is called commercial bank,
the other is investment bank.
一種是商業銀行，
18:42
Commercial bank is
supposedly, you're taking deposits and
lend out the money, and doing more
commercial services.
商業銀行
18:52
Investment bank supposed to
focus on the capital markets, raising capital, trading,
and asset management.
投資銀行則理應
19:01
But obviously, after 1999, the
Glass-Steagall was repealed.
但顯然，在 1999 年，
19:06
There's no longer that.
不再有那種區分了。
19:08
Some people blame
that, and probably for a very good reason, for the
cause of 2008 financial crisis.
有些人將其歸咎於此，
19:17
But I want to tell you how
currently investment banks are organized.
但我想告訴你目前
19:25
Vasily just mentioned he
works in the fixed income.
瓦西里剛提到他
19:30
So banks typically organized
by institutional business and asset management.
所以銀行通常依
19:36
So, within the institutional
client business, it has typically
three main parts.
所以，在機構客戶業務中，
19:43
Fixed income, which
trade the debt and the derivative products.
固定收益，交易
19:49
Equity, trade stocks and
the derivative products.
權益，交易股票
19:53
And IBD, stands for
Investment Banking Division, which really covers
corporate finance, raising capital, listing
a stock, IPO, and merger and acquisition, and advisory.
IBD 是投資銀行部門的縮寫，主要負責企業金融、籌集資本、股票上市、IPO，以及併購與顧問服務。
20:08
So that's how banks
are organized.
這就是銀行的組織架構。
20:10
Outside banks, other players,
basically, the asset managers, are obviously a very big force
in the financial markets.
在銀行之外，其他主要參與者，也就是資產管理公司，無疑是金融市場中的一股重要力量。
20:22
So the question a
lot of people ask is, is this a zero sum game?
所以很多人會問，這是否是一場零和遊戲？
20:27
I'm sure you've heard
this many times.
我相信你聽過很多次了。
20:30
So, in the financial
markets, some people win, some people lose.
在金融市場中，有人賺錢，有人賠錢。
20:36
A lot of times, it depends
on the specific products you trade, the market you're in.
很多時候，這取決於你交易的具體產品，以及你所在的市場。
20:43
It is, lot of times,
pretty net zero.
很多時候，這其實是淨零的。
20:46
But why do we need
financial markets?
但我們為什麼需要金融市場？
20:49
This comes back to what
I described before.
這又回到我之前描述的內容。
20:52
Because something
existed-- actually, there's a need for it.
因為某種事物存在——實際上是因為有需求。
20:57
It's really the need to
bridge between the lenders and the borrowers.
這其實是為了在放款者與借款者之間建立橋樑的需求。
21:03
That's really coming down to
the essential relationship.
這最終歸結為一種基本關係。
21:08
So, investors who
have money need to have better yield or better
return, better interest.
所以，有錢的投資者需要獲得更好的收益率或回報、更好的利息。
21:15
In the current environment,
when you have a savings account, you don't really
earn much at all.
在目前的環境下，當你有儲蓄帳戶時，你其實賺不了多少利息。
21:22
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.
所以，當某人有錢，當你交易股票時，本質上——你買進股票，就是把錢給了某個地方。
21:43
Supposedly, it will
go to the company.
理論上，這筆錢會流向公司。
21:46
Company use the money to
generate a better return.
公司利用這筆錢來創造更好的回報。
21:49
And for the borrowers,
whoever needs money, they need to have
access to the capital.
而對於借款者，也就是任何需要資金的人，他們需要取得資本的管道。
21:55
So obviously, different
borrowers have different risks.
所以顯然，不同的借款人有不同的風險。
21:59
Some people borrow
money, never return.
有些人借了錢，卻從不歸還。
22:02
So, never generate any
returns, or never even return the principal.
因此，從未產生任何回報，甚至從未歸還本金。
22:07
And so the trade between
lenders and the borrowers, is again, essentially
the main driver of the financial markets.
所以，貸款人與借款人之間的交易，再次成為金融市場的主要驅動力。
22:20
So, a few more words about
the market participants.
那麼，再多談談市場參與者。
22:24
So, banks and so-called dealers
play the role of market making.
銀行和所謂的交易商（dealers）扮演著做市（market making）的角色。
22:29
What is market making?
什麼是做市？
22:31
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.
當你或某些終端用戶去到市場，想要買或賣時，通常如果沒有市場，你其實找不到交易對手。
22:42
And some of the products
you want to buy or sell may not necessarily be liquid.
而且你想買或賣的部分產品，流動性可能沒那麼好。
22:49
So, the dealers step in the
middle, make you a price.
所以，交易商會介入中間，向你報價。
22:53
Say, OK, you want
to buy or sell.
說，好的，你想買或賣。
22:56
I can tell you-- this
stock, I make you price.
我可以告訴你——這支股票，我給你一個價格。
23:00
$0.99, and that's my bid.
0.99 美元，這是我的買價（bid）。
23:02
$0.95, that's my offer.
0.95 美元，這是我的賣價（offer）。
23:04
So, that's the price I'm
willing to buy or sell.
這就是我願意買或賣的價格。
23:08
But what the result of
the trade-- the dealer actually takes the other
side of your trade.
但交易的結果是——交易商實際上承接了你交易的另一方。
23:15
So, they take principal
risk, in this case.
所以，在這種情況下，他們承擔了本金風險。
23:19
So, that's the difference
between dealers and the brokers.
這就是交易商與經紀人（brokers）的區別。
23:24
So, brokers don't really
take principal risks.
所以，經紀人並不會真正承擔本金風險。
23:27
If you want to buy
something or sell something, if I'm a broker, I
don't make you a price.
如果你想買東西或賣東西，如果我是經紀人，我不會向你報價。
23:35
I go to the market makers.
我去找造市者。
23:37
I actually put two
people together, matchmaking, make
that trade happen.
我實際上是把兩方湊在一起，做媒合，讓交易得以完成。
23:43
So, I earn the commission.
所以，我賺取佣金。
23:45
So, that's a broker's role.
這就是經紀商的角色。
23:47
So obviously, there are
individual investors, retail investors, same meaning.
所以很明顯，有個人投資者、散戶投資者，意思是一樣的。
23:53
Mutual funds, who actually
manage public investors' money, typically in the
long-only format.
共同基金，實際上是管理大眾投資者的資金，通常是以只做多（long-only）的形式。
24:00
Long means you buy something.
做多（Long）的意思是你買進某個標的。
24:03
So, you don't really short
sell a particular security.
所以，你並不會放空特定的證券。
24:07
Insurance companies
has large asset.
保險公司擁有龐大的資產。
24:10
They need to generate a
return, generate cash flow to meet their liability needs.
他們需要產生回報、產生現金流，以滿足其負債端的需求。
24:16
So, they need to invest.
所以，他們需要投資。
24:18
And the pension
funds, same thing.
而退休基金，也是同樣的道理。
24:21
As inflation goes
higher, they need to pay out more to the retirees,
so where do you get the return?
隨著通膨走高，他們需要支付給退休者更多的錢，那麼你要去哪裡取得回報呢？
24:28
Sovereign wealth fund,
similarly, endowment funds-- they all have
this same situation, have capital and needs to deploy
and to make better return.
主權財富基金、同樣的，捐贈基金——它們都面臨同樣的情況，擁有資本並需要配置資產以獲得更好的回報。
24:39
So this other type of
players, hedge funds.
再來是另一類型的參與者，避險基金。
24:43
So, how many of you
have heard hedge funds?
那麼，在座有多少人聽過避險基金？
24:46
OK good.
好的，很好。
24:46
Almost everyone.
幾乎每個人。
24:48
And Peter mentioned that he
used to work at a hedge fund.
Peter 提到他以前在避險基金工作過。
24:52
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.
私募股權是另一種不同類型的基金。
25:19
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.
顯然，政府對市場有巨大的影響。
25:39
So, we know in the financial
crisis, government intervened.
我們知道在金融危機期間，政府曾進行干預。
25:43
And not only that, at the
normal market condition, government always have a very
large impact on the market, because they are
the policymakers.
不僅如此，在正常市場狀況下，政府對市場始終有非常大的影響，因為他們是政策制定者。
25:53
They decide the interest
rate and interest rate curve.
他們決定利率和收益率曲線。
25:56
And the different policies
they push out, obviously, will generate different
outlook for the future markets, therefore profitability.
他們推出的各項政策，顯然會為未來市場帶來不同的前景，從而影響獲利能力。
26:06
Then the corporate hedges
and the liabilities.
接著是企業避險與負債。
26:09
When corporates borrow
money, they create some risk, so they need to be sensitive
to the market, it changes.
當企業借錢時，會產生一些風險，因此他們需要對市場變化保持敏感。
26:20
So, to summarize the
types of trading.
總結一下交易的類型。
26:23
The first type is
really just hedging.
第一種類型是避險（Hedging）。
26:26
That means you're
not proactively adding risk to what you have.
這意味著你並沒有主動為你現有的部位增加風險。
26:31
You already have some exposure.
你已經有一些曝險部位。
26:37
Just give you an example.
舉個例子來說。
26:40
Let's say you borrow
money, you bought a house, so you have mortgage.
假設你借錢買了一棟房子，所以你有房貸。
26:45
So, let's say it's a floating
rate mortgage payments.
假設這是一筆浮動利率的房貸付款。
26:50
And you're worried about
interest rates going higher, so you can lock that rate in
into the fixed rate format.
你擔心利率會上升，所以你可以將該利率鎖定為固定利率形式。
26:59
Or you can find ways
to hedge your exposure.
或者你可以尋找方法來避險你的曝險部位。
27:03
Or your corporate has a large
income coming from Europe.
或者你的公司有一筆來自歐洲的大筆收入。
27:08
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.
所以你有歐元進帳，但你不確定未來歐元對美元匯率會走強還是走弱。
27:19
If you think it will be
stronger, you just leave it.
如果你認為它會走強，你就持有它。
27:23
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.
但如果你認為它會走弱，你可能想要進行避險，意思是你想要賣出歐元並買入美元。
27:31
And so that's the hedging type.
這就是避險類型。
27:34
The second type, as I
mentioned, is a market maker.
第二種類型，正如我所提到的，是做市商。
27:37
So, market maker also
takes principal risk, but the main source of profit
is really to earn the bid offer.
所以，做市商也承擔本金風險，但主要的利潤來源其實是賺取買賣價差。
27:45
I gave you the example
$0.90 bid, $0.95 offer.
我給你舉個例子，買價 0.90 美元，賣價 0.95 美元。
27:48
So, that's what the market
maker is trying to profit from.
這就是做市商試圖從中獲利的方式。
27:53
But obviously, they
have residual risks sitting on the book.
但顯然，他們的帳簿上仍存在剩餘風險。
27:58
Not every trade is matched.
並非每一筆交易都能配對成交。
28:00
So, how to optimize
those group of trades, that's what market
maker is doing.
所以，如何優化那一組交易，就是做市商正在做的事。
28:06
Most of the bank's
dealers are market makers.
大多數銀行的交易員都是做市商。
28:10
In the new regulation,
obviously, proprietary trading is banned, right?
在新規定下，自營交易顯然是被禁止的，對吧？
28:16
And so the third type is
really the proprietary trader, the risk taker.
所以第三種類型就是自營交易員，也就是風險承擔者。
28:22
So, these are the hedge funds
or some portfolio managers.
這些是避險基金或一些基金經理人。
28:27
They need to focus on generating
return and control the risk.
他們需要專注於創造回報並控制風險。
28:33
So, that's where the beta and
alpha, the concept comes in.
這就是貝塔（beta）和阿爾法（alpha）概念的由來。
28:38
So, if you're a portfolio
manager, some people say, don't worry.
所以，如果你是基金經理人，有些人會說，別擔心。
28:44
Don't go pick any stocks.
不要去挑選個股。
28:46
Just buy S&P 500 index fund.
直接買進標準普爾 500 指數基金就好。
28:49
Very cheap.
非常便宜。
28:50
You can pay very
little cost to do it.
你可以用非常低的成本來做這件事。
28:53
That's true.
沒錯。
28:54
But if you want to
beat the S&P 500 index-- let's assume we call
S&P 500 index fund is asset b.
但如果你想打敗 S&P 500 指數——讓我們假設我們稱 S&P 500 指數基金為資產 b。
29:03
So, the return of that, R(b).
所以，它的報酬率是 R(b)。
29:05
That's a return of that index.
那是該指數的報酬率。
29:08
Now, you have a portfolio a.
現在，你有一個投資組合 a。
29:11
Your time series of
return of your asset a, obviously, you can
do linear regression.
你的資產 a 的時間序列報酬率，顯然，你可以做線性迴歸。
29:19
A lot of you are
math major here, and you can find a correlation
between those two time series.
你們這裡很多人是數學系的，你可以找出這兩個時間序列之間的相關性。
29:27
So, how the two returns are
related in a simplified form.
所以，這兩個報酬率是如何以簡化的形式相關的。
29:32
So you can say, this
actually-- somehow it came out.
所以你可以說，這個其實——不知怎麼地就出來了。
29:36
It's supposed to
be alpha and beta, but it turned out
to be the letters.
它本來應該是 alpha 和 beta，但結果變成了字母。
29:43
So, in a short description,
beta is really-- just think as correlated move
with the other asset.
所以，簡單來說，beta 真的是——只要想成是與另一項資產的相關性波動。
29:51
Alpha is really the
difference in the return.
Alpha 真的是報酬率的差異。
29:55
It's a format.
這是一個格式。
29:57
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.
你想打敗 S&P 500，所以你基本上想對這個指數有某種追蹤，但你想在此之上獲得更多回報。
30:10
So let me just go
in bit of details of how each type of
trade actually occurs.
讓我稍微詳細說明每種交易類型是如何發生的。
30:16
So, when we talk
about hedging, I mentioned the currency example.
所以，當我們談到避險時，我提到了貨幣的例子。
30:22
Let me give you another example.
讓我給你另一個例子。
30:24
There are a lot of people
issue bonds, or issue debt.
有很多人發行債券或發行債務。
30:28
So this example I'm
going to give you is, let's think about
Australian corporate.
所以我要給你的這個例子是，讓我們想想澳洲企業。
30:35
Because interest
rate in Australia is higher than in
Japan, so typically, people like to borrow
money in Japan, because you pay smaller interest.
因為澳洲的利率比日本高，所以通常人們喜歡向日本借錢，因為你支付的利息較少。
30:46
And they invest it in Australia.
然後他們把錢投資到澳洲。
30:49
You earn higher interest rate.
你可以賺取更高的利率。
30:52
So let me ask you a question.
那麼讓我問你們一個問題。
30:54
Who can tell me,
why don't people just do that all day long,
just borrow from Japan and invest it in Australia?
誰能告訴我，為什麼人們不整天只做這件事，一直向日本借錢然後投資到澳洲？
31:03
Then that interest
rate, I'm giving you example of a difference is about
3.5% for the roughly 10 year swap rates.
那麼這個利率差，我給你們舉例，大約是 3.5%，這是大約 10 年期的交換利率。
31:12
Yeah, go ahead.
好，請說。
31:14
AUDIENCE: [INAUDIBLE].
聽眾：[聽不清楚]。
31:16
JAKE XIA: Right.
JAKE XIA：對。
31:17
Because you invest
in the Australia Ozzie, Australian dollar.
因為你投資的是澳洲澳幣，也就是澳元。
31:22
The Australian dollar may
become weaker to the yen.
澳元對日圓可能會變弱。
31:26
You may lose all your
profit, or even more.
你可能會損失所有的利潤，甚至更多。
31:30
And further, if everybody
plays the same game, then when you try to exit, you
have the adverse impact of your trade.
此外，如果每個人都玩同樣的遊戲，那麼當你試圖出場時，你的交易會產生不利的影響。
31:38
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.
所以，假設你認為那是執行的好時機，但到了某個時候，你醒過來，你說，嗯，我覺得做這件事的人太多了。
31:48
I want to hedge myself.
我想對沖我自己。
31:49
So, what do you do?
那麼，你會怎麼做？
31:51
AUDIENCE: [INAUDIBLE]?
聽眾：[聽不清楚]？
31:55
JAKE XIA: Yep.
JAKE XIA：沒錯。
31:56
So, you try to lock in, right?
所以，你試圖鎖定，對吧？
31:58
So basically, you sell
the Australian dollars, buy the Japanese yen.
所以基本上，你賣出澳元，買入日圓。
32:03
Or on the interest
rate terms, you say you'll basically pay the
Australian dollar in the swap leg, and receive yen.
或者在利率條款方面，你說你基本上會在互換交易中支付澳元，並接收日圓。
32:14
This involves foreign exchange
trade, interest rate swap, and the cross-currency swap.
這涉及外匯交易、利率互換以及跨幣別互換。
32:21
So, your answer about currency
forward is roughly right, but obviously involves a bit
more in actual execution.
所以，你關於貨幣遠期的回答大致是對的，但在實際執行上顯然涉及更多細節。
32:29
So that's just to
give you example.
這只是舉個例子給你們聽。
32:32
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.
即使你不是財務背景，在企業工作，只是從事進出口或興建工廠，你也必須實際了解風險敞口是什麼。
32:44
So, risk management, nowadays,
becomes pretty widespread responsibility.
因此，風險管理如今已成為非常普遍的職責。
32:50
It's not just the corporate
treasury's responsibility.
這不再只是企業財務部的責任。
32:54
So, that's on the hedging side.
以上是有關避險的部分。
32:57
Obviously, if you are
Intel, for example, you sell a lot of
chips overseas.
顯然，如果你是像 Intel 這樣的公司，你在海外銷售大量晶片。
33:03
And your income--
actually, Intel does have lot of overseas income
sitting outside the States.
而你的收入——實際上，Intel 確實有大量海外收入留在美國境外。
33:11
So, the exposure to them is if
the exchange rate fluctuates, dollar becomes a lot stronger,
they actually lose money.
所以，對他們來說，如果匯率波動、美元大幅走強，他們實際上會虧損。
33:20
So, they need to think about how
to hedge the revenue produced overseas.
因此，他們需要思考如何避險海外產生的營收。
33:26
And obviously, for
import-exporters, that's even more apparent.
而對於進出口商來說，這點更加顯而易見。
33:31
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.
如果你正在進行一樁合併案，一家公司收購另一家，你需要對潛在的貨幣風險敞口和利率風險敞口進行避險。
33:43
And whatever is on the
assets, or the liability, or the balance sheet, you
need to hedge your exposure.
無論是資產、負債還是資產負債表上的項目，你都需要對你的風險敞口進行避險。
33:56
So we talked about
hedging activity.
我們談過了避險活動。
33:58
Let's talk about market making.
現在來談談做市（Market Making）。
34:00
So if it's a simple
transparent product, everybody pretty much
knows where the price is.
如果是簡單透明的產品，大家大概都知道價格在哪裡。
34:06
So, if you buy Apple stock,
I think a lot of people know pretty much where it is.
所以，如果你買蘋果股票，我想很多人都知道大概價格是多少。
34:11
You may even have it
on your cellphone, know where that stock is.
你甚至可以在手機上看著，知道那支股票的價格。
34:16
But if it's not transparent,
so what do you do?
但如果它不透明，那該怎麼辦？
34:19
So, if instead of asking
you where Apple is, probably you're going
to tell me $495 today.
所以，如果我不是問你蘋果股價現在是多少，你大概會告訴我今天是 495 美元。
34:25
AUDIENCE: I don't really know.
觀眾：我真的不知道。
34:27
JAKE XIA: OK.
JAKE XIA：好的。
34:28
But if I asked you instead,
what is the call option on Apple stock in
two month's time?
但如果我改問你，兩個月後的蘋果股票選擇權買權（call option）是多少？
34:35
I'll give you a
strike, let's say, 500.
我會給你一個履約價，假設是 500。
34:38
So you're probably
less transparent.
所以你大概就沒那麼透明了。
34:41
So that market maker comes
in to provide that liquidity, and then takes the risk.
所以做市商（market maker）進場提供流動性，然後承擔風險。
34:47
They manage the book by
balancing those Greeks, which I mentioned earlier.
他們透過平衡我剛才提到的那些希臘字母（Greeks）來管理帳簿。
34:53
Delta, which describes the
[INAUDIBLE] relationship of this whole book to the
underlying stock, or underlying whatever currency.
Delta，描述了這整個帳簿與標的股，或標的貨幣之間的 [聽不清楚] 關係。
35:03
That's called delta.
那就叫做 Delta。
35:05
Gamma is really the
change of the portfolio.
Gamma 則是投資組合的變化。
35:09
Take the derivative
to the delta, or to the underlying spot.
對 Delta 或對標的現貨取導數。
35:14
So, that's second-order
derivative.
所以，那是二階導數。
35:17
Delta is the first order.
Delta 是一階。
35:20
So gamma, now you have curvature
or convexity coming in.
所以是 Gamma，現在有了曲率或凸性（convexity）。
35:25
And theta is really-- nothing
changes in the market.
而 Theta 其實是——市場沒有任何變化。
35:29
Nothing changes
in your position.
你的部位也沒有任何變化。
35:32
How your trading book is
carrying or bleeding away money.
你的交易帳簿是如何持有或虧損資金的。
35:38
And we talk about the
volatility exposure was vega.
而我們談到的波動性曝險則是 Vega。
35:42
And on top of that,
what are the tail risks?
此外，尾部風險是什麼？
35:47
What are the events can actually
get you into big trouble?
哪些事件會讓你陷入大麻煩？
35:51
So people use value at risk.
所以人們使用風險值。
35:53
So you will hear
this "VaR" concept in some of the lectures,
which is also, obviously, a very important concept.
因此，你會在某些講座中聽到「VaR」這個概念，這顯然也是一個非常重要的概念。
36:01
I think Peter will-- or
Choongbum will-- probably Peter will teach.
我想 Peter 會——或者 Choongbum 會——大概會是 Peter 教。
36:06
Then capital.
再來是資本。
36:07
How much capital are you using?
你使用了多少資本？
36:09
It becomes a very
important issue nowadays.
這在當今成為一個非常重要的議題。
36:12
And balance sheet.
還有資產負債表。
36:14
Again, you have asset,
you have liability.
同樣地，你有資產，也有負債。
36:17
How do you leverage?
你如何運用槓桿？
36:18
How much leverage you have?
你的槓桿倍數是多少？
36:21
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.
所以當市場稍微波動，你就會被清零。
36:32
That's really what amplified
in the 2008 financial crisis.
這正是在 2008 年金融危機中被放大的問題。
36:36
And how do you measure
the asset in balance sheet when you have derivatives
rather than a straightforward notional?
當你擁有衍生性商品而非單純的名目本金時，你該如何衡量資產負債表中的資產？
36:50
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.
所以很多量化背景的人比較喜歡專注在承擔風險這一面，因為大家聽過一些避險基金運用高等數學的成功案例。
37:03
They generated very
impressive returns and they seem to have an edge.
它們產生了非常亮眼的報酬，而且似乎擁有優勢。
37:08
So now, people focus
on trading strategies.
所以現在，人們專注於交易策略。
37:11
So that falls into the category
of proprietary trading or risk taking.
這屬於自營交易或風險承擔的範疇。
37:16
So that you can just simply
doing directional trading strategies.
這樣你就可以簡單地進行方向性交易策略。
37:21
Just go long or short the stock.
就是做多或做空股票。
37:24
That's very simple.
非常簡單。
37:25
Those so-called the gut
traders, gut feeling.
那些所謂的直覺交易者，憑直覺行事。
37:29
Go with your gut.
跟著你的直覺走。
37:31
You don't even think.
你甚至不用思考。
37:33
You say, I'm eating curry
today, so I go long.
你說，我今天吃咖哩，所以我做多。
37:37
I'm eating rice
tomorrow, so I go short.
我明天吃飯，所以我做空。
37:40
So, this arbitrage.
所以，這是套利。
37:42
Arbitrage is really to find the
relationships between prices, and try to profit from those
relationship mispricing.
套利其實是找出價格之間的關係，並試圖從這些關係的錯誤定價中獲利。
37:52
This is actually
very interesting.
這其實很有趣。
37:55
Not many people
focus on arbitrage, because lot of people
are gut traders.
沒有多少人關注套利，因為很多人都是直覺交易者。
38:01
You essentially just
watch your own market.
你基本上只關注你自己的市場。
38:06
You don't really
care what's going on.
你並不太關心其他市場發生什麼事。
38:08
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.
如果你在美國交易黃金，亞洲和歐洲發生的黃金價格波動也很重要，對吧，因為你交易的是同一個東西。
38:17
If they are not
priced the same way, you can profit from
the difference.
如果它們的定價方式不同，你就可以從價差中獲利。
38:22
And that's just
a simple example.
這只是一個簡單的例子。
38:24
But a spot price versus
forward price, that's a deterministic relationship.
但現貨價格與遠期價格之間的關係是確定性的。
38:30
It's a mathematical
relationship.
這是一種數學關係。
38:32
If that relationship breaks
down, you can also profit.
如果這種關係破裂，你也可以獲利。
38:36
So there are many examples
mathematical relationship which gives you the
arbitrage opportunity.
因此，有許多數學關係的例子，能為你提供套利機會。
38:43
The other type is called a
value trader, or relative value strategies.
另一種類型稱為價值交易者，或相對價值策略。
38:51
Think there's a deterministic,
temporary mathematical relationship.
想像存在一種確定性的、暫時的數學關係。
38:56
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.
你觀察較長的時間範圍，試圖確定某個特定工具的真正基礎價值，然後根據相對價值進行交易。
39:08
Obviously, there are successful
value investors out there.
顯然，市場上存在成功的價值投資者。
39:12
And the systematic trader
builds computer models.
而系統性交易者則建立電腦模型。
39:16
One example is trend following,
so just follow the price trend.
一個例子是趨勢跟隨，也就是順著價格趨勢操作。
39:21
That used to be an effective
strategy for some time, but when lot of people
doing the same thing, that becomes much less effective.
這在過去曾是一段時間內有效的策略，但當太多人做同樣的事時，效果就會大打折扣。
39:31
Or momentum, same thing.
或者動量策略，也是同樣的道理。
39:33
Stat arb, finding
statistical relationship among large number
of stocks, then trade at the higher frequency.
統計套利（Stat arb），在大量股票中尋找統計關係，然後以高頻率進行交易。
39:42
And fundamental
analysis, you're really trying to understand what's
going on in the world.
而基本面分析，你真正試圖理解世界上正在發生什麼事。
39:49
What is the trade balance?
貿易餘額是多少？
39:51
What is the earning
potential of a company?
一家公司的獲利潛力如何？
39:55
What's the trade
balance of a country?
一個國家的貿易餘額是多少？
39:58
What is a policy change?
政策有什麼變動？
40:00
What does it mean
when Federal Reserve announce they're going to
taper the quantitative easing?
當聯準會宣布將縮減量化寬鬆時，這意味著什麼？
40:08
Why the stock market is sold
off in the last couple months, especially why stocks in
India, Brazil, Indonesia, sold out more.
為什麼股市在過去幾個月遭到拋售，特別是為什麼印度、巴西、印尼的股票跌幅更大。
40:18
Why is that?
為什麼會這樣？
40:19
So it goes through those
fundamental analysis.
這就要透過這些基本面分析來理解。
40:22
And there are
special situations.
此外，還有特殊情況。
40:25
Some companies are going
through particular difficulties, assets are priced very cheaply.
有些公司正經歷特別的困難，資產定價非常便宜。
40:32
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 from my personal experience,
I joined the market, really start to working
on pricing models.
根據我的個人經驗，我進入市場後，真正開始致力於定價模型。
41:09
So, that's the first area.
這是第一個領域。
41:11
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.
數學非常有效，因為當你、你的銀行或你的企業想要購買某些金融商品時，你必須知道價格是多少。
41:24
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.
在市場上觀察一檔股票很容易，但當涉及到更複雜的產品時，它們在複雜度上又更進一步，那就是選擇權。
41:36
You have to know how
to price an option.
你必須知道如何為選擇權定價。
41:39
So, that's where
the math comes in.
這就是數學發揮作用的地方。
41:42
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.
你實際上必須能夠解微分方程來得到模型價格，然後顯然要根據你的假設進行調整，以符合市場情況。
41:53
So, pricing model, which Vasily
and many of his colleagues can tell you more--
which is very much a very interesting
and challenging area.
And when I say pricing, it's
not in the narrow definition of just coming up
with the price.
當我說定價時，不僅僅是狹隘地定義為算出價格而已。
42:12
When you build a
pricing model, you also generate the risk parameters
of these instruments, and how do you risk manage them.
當你建立一個定價模型時，你也會生成這些商品的風險參數，以及如何對它們進行風險管理。
42:20
So, that comes to
the second part.
這就引出了第二部分。
42:23
So math is very useful
in risk management, which I will give you
some -- not quiz -- questions after this slide.
數學在風險管理中非常有用，稍後這張投影片結束後，我會給各位一些——不是測驗——問題。
42:31
You can see that risk management
itself is very challenging.
你可以看到風險管理本身非常具有挑戰性。
42:35
It's not a purely
mathematical question, but yet, math plays
a very important role to quantify how much
exposure you have.
這不是一個純粹的數學問題，然而，數學在量化你的風險敞口方面扮演著非常重要的角色。
42:44
Then, the third is
trading strategies.
接著，第三點是交易策略。
42:46
Again, I think a lot of
people with math background, or in general,
people are looking for the so-called holy
grail trading strategies.
再者，我認為許多具備數學背景的人，或者一般人，都在尋找所謂的聖杯交易策略。
42:56
It's almost like perpetual
motion machines people looking for 100 years ago.
這幾乎就像一百年前人們尋找的永動機一樣。
43:01
You just turn it on.
你只需將它啟動。
43:02
It makes money by itself.
它會自己賺錢。
43:04
You go to sleep, you go on
vacation, you come back, you'll have more in
your bank account.
你去睡覺、去度假，回來時你的銀行帳戶裡就會有更多的錢。
43:11
Obviously, that's
not going to happen.
顯然，這不會發生。
43:14
The robotrader, a robotic
trader, is a dream.
機器人交易員（Robotrader）是一個夢想。
43:18
It has its place or its use,
but it's a fast evolving market.
它有其定位或用途，但這是一個快速變化的市場。
43:23
You have to constantly
either upgrade your research and adjust your strategies.
你必須持續地升級你的研究並調整你的策略。
43:30
There's no such thing you
can build and leave it alone, it runs for itself forever.
根本沒有那種你可以建立後就放著不管、讓它永遠自己運行的東西。
43:37
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.
但我只是想提一下這點，因為也許在學期快結束時，你會覺得，嗯，我想出了這個絕妙的交易策略。
43:50
I think it's going to
make money forever.
我認為它會永遠賺錢。
43:53
Please let me know first.
請先讓我知道。
43:55
AUDIENCE: And me second.
聽眾：那我呢，第二個。
43:57
PROFESSOR: So, I want to
leave some time to Vasily.
教授：好的，我想留一些時間給瓦西里。
44:02
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.
但在把時間交給瓦西里之前，讓我先問大家幾個問題。
44:20
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.
我只是想——不算是要考你們，只是讓你們感受一下數學、直覺與判斷力是如何融為一體的。
44:32
So, let me first give you an
example I call risk aversion.
首先，讓我給大家舉個例子，我稱之為風險趨避。
44:37
So, you are facing two choices,
choice A and a choice B.
現在，你面臨兩個選擇，選擇 A 和選擇 B。
44:43
Choice A being you have 80
chance to lose $500.
選擇 A 是你有 80% 的機率輸掉 500 美元。
44:47
You have 20% chance to win $500.
你有 20% 的機率贏得 500 美元。
44:50
That's pretty clear, right?
這很清楚，對吧？
44:53
That's choice A.
這是選擇 A。
44:54
Or
choice B, you basically just lock in you have
100% chance to lose $280.
或者選擇 B，你基本上直接鎖定，有 100% 的機率輸掉 280 美元。
45:02
Let me ask you, for whoever
likes to choose choice A, please raise your hand.
讓我問一下，喜歡選擇 A 的人，請舉手。
45:15
One two three four.
一、二、三、四。
45:16
About six out of say,
let's call it 50.
大概 50 個人中有六個。
45:19
So, can I ask you why you
think choice A makes sense?
那麼，我能問一下為什麼你們認為選擇 A 是合理的嗎？
45:23
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?
I think if you have the
discipline to get out, that's great.
我想如果你有紀律能夠出場，那很棒。
47:12
Trading is really all about
how do you risk manage, have the discipline, and
how to manage your losses.
交易的關鍵完全在於如何風險管理、保持紀律，以及如何管理你的虧損。
47:20
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.
很多人的自然傾向是，嗯，我想有 20% 的機率會回升，而且我還想再多賺 500 元。
47:30
Why do I want to lock in
to stop myself out at 280?
我為什麼要在 280 的時候停損出場，把自己鎖在虧損裡？
47:35
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.
所以，即使以期望值來看——我想很多人說過，你在選擇 A 中損失了期望值，也就是 300 元，但你仍然不會選擇選擇 B，因為你不想承認那 280 元的虧損。
47:51
Again, I'm not trying to inject
the idea to you of which one is right or wrong,
but think about it.
再次說明，我並不是要灌輸
48:00
So, that's really the common
behavior, which mathematically may not make sense, but lot of
people still would like to do.
這真的是很常見的行為，
48:10
And also, really, when
you think about it, depends on your situation.
而且，真的，當你仔細思考時，
48:15
And let's say, you
think the market-- I'm giving you the
stock example again.
舉例來說，如果你認為市場——
48:21
If you're not purely following
the discipline of stop loss, but you just think the
fundamental picture has changed.
如果你並不是嚴格遵守停損紀律，
48:31
You really don't think the
stock should go up anymore.
你真的認為這支股票
48:35
Obviously, at whatever level
you should get out, regardless how much loss you lock in.
當然，無論在什麼價位你都應該出場，
48:44
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.
但如果你認為基本面的故事
48:53
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.
但無論如何，
49:07
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.
但我認為如果你問更廣大的受眾，
49:21
Now, let me change the
question a little bit.
現在，讓我稍微改變一下
49:25
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.
所以，方案 A 變成不是 80% 機率賠錢，
49:37
Choice B, you have 100%
chance to win $280.
方案 B，你有 100%
49:41
Who would choose choice A?
誰會選擇方案 A？
49:48
Again, minority
of this audience.
再次說明，是少數
49:50
Let's say less than 10%.
假設不到 10%。
49:53
Who would choose choice B?
誰會選擇方案 B？
49:55
The rest of you.
其餘的各位。
49:56
All right.
好的。
49:57
Can someone choose choice A give
me an argument why would you?
有選擇方案 A 的人能
50:03
AUDIENCE: [INAUDIBLE] JAKE XIA: Yep.
觀眾：[聽不清] 夏傑：是的。
50:16
Anyone want to give me
a reason for choice B?
有誰想告訴我
50:20
AUDIENCE: Higher Sharpe.
視眾：夏普指數較高。
50:22
JAKE XIA: Higher Sharpe?
夏傑：夏普指數較高？
50:24
Mm-hm.
嗯哼。
50:24
Yup.
是的。
50:24
Well, let me just leave it here.
好，我就先講到這裡。
50:27
Again, I think we can talk a
bit more along in the class.
再次強調，我想我們在課堂上
50:32
I mean, the last
day of the class, hopefully we'll have much
deeper discussion on this.
我是說，希望在最後一天的課，
50:39
It's not unique.
這並非唯一的答案。
50:40
The answer, I think it can go
you either way, as you said.
我想，就像你說的，
50:45
If your bank account
balance is-- let's say you are a freshman student.
如果你的銀行帳戶餘額是——
50:51
Your bank account is $800.
你的銀行帳戶裡有 800 美元。
50:54
Your choice will be very
different from someone has $100,000 in his bank account.
你的選擇將會與
51:02
And also, your risk tolerance,
how much you can tolerate.
還有，你的風險承受度，
51:07
I'm not going to give you
say, this is right or wrong.
我不會告訴你
51:12
But with that, let me move on
and give you some homework.
但既然提到這裡，我就繼續往下講，
51:23
So, before I give
you the homework, I want to make a
few more comments.
所以，在給作業之前，
51:28
Do people always learn
from their experiences?
人們總是會從經驗中學習嗎？
51:31
In science, we collect
evidence, we build models.
在科學上，我們收集證據，
51:34
We first understand the physics.
我們首先理解物理學原理。
51:37
We build mathematical models,
then we verify in physics, doing experiments.
我們建立數學模型，然後在物理學中透過實驗進行驗證。
51:42
But is that the same
investigation process in finance?
但金融領域的調查過程是否相同？
51:46
Market cycles are
typically very long, but people tend to
have short memories.
市場週期通常非常長，但人們往往記憶短淺。
51:51
So, how do people really
learn from their experiences?
那麼，人們究竟如何從經驗中學習？
51:55
A very interesting question.
這是一個非常有趣的問題。
51:57
And very natural tendency
is to extrapolate historical experience.
人們很自然地會去推斷歷史經驗。
52:02
What happened in 2008?
2008 年發生了什麼事？
52:04
People still remember.
人們仍然記得。
52:06
What happened in 1970s?
1970 年代發生了什麼事？
52:07
Maybe some people
still remember.
也許有些人仍然記得。
52:10
What happened 100 years ago?
100 年前發生了什麼事？
52:12
So, people tend to extrapolate,
drawing conclusions from very recent experience.
因此，人們傾向於根據近期的經驗進行推斷並得出結論。
52:18
And deterministic relationship
versus statistical relationship is very interesting, as well.
確定性關係與統計關係的差異也非常有趣。
52:25
When you try to trade on those,
how do you really build models?
當你試圖以此進行交易時，究竟該如何建立模型？
52:29
Is the market really efficient?
市場真的有效率嗎？
52:35
What part is efficient?
哪一部分是有效率的？
52:37
How do you really
apply those theories in your day-to-day risk
management or trading activities?
你究竟該如何將這些理論應用於日常的風險管理或交易活動中？
52:45
And sometimes, people
tend to oversimplify.
有時候，人們往往過度簡化。
52:49
Just say, oh, I can model this.
只是說，哦，我可以對此建模。
52:51
This is one important parameter.
這是一個重要的參數。
52:54
I just take that.
我就直接採用了。
52:55
So I just give you
all the warnings that the-- again,
very young, new field and largely, often, this
is art, than science.
所以我要再次提醒各位，這是一個非常新興的領域，而且在很大程度上，這往往更像是一門藝術，而非科學。
53:05
So keep that in mind,
even though we're talking about mathematics in finance.
所以請牢記這一點，即使我們正在討論金融數學。
53:11
Math is very powerful
and useful in finance.
數學在金融領域非常強大且實用。
53:15
So learn the math,
learn the finance first, but keep those
questions along the way when you are learning
during this class.
所以請先學習數學，再學習金融，但在這門課的學習過程中，請隨時保持這些疑問。
53:27
So suggested homework, optional.
這是建議的作業，選修性質。
53:32
I mentioned a lot of
terminologies today.
我今天提到了很多術語。
53:35
Go to the course website,
read what we have put up for the financial glossary.
請前往課程網站，閱讀我們上傳的金融詞彙表。
53:41
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.
如果還有不明白的地方，請整理一份自己的金融概念清單，可以上網搜尋，甚至可以問我們。
53:52
But I encourage you to do that.
但我鼓勵大家這麼做。
53:54
It will prepare you well.
這會讓你準備得更充分。
53:56
So, that's really-- and
read other materials on the course work.
另外，也要閱讀課程的其他材料。
54:01
So we got maybe--
how about this?
那我們大概——這樣如何？
54:03
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.
Well, first of all, no offense
to people who were [INAUDIBLE], but I just wanted to give
an example of [INAUDIBLE].
嗯，首先，對 [聽不清楚] 的人沒有惡意，但我只是想舉個 [聽不清楚] 的例子。
54:51
AUDIENCE: [INAUDIBLE].
觀眾：[聽不清楚]。
55:01
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.
其中一個項目是 [音訊不清] 負責的，是關於估算有噪聲的導數。
55:29
Derivative is called delta.
這個導數被稱為 Delta。
55:31
Delta is usually the first
derivative to a function.
Delta 通常是一個函數的一階導數。
55:36
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 obviously, there is a noise
to your answer every time.
因此，顯而易見，你的答案每次都會有噪聲。
55:56
So, if you want to
differentiate this functions and get a derivative, then this
derivative will be quite noisy.
所以，如果你想要對這些函數進行微分並得到一個導數，那麼這個導數將會充滿噪聲。
56:05
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.
顯然，這裡也存在一個權衡，因為你可以運行更多的路徑，投入更多的運算能力，這將會縮小你的置信區間。
56:33
You will know better where
you are, more precise.
你會更清楚自己的位置，更精確。
56:37
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.
基本上，這樣可以降低誤差的顯著性，你將有望得到更好的近似值。
57:00
So obviously, there is somewhere
balance, and the question was, is there an optimal shift
size to get the derivative?
所以顯然，這裡存在某種平衡，而問題是，是否存在一個最佳的偏移量來獲取導數？
57:12
And that's what-- uh oh,
the slide got corrupted.
而這就是——哎呀，投影片損壞了。
57:17
So, there was quite
a bit of mathematics involved and minimization
and optimization.
所以，這裡面涉及了大量的數學、最小化和最佳化。
57:25
There was an answer.
有一個答案。
57:27
And that's actually what
we finally arrived at.
這其實就是我們最終得出的結果。
57:32
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.
而如果你使用 [音訊不清] 計算出的最佳偏移量，它會平滑得多，也精確得多。
58:00
So, that's one of example,
and that's what he did.
這是一個例子，
58:05
And we actually are implementing
it in our systems and plan to use it in practice.
我們實際上正在我們的系統中實施它，並計劃在實踐中使用它。
58:13
Another project was
actually quite different.
另一個專案則截然不同。
58:17
And it was about
electronic trading and basically how to better
predict prices of currencies and exchange rate.
它是關於
58:28
And funny enough, it
was on ruble/US dollar, because it was actually
aimed for our Moscow office.
有趣的是，
58:38
And basically, what we had,
we had the noisy observation of broker data and
it was coming out at different non-uniform times.
基本上，我們有的是
58:51
Basically, at random times.
基本上，是在隨機時間。
58:54
So, we decided to
use Kalman filter and to study how it can predict.
所以，我們決定
59:01
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.
這是他製作的其中一張
59:20
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.
所以，這只是幾個例子，我想給你們
59:33
Just to remind, the website
is fully functional.
提醒一下，網站
59:37
We put syllabus there, a
short list of literature.
我們在上面放了教學大綱，
59:42
We will be posting a
lot of materials there.
我們將在上面發布
59:46
Probably most lectures
will be published there.
可能大多數講座
59:51
Jake's slides are there already.
Jake 的投影片已經在上面了。
59:54
So, any questions?
那麼，有問題嗎？
59:59
JAKE XIA: Please hand
back the sign up sheets.
JAKE XIA: 請把
1:00:02
We like to get your
emails so we can put you on the website for
further announcements, but you can also add
yourselves.
我們希望取得你們的
1:00:10
[INAUDIBLE].
[聽不清]。
1:00:11
But it's probably easier
if you put your email on the sign up sheet,
so we can [INAUDIBLE].
但如果你們把電子郵件
1:00:17
VASILY STRELA: Yeah,
but please visit and sign up here,
because there will be announcements to the class.
5Whatdo 'Alpha' and 'Beta' representinthecontextofportfoliomanagement?在投資組合管理的背景下，「Alpha」和「Beta」分別代表什麼？Whatdo 'Alpha' and 'Beta' representinthecontextofportfoliomanagement?
