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  • PROFESSOR ROBERT SHILLER: OK, good morning.

  • Well, today I want to talk about what, to me, is a very

  • interesting topic, and that is futures markets.

  • Not very interesting to most people.

  • Most people have no idea what they are.

  • But I think that, well, futures markets, what we're

  • really talking about is --

  • There are different ways of viewing it.

  • Futures markets for things like agricultural commodities,

  • or interest rates, or financial securities, are

  • markets about the future.

  • They're markets that, in some sense, predict the future.

  • And future matters, right?

  • We live a life.

  • We have a long horizon.

  • I said before, I think that your planning horizon must be

  • at least a century, because you'll probably live that long

  • anyway, with modern medicine.

  • And you care about other people, too.

  • So, the beauty of futures markets is that we have prices

  • for the future.

  • We talked already about forward markets.

  • We talked about forward interest rates.

  • And that is related to what we're talking about.

  • Forwards and futures are similar concepts.

  • Futures is the more precise concept.

  • Or the more developed concept.

  • And I'll explain the difference between forwards

  • and futures.

  • But just in a nutshell, futures markets are organized

  • markets, like the stock market, that trade

  • standardized contracts, representing things that will

  • happen at future dates.

  • And because they're

  • standardized, they're worldwide.

  • Everybody looks at them and uses them.

  • Whereas forward markets are more specialized markets that,

  • typically, are not as easy to interpret or as clear.

  • So, futures markets are, in some sense, more fundamental

  • and important.

  • I have a particular interest --

  • I've been interested in futures markets myself for

  • many years.

  • And wondering, why they're not even

  • bigger and more important.

  • So, in 1993, I wrote a book called Macro Markets, about

  • let's make our markets bigger and more

  • important, and more pervasive.

  • And I've been trying to do that.

  • Notably, in 2006, I was working with the Chicago

  • Mercantile Exchange, which is the biggest futures

  • market in the world.

  • And we created home price futures.

  • And they've been trading now for five years.

  • But I'm not really going to talk about them, because they

  • have so far disappointed.

  • They're not important, at least not yet.

  • But I'm going to talk about some

  • important futures markets.

  • First, I want to put just a couple of definitions up.

  • Futures, that's what we're going to talk about most in

  • this lecture, and it has a special meaning in finance.

  • And I was contrasting that to forwards.

  • But both of these together are derivatives.

  • And that means that the price in these markets derives from

  • a price in some other market.

  • There's a primary or underlying market, which has

  • its own price.

  • And then there's a derivative market that has a futures

  • price or a forward price.

  • I guess I'm speaking in kind of abstract terms. Well, let

  • me just start --

  • I want to give you an example, and we'll see better what I'm

  • talking about.

  • But let me just first comment just on this word,

  • derivatives.

  • To people in finance, derivatives are an exciting

  • development of financial markets.

  • We start out with a simple market and we develop

  • derivative markets, that add more detail and information

  • than was in the underlying or primary market.

  • That's exciting.

  • I find it exciting.

  • However --

  • I don't know how often you hear this word, derivative --

  • it's become a four-letter word.

  • It's become an ugly word.

  • Why is that?

  • I think it's, because people blame the current financial

  • crisis on derivatives, whether rightly or wrongly.

  • And it's because, I think, there's a public anger about

  • derivatives that is largely due to misunderstanding.

  • I mentioned before that I think that finance tends to

  • attract sociopaths.

  • I mentioned that, I defined that for you.

  • People who want to manipulate, and fool, and deceive people.

  • But I don't think the financial community is

  • particularly populated by sociopaths.

  • You might think so, reading some accounts.

  • But I think, it's not true.

  • And I think, it's not true, because the financial

  • community knows about this problem

  • and ejects such people.

  • They get caught.

  • And you can't make a career in finance if you're a sociopath.

  • So, if you think you have this problem, that you have

  • sociopathic tendencies, I would advise you not to go

  • into finance, because you will get caught and ejected.

  • So, save yourself the trouble.

  • Don't go into finance.

  • Pick some field where you can't hurt anybody.

  • And that would be a smart thing to do, if

  • you have such a problem.

  • So, I think we need to regulate derivatives markets,

  • and that's what I'm talking about.

  • And we need self-regulation of the markets themselves, but we

  • need government regulation as well.

  • But there's nothing evil about derivatives.

  • And in fact, derivatives are fundamental to the way I think

  • a modern economy works.

  • So, I had you read an article --

  • I put it on an earlier section of the reading list --

  • by Charles Conant, who wrote a book in 1904 called Wall

  • Street and the Country.

  • And you should have read that by how.

  • He starts out by saying, it's just amazing, how public

  • opinion thinks that speculation is evil.

  • And they don't understand that speculation is just business.

  • I mean, business decisions involve

  • guesses about the future.

  • And so, when you have well-developed markets, these

  • guesses become market prices.

  • And so, the prices go into the calculations

  • that everyone makes.

  • And the calculations are just done better.

  • Somehow, there's just a failure for most people to

  • understand it.

  • And I'm hoping in this lecture to try to give some more

  • understanding of these markets.

  • I think they're fascinating.

  • Most people apparently don't, because you don't hear them

  • brought up very much.

  • I want to just say a little bit more about hostility

  • toward derivative markets and futures markets, and

  • speculation in general.

  • In 1991, that was 20 years ago, I wrote a joint

  • paper with a --

  • I don't remember whether I mentioned this,

  • probably not --

  • with a Russian, a young man from Russia that I met when I

  • was visiting the Soviet Union, just before the end of the

  • Soviet Union.

  • And we were talking about how antagonistic Russians are

  • toward capitalism.

  • And he said, this is a big problem.

  • Russia just can't embrace capitalism.

  • These people hate it.

  • They hate the profit makers and the financiers.

  • And I said to him, well, you know, it's the same in the

  • U.S. How do you know it's any worse in Russia?

  • And so, we decided to do a questionnaire survey.

  • And I was going to read one of the questions, comparing

  • people in Moscow and people in New York, to see, which one

  • understands capitalism better.

  • So, one of the questions that we had was the following --

  • We wrote these questions and translated them into Russian.

  • And we tried to make them exactly the same questions

  • between Russian and English.

  • So, here's the question we asked in both cities: ''Grain

  • traders in capitalist countries sometimes hold grain

  • without selling it, putting it in temporary storage in

  • anticipation of higher prices later.

  • Do you think this speculation will cause more frequent

  • shortages of flour, bread and other grain products?

  • Or will it cause such shortages to become rarer?''

  • What do you think, people said?

  • Does the process of speculating in grain cause

  • problems or solve problems?

  • Well, we found that, in the USA, 66% said it will make

  • shortages more common.

  • But in the Soviet Union, in Moscow, only 45% thought it

  • would make shortages more common.

  • Both of them were wrong.

  • A lot of them were wrong, but the Russians were better,

  • closer to the truth than the Americans.

  • Living in the financial capital of the USA, most

  • people think that speculating in grain creates problems. But

  • wait a minute, what is speculation in grain?

  • That means holding it off, expecting higher

  • prices later, right?

  • Isn't that what you have to do if you are

  • managing a grain market?

  • Now, think of it this way -- and I'm coming now to

  • agricultural futures.

  • In the simplest world, there's one harvest

  • of wheat every year.

  • And that harvest comes in a certain time of the year,

  • every year.

  • Once a year.

  • And it has to be held in storage over the year, right?

  • Because people don't eat it all at once.

  • You eat it over the whole year.

  • So, somebody is storing grain.

  • This is a fundamental problem.

  • That's a business.

  • So, you have to know that somewhere there's some

  • warehouse holding the grain that you will be consuming in

  • six months time.

  • And that warehouse is run by some

  • professionals who do that.

  • If they think prices are higher later, they'll keep it

  • longer in the warehouse.

  • And what does that do?

  • That evens out the price.

  • It doesn't make it worse.

  • If they think there's going to be a shortage of grain, they

  • hold it back now and the price of grain goes up.

  • And so, everyone starts consuming a little less

  • because of the higher price, and it smoothes things out and

  • it works better.

  • And this is elementary economics, but it's not

  • understood, I think, by most people.

  • And the futures markets are just sophisticated markets

  • that help that process.

  • So, I'm going to start with agricultural futures in

  • talking about this.

  • And I want to start also with a very homely -- it's not

  • homely -- it's a very elementary example, because

  • it's the first futures market.

  • So, where do you think futures markets started?

  • You would think, it started in New York, or Chicago, or

  • London, or Paris.

  • It actually started in Japan in a place called Dojima,

  • which is in the city of Osaka.

  • And they started in the 1600s.

  • So, let's go back.

  • If we can go back to the year 1673, in Osaka in Japan.

  • Japan was heavily dependent on rice.

  • And the rice farmers would farm all over Japan, but there

  • was a rice market in Dojima, which was the

  • national rice market.

  • And I have data here.

  • According to a study, there were 91 rice warehouses in

  • Dojima in 1673.

  • That's a long time ago, isn't it?

  • So, it was a big storage place for rice, and they were

  • storing it all year.

  • And people would come, people who were merchants for rice,

  • and they would come to Dojima and they would sign contracts

  • to get rice.

  • I live in some town 20 miles from

  • here, I'm a rice merchant.

  • I need a regular supply of rice from your warehouse.

  • Can you supply it to me?

  • And the guy would give you a terms, and that would be a

  • forward contract.

  • And this is what was happening before the futures market.

  • Forward contracts precede futures contracts.

  • So, do you see what it is?

  • You're a rice merchant.

  • You make a deal.

  • You sign a contract that I will pay you so much in

  • currency at every month, and you'll give me so much rice.

  • And you'll deliver it here, and I'll take it, and I'll

  • sell it in my town.

  • Problems developed in the forward market that led to the

  • development of a futures market.

  • And the problem is, one of the problems is that there's

  • counterparty risk.

  • You are a rice merchant.

  • You make a deal with a warehouse.

  • That's one person dealing with one person, right?

  • What if one of the guys reneges on the deal?

  • So, for example, what if the price of rice falls?

  • Then you, the merchant, will say, I'm not going to go back

  • and buy according to this contract, because

  • it's cheaper now.

  • I'll buy it somewhere else.

  • So, I just don't show up, and then the warehouse is saying,

  • what happened to our contract?

  • And you're nowhere to be found.

  • Or if it goes the other way, if rice goes up, the warehouse

  • might renege.

  • They'd say, we signed this contract but there's something

  • wrong with it, and we're not going to honor it.

  • So, it messes up.

  • It is also possible that one of the two counterparties is

  • just a sociopath or something, or is an alcoholic, or

  • something is wrong.

  • So, the market doesn't work well.

  • So, what they invented in Japan was the first true

  • futures market.

  • And the market worked like this: There was a trading

  • floor in Dojima.

  • And rice traders would come there, and there were certain

  • hours of the day, when you would trade contracts for

  • future delivery.

  • But they were standardized contracts, mediated by the

  • exchange, so that there would be no

  • problem with the contract.

  • And then every day, there would be a trading time, and

  • you could buy and sell contracts for future delivery.

  • Moreover, they enforced trading hours.

  • And this is something that's kind of

  • an interesting invention.

  • They didn't have --

  • I guess they didn't have clocks.

  • I don't know what they had.

  • But they had a certain time, when trading would stop, and

  • they wanted to stop all the trading at the same time.

  • They didn't want people dribbling out.

  • They wanted it to be a good market.

  • So, they would light a fuse, and it would be a bright light

  • in the middle of the trading floor.

  • And you'd see the fuse burning down, and when it burned out,

  • all trading stopped.

  • So, they had trading hours.

  • Moreover, they had a problem that some of the traders

  • wouldn't stop trading.

  • So, this is something that they did in Dojima, they had

  • men called watermen, who came out with buckets of water.

  • And they would throw the buckets of water on anyone who

  • was still trading.

  • So that worked.

  • It stopped trading.

  • They also had hand signals.

  • This was big.

  • This is big time.

  • You were trading rice for all of Japan.

  • And you may think the 16- or 1700s are long ago, but a lot

  • of rice was traded and it got really noisy and difficult.

  • They found that it was so many people trading on the floor,

  • that you couldn't hear anyone talk.

  • And there'd be shouting and it was noisy, and so, they

  • devised a system of hand signals.

  • And the Dojima hand signals were, I don't know exactly,

  • but something like this.

  • If your hand was out, you put your hand

  • out, that means sell.

  • You put your hand this way, it meant buy.

  • And if you put three fingers up, it means

  • selling three contracts.

  • That kind of thing.

  • I don't know the whole system, but that's where it started.

  • That whole concept was copied all over the world in

  • subsequent centuries.

  • So, what is it that happened?

  • And the other thing is, what were the contracts that you

  • bought and sold?

  • The problem with the forward market is that the contracts

  • are all different.

  • One guy made a contract with one guy, and he said, I want

  • my delivery here.

  • And I don't like this kind of rice.

  • I want this kind.

  • And you better make sure that there's not a single insect in

  • it, or I'm going to reject the whole thing.

  • But that's all different.

  • So, you don't know what --

  • these contracts, you don't even know what the

  • price of rice is.

  • If someone said, I paid so much to get rice

  • in the future --

  • but you have to say, well, under what circumstances?

  • And what kind of rice?

  • And where?

  • And what are the terms for possible failure?

  • You know, there's so many terms in the contract, so you

  • don't even know what the price of rice is.

  • But at the futures market, they

  • standardized the contract.

  • So, it may not be exactly what you want, but it's

  • standardized.

  • So, you deliver rice --

  • I don't know all the details of Dojima, but I'm talking

  • about futures markets, as they evolve.

  • In a modern futures market, agricultural futures market,

  • you deliver your --

  • the contract is to deliver some commodity like rice at a

  • specified future date, at a specified future warehouse,

  • which would be run by the exchange.

  • And there's inspectors at the warehouse who

  • are expert on grain.

  • And they verify, because they know rice.

  • They know it really well.

  • And they know that some rice has bugs in it.

  • They know how to find out.

  • They have a standard.

  • Of course, there can always be some bugs in it, but they have

  • a standard and they have a way of measuring,

  • and they get it right.

  • And so, all those contracts are exactly the same.

  • And so, they become the price.

  • It turns out, funny thing, the futures market almost becomes

  • the real market, because they're all standardized.

  • The futures price --

  • You know where it's delivered.

  • You know what's delivered, exactly.

  • The futures market becomes the market, in a sense.

  • The fact that it's in the future is, in effect, a help,

  • because since it's a comfortable time in the

  • future, it's well defined.

  • Whereas the spot market --

  • the spot market is the market for rice, or whatever it is,

  • today as it's traded.

  • The spot market is inscrutable.

  • It's hard to understand.

  • So, let's think about a farmer today, who grows rice, or

  • wheat, or soybeans, or something.

  • If you drive through farming countries, listen to the

  • radio, regularly they'll give prices.

  • Soybeans, wheat, rice, et cetera.

  • Why do they give that?

  • Because farmers care.

  • They're raising this stuff.

  • It's their whole livelihood, whether they make a profit or

  • not, depends on it.

  • What prices do they quote?

  • They quote the futures prices, even though

  • they're in the future.

  • But they quote them, because they mean something and

  • they're standardized.

  • So, that's why the futures market

  • becomes the central market.

  • I want to just say something about futures --

  • Japan started the futures markets in the 1600s, and they

  • were the world leader in rice futures until 1939.

  • And then, at World War II, the Japanese government shut the

  • futures market down.

  • And to this day since, there is no rice

  • futures market in Japan.

  • Believe it or not.

  • The inventors, they're talking now of starting it up again.

  • Where do they trade rice futures?

  • Well, the USA is the main market, even though you don't

  • think of the U.S. as a market for rice.

  • But the point is, that markets have to be centralized.

  • And that people want the centralized market, and if it

  • happens to be in Chicago, so be it.

  • So, it becomes a huge international rice market.

  • And so, I looked up --

  • this is called Rough Rice Futures, and this is the

  • futures curve as of last Friday

  • [addition: March 18, 2011].

  • So, what we have is different delivery months.

  • This is May of this year.

  • And then, there's other delivery months, and then

  • there's next year.

  • It goes out about a year, different delivery dates.

  • And this is cents per 100 weight.

  • 100 weight is 100 pounds of rice.

  • And since this is USA, we mean 100 U.S. pounds of rice.

  • But anyone in the world can figure this out and trade in

  • this market.

  • And it's in dollars, because it's what we're

  • trading in the USA.

  • So, someone in Japan, who wants to trade in the futures

  • market, has to come to the USA, change their yen into

  • dollars, and do this.

  • Now, you see that the futures price is going up.

  • This was all quoted last Friday

  • [addition: March 18, 2011].

  • This is the market, essentially, right now.

  • But you see, it's a futures market, because it's giving

  • prices of rice at dates in the future.

  • These prices way out here, next year, are not so

  • reliable, because there's not much trade.

  • The trade tends to dominate at the front months.

  • So, here's where most of the trade is.

  • They're trading May, and maybe this is July.

  • I forgot exactly.

  • Is that clear, what this means?

  • It's going up.

  • And it's going up pretty fast, isn't it?

  • From about less than $0.13 to $0.15.

  • What this means is that, in effect, the market is

  • expecting huge increases in the price of rice.

  • So, that's interesting.

  • Anyone who's doing business in rice looks at this and says,

  • look, there's price increases anticipated.

  • Now, I just want to talk about the world at this point in

  • history, and try to interpret this curve.

  • You must have heard that there is a food shortage in the

  • world developing.

  • And it's a source of crisis.

  • It's developing in the Middle East.

  • One reason why that's been given for the revolutions that

  • have happened in the Middle East are,

  • that people are hungry.

  • There's dissatisfaction when the price of food goes up.

  • A lot of people are living much more at the margin than

  • you'd imagine.

  • So, this increase in rice prices matters a lot.

  • So, it's very interesting that it's showing this steep

  • increase in the price of rice.

  • But the first thing you want to think of as a financier is

  • how much is this going up?

  • I didn't actually do the calculation.

  • It goes up from 14 --

  • under 13.75 to 15.5.

  • That's quite an increase in six months, right?

  • So, it sounds like there's a profit opportunity here.

  • Buy rice today and sell it on the futures market.

  • This is a good time to sell it.

  • I'll sell it in 2012.

  • And that's my futures profit.

  • I can lock in this price today, because that's what the

  • futures market does.

  • The contract is a contract to deliver rice as of that future

  • date, and this would be in Chicago, OK?

  • And so, I could make a profit.

  • This is a very professional market with real expertise.

  • You talk to the rice traders or the wheat traders, they

  • know what they're doing.

  • Believe me, they know what they're doing.

  • We're looking at this for the first time.

  • People who trade this all their lives --

  • And if you ask, why is it?

  • Look how much it's going up, this is a big profit

  • opportunity.

  • They'll tell you, why it isn't.

  • Why it isn't such an opportunity as you think.

  • There must be some reason, why I can't make huge money by

  • trading in rice, because otherwise other

  • people would do it.

  • This is such a liquid market, open to

  • everybody in the world.

  • So, somebody's going to take advantage of this.

  • You understand, this is futures prices quoted as of a

  • single date, for various horizons in the future.

  • Don't get confused by it.

  • This is not a plot through time.

  • This is now.

  • This is what's quoted now.

  • And so, when you have an upward slope in futures curve

  • like that, we call that contango.

  • And that is what we usually see, maybe not upward sloping

  • so much as this.

  • The opposite is called backwardation, if futures

  • prices are declining through time.

  • That happens, and I'll show you that in a minute.

  • But it's not happening in rice.

  • So, not happening now in rice.

  • It must be that there's something that prevents you

  • from just making a killing by buying rice and selling it on

  • the futures market.

  • Do you understand, this is riskless?

  • If I sign a contract to sell rice in Chicago on the futures

  • market, that is riskless [addition: only if I own the

  • underlying commodity].

  • And so, why don't I just do that?

  • I think that there must be some --

  • in some level, there must be some storage cost problem.

  • In order to actually do this, you'd have to buy the rice and

  • store it for six months.

  • And I'm thinking, that must explain it.

  • It must be that at this point in time, storage costs are, in

  • some sense, too high for this to be a real profit

  • opportunity.

  • So, this is what happens now in the real world.

  • There are people who store rice.

  • There has to be, right?

  • I think, rice comes in more than one harvest, because

  • there's different kinds, but there's no more than a few

  • harvests in the year.

  • And some of them are bigger than others.

  • And so, it's got to be stored.

  • And this really, really matters, because if it's not

  • stored, some people are going to starve to death.

  • So, it really matters.

  • And you have professional warehouse operators, who --

  • they sure do know what this curve says.

  • And they're thinking, right now, I'm sure lots of people

  • looked at this curve yesterday, and they thought,

  • look at that contango, wow.

  • I'm going to see if I can get some other warehouse.

  • Can I get another one?

  • There's an empty building on the south side of Chicago,

  • maybe I can fill it up with rice.

  • And so, I have to look up, and I have to get inspections, and

  • sanity checks --

  • sanitation checks.

  • And think about insurance.

  • And they're thinking about that.

  • But, you know, they find out that it's not going to work,

  • and they're trying.

  • This generates, when you have a lot of contango on the

  • market, it generates enthusiastic efforts by smart

  • people to try to store more rice.

  • And you see, what that's doing.

  • It's helping prevent a famine.

  • And this goes back to --

  • I know, I'm putting it in dramatic terms --

  • but this goes back to Adam Smith, who in his Wealth of

  • Nations in 1776, has a famous passage, which I can't quote

  • exactly, but it was something to the effect that, you know,

  • there's a lot of people who express benevolent impulses.

  • They give to charity.

  • They go to church regularly, and they talk about ''love thy

  • neighbor.'' But they're not doing a single thing to

  • prevent the next famine.

  • They're not thinking about it.

  • The people who are really effective are these quiet guys

  • dealing in the markets.

  • And they see a contango, and they see something coming.

  • And so, they get in the business of storing.

  • And it's purely out of self interest. So, the famous quote

  • that is quoted a million times from Adam Smith is, these

  • people operating in their own self interest seem to be more

  • important in promoting human welfare than all the

  • benevolent people combined.

  • I'm quoting him roughly.

  • Well, there has to be an element of truth to that.

  • You know, people who do these storages of grains do not get

  • much respect.

  • And at dinner conversations, nobody cares what they do.

  • They're really good at what they do, and

  • they know this market.

  • And, you know, they're not saints, either.

  • They're speculators.

  • They're trying to make a profit.

  • Now, one thing I wanted to say about futures also, which I

  • didn't really clearly --

  • in forward markets, which are markets between a pair of

  • counterparties, there's always counterparty risk.

  • I'll write that.

  • That means, you've got a contract.

  • You had a lawyer.

  • A lawyer wrote up the terms. You can take this guy to

  • bankruptcy court or something, but that's all a nuisance and

  • it costs money.

  • You never know.

  • Futures markets get rid of counterparty risk, or

  • essentially get rid of it.

  • And how do they do that?

  • The system is a standardized retail market that anyone can

  • play in, but you have to post margin --

  • and that's the idea, margin, when you

  • either buy or sell futures.

  • OK, so this is what happened.

  • This is what a futures contract looks like.

  • You can do this.

  • I don't know what would happen, if you called up a

  • broker at your age, but essentially you can do this.

  • I know, Jeremy Siegel, my friend, said, he would

  • actually lend money to students and let

  • them play the markets.

  • His own money.

  • I have never done that, so don't ask me to do that.

  • But you can basically call up a broker and say, I'm

  • interested in rice futures.

  • It sounds like fun to me.

  • I'd like to play that game.

  • So, the broker would say, fine, I'll

  • open a margin account.

  • How much money are you going to put in?

  • All right.

  • The first question is, money.

  • He doesn't know who you are, but money talks.

  • So, you say, all right --

  • you have to come up with some money to do this.

  • Let's say, I'll put in $5,000 into a futures

  • account at your brokerage.

  • And he would then say, OK.

  • Now, you have $5,000.

  • And the margin requirement for rice futures, I don't remember

  • what it is, say it's something like 3% or 5%.

  • You can buy or sell up to the limits imposed by your margin.

  • Your margin has to be whatever percent of the

  • contract that you sign.

  • You're only putting up $5,000, I'll let you buy and sell

  • $100,000 worth of rice.

  • So, this would happen.

  • You say, OK, I want to buy --

  • what do I want?

  • What do I want to do?

  • I'm going to store rice, and then I want to sell it.

  • So, I want to sell futures.

  • It doesn't matter, whether you buy or sell.

  • Either way, you've got to put up money.

  • Let say, I'm going to do this rice storage business.

  • I can do it.

  • It's open to anybody in the world.

  • I can find a warehouse.

  • I can buy some rice.

  • I can store it.

  • And I can sell it at that price.

  • So, I want to sell futures.

  • I can sell $100,000, even though I've only

  • got $5,000 put up.

  • But then, you know what happens.

  • Every day, they look at the change --

  • the futures price is the price on that contract today, but

  • it's not a price that you pay today.

  • You would pay it at the end, effectively, when the

  • contract comes due.

  • Or in the case of selling, you'd be receiving it.

  • So, if I sell futures for, say, May of 2012, then I am

  • promising to deliver rice to the warehouse in Chicago on

  • that date in 2012, and take the price.

  • OK, but now, the futures price today is the price that the

  • market has today.

  • Tomorrow, the futures price will be different.

  • And so, what they have in the futures markets is daily

  • settlement.

  • And that means that if I sold futures --

  • I'm storing rice and selling futures --

  • if the price goes down --

  • I'm sorry, if the price goes up --

  • it works against me, because I've locked

  • in the lower price.

  • So, the broker debits my margin account by the daily --

  • every day they change my margin account.

  • So, if I've sold futures and the price goes up, they take

  • it out of my margin account.

  • If the price goes down, they put it into my margin account.

  • And I can quickly deplete my $5,000.

  • The post price keeps going up.

  • Then I say, gee, I wish I hadn't signed that contract,

  • because I could have waited a few days and

  • gotten a better price.

  • Meanwhile, the broker calls you on the phone and says, I'm

  • sorry, your margin account is almost depleted.

  • Do you want to put up more margin?

  • And this is where you get the reality of futures trading.

  • Because there's no counterparty risk.

  • That means, that if you don't put up more margin, the broker

  • closes you out and says, here's your money.

  • Do you understand how this works now?

  • So, there's no counterparty risk, because it doesn't

  • matter, whether you're a drunk or a sociopath, the broker has

  • you trading.

  • And it doesn't matter at all what you do.

  • Once you put up the money, and if you just don't answer the

  • phone -- if you, say you don't answer the phone, the broker

  • will close you out, when the margin is depleted.

  • So, the broker takes no risk.

  • The counterparty is not even given to you.

  • You don't even know, who's on the other side of that

  • contract, because the other side is making --

  • you're both making a contract with the exchange.

  • And so, you don't care about counterparty risk, and there's

  • no risk to this contract.

  • That means, these prices are pure prices, and they don't

  • have any counterparty risk.

  • I wanted to show you another futures contract.

  • This is Soft Red Winter Wheat, which is a major crop in the

  • U.S. Winter wheat, you plant it in the fall.

  • Believe it or not, some people are surprised to hear this.

  • You plant it in the fall, and then it stays in the ground

  • over all the winter, and it comes up really

  • early in the spring.

  • And then, it's harvested in early summer.

  • And the Soft Red Winter Wheat is very good for biscuits, and

  • cold cereal, and cakes, but not so good for bread.

  • So, it's a particular kind of wheat that is grown.

  • So, this is the futures curve, as of Friday

  • [addition: March 18, 2011],

  • for this.

  • And this is in cents per bushel.

  • So, this is the front month future, and it's --

  • it looks like it's 723 cents, $7.23 a bushel.

  • And now, we see this sharp contango again, and the prices

  • are going up really rapidly through time.

  • Again, this is all prices quoted last Friday.

  • This is futures contracts and different maturities.

  • And then, you see sometime around summer of 2012, it

  • loses contango, and it becomes, actually, declining.

  • And then, this market goes out to 2013, and stops.

  • That's as far out as they trade futures.

  • So, why is it declining in 2012?

  • Well, there's probably a million factors in it.

  • You need to talk to a futures expert.

  • But I think, one thing that comes to my mind, is the

  • harvest. And so, they harvest grain

  • sometime around that time.

  • You know, you shouldn't be storing grain at the harvest.

  • This contango is a compensation

  • for the cost of storage.

  • So, you shouldn't be storing grain in the harvest time.

  • You should be clearing out your warehouses, and sweeping

  • them out, and cleaning them up, and waiting for the new

  • harvest to come in.

  • So, you don't expect contango to continue.

  • There's a seasonal --

  • it's not so clear here.

  • It's not dropping very much.

  • I don't know, there's many factors that

  • determine these prices.

  • But I wanted to just give a little bit of simple

  • mathematics about futures pricing.

  • The basic formula is that --

  • you have to think of futures markets as storage markets.

  • And the basic equation is, that the price of any futures

  • contract, p sub f, is the futures price on one of those

  • dates, is equal to 1 plus r, plus s, times the spot price.

  • Where the spot price, p sub s --

  • I'll write it out, p spot, is the price today.

  • Now, this is kind of theoretical, because I just

  • told you, nobody ever knows what the price today is

  • anyway, because the only way you ever know prices is

  • through futures markets.

  • But let's just think a little bit abstractly.

  • Say, there's a cash market for wheat, that it's

  • bought and sold with.

  • And we know what the price is on that market.

  • So, this is the interest rate between now --

  • it's not the annual interest rate.

  • It's the total interest as a percent between now and the

  • maturity of the contract.

  • So, if it's one year and the interest rate is

  • 5%, then r is 0.05.

  • But if it's one and a half years, it's going to be more

  • like 0.075, because the total interest between now and one

  • and a half years in the future is 7.5%.

  • And s is the storage cost.

  • So, this is called fair value, and what it means is, normally

  • you think futures prices should behave like that.

  • So, the normal situation in futures markets is contango,

  • which means that prices are normally going up through

  • time, because the longer in the future we're looking at,

  • the longer time that we're losing interest and storage.

  • See what this really is, this fair value equation, is just

  • the equation that defines, when it is that there's just

  • no profit to storing grain.

  • There's only a normal profit, right?

  • If people who do it --

  • This equation can't hold exactly.

  • Or if it held exactly, then no one would store grain, but it

  • has to be approximately valuable.

  • So, do you see?

  • How else do I say this?

  • It shows that normally the futures price is above the

  • spot price.

  • And as time goes on --

  • I don't mean time in this sense, I mean calendar time --

  • the futures price will converge on the spot price,

  • because the interest rate, the horizon for the interest rate

  • and the storage costs --

  • this is in percent, and this is in percent --

  • goes down.

  • So, let me just clarify that.

  • Let's talk about a perfect world, where there's no

  • harvest uncertainty, nothing happens except the crop is

  • normally produced.

  • And it's wheat.

  • And let's say --

  • I'm going to do a plot.

  • And this is time.

  • This is calendar time, not maturity time

  • like on this plot.

  • And this is the price of --

  • I'm going to plot the price of wheat.

  • Now, what does wheat do over the year?

  • It has a seasonal pattern.

  • I'm going to do an abstract form of seasonal.

  • This is what the price of wheat does.

  • And this is a year.

  • This is year 1, this is year 2, this is year 3, year 4.

  • This is the price of wheat in each of these years.

  • It falls every harvest time, right?

  • It has to be rising until harvest, because somebody has

  • to be storing grain.

  • And the price has to go up, because they're

  • facing storage costs.

  • And then, every spring, every harvest time, it collapses.

  • And it does it again every year.

  • No uncertainty.

  • What do futures prices do?

  • Well, let's consider a futures market that's --

  • a futures contract that has a maturity right here at the

  • peak, just before the harvest. But if there were no

  • uncertainty, the futures price would just be constant

  • throughout that whole time.

  • It would always equal the expected spot price on that

  • future date.

  • And again, it would repeat the next year.

  • Futures contracts have no expected price change in this

  • perfect world.

  • Do you see what I'm saying?

  • This equation always holds, because, as this contract

  • matures, the time to the expiration date goes down.

  • And so, this r goes down, and s goes down.

  • And eventually, it hits 0 on the expiration date.

  • And the futures price equals the spot price on the

  • expiration date.

  • But in reality, we don't see such a nice and perfect match.

  • I want to talk about another futures market, which is maybe

  • the most important futures market of all.

  • I've been talking just about agricultural futures.

  • Agricultural futures are the origins of futures markets.

  • And I like to talk about them, because I like to imagine --

  • well, our ancestors all lived on farms, once in the past.

  • And it just seems like such a family story that we all

  • should know about farming.

  • It's our history.

  • But now let's move forward into other classes --

  • we can have futures markets for oil as well.

  • So, this is last Friday's [addition: March 18, 2011]

  • futures curve for Light Sweet Crude Oil.

  • This used to be at the New York Mercantile Exchange, but

  • the Chicago Mercantile Exchange has been buying

  • everybody up.

  • And now, it's the CME.

  • They call it the CME group, actually, Chicago Mercantile

  • Exchange Group.

  • And this is the price of oil.

  • Look, what's happening here.

  • Isn't this something, this curve?

  • The price of oil as of last Friday, on the nearest month

  • future, was selling at $101 a barrel.

  • It's gone up a lot.

  • This is part of the crisis now around the world.

  • People need food and they need oil.

  • Incidentally, the two markets are related, because we can

  • turn fuel --

  • we can create fuel from food by using grains to produce

  • ethanol, and that substitutes for oil.

  • So, it's not independent.

  • These two markets are not independent.

  • Now, oil is so important.

  • It's the energy that drives the world economy.

  • And any events, like the recent earthquake in Japan and

  • the nuclear disaster in Japan, it affects this market.

  • Everyone's thinking, what does it mean for oil?

  • Maybe, we won't have so many nuclear plants anymore, so

  • that's going to mean, oil's going to go up.

  • The other thing that's happening is, at this point in

  • history, there's a crisis in the Middle East, and it's

  • cutting off the flow of oil.

  • So, people are trying to predict it, and those

  • predictions come into this market.

  • So, here's what we see.

  • We see right now, the market is predicting increases of oil

  • until December, and then, a collapse of oil prices,

  • bottoming out in January of 2015.

  • This market goes all the way out to almost 2020.

  • That's a long time.

  • That's because it's such an important commodity.

  • So, this futures curve matters for --

  • The total value of oil in the ground in the world is

  • probably over $100 trillion.

  • It's bigger than the GDP of just about any country.

  • It's huge and important.

  • And people who are thinking of extracting their oil, they're

  • looking at -- everyone's looking at this curve.

  • So, why does it peak in December

  • 2011, and then collapse?

  • I'm guessing that has something to do with the

  • crisis in the Middle East, that the people who trade in

  • these markets are thinking, that the crisis will be over

  • by then and prices will start coming down.

  • So, we're seeing contango here, and backwardation here.

  • I'm using a simple definition of contango and backwardation.

  • There's more subtle definitions, but

  • we'll keep it simple.

  • We're seeing an increase, expected in oil prices, and

  • then it decreases.

  • And then, it has it going up again.

  • Is this right?

  • Well, if it isn't right, there's a profit

  • opportunity for you.

  • If you know better, you can get in and you can do it with,

  • I think, all you need is something like $5,000.

  • I'm not trying to entice you to trade this, but I'm just

  • trying to give the idea of what these

  • markets really mean.

  • That the oil, it means survival for people.

  • I mean, oil and food are what keeps people going and alive.

  • And there's not enough.

  • There's not enough for everybody.

  • And so, this market is all about extracting oil at a good

  • rate, thinking about when to sell it, so that it,

  • ultimately, I think, serves the purpose of humanity.

  • Now, incidentally, what's happening here?

  • When you see the curve falling, how can that be?

  • I just wrote this equation here, saying that the futures

  • price has to equal 1 plus r, plus s, times the spot price.

  • So, the futures price has to be greater

  • than the spot price.

  • I just wrote that, right?

  • But you can see that this futures price, this is

  • essentially the spot price.

  • This is the front month future, and it's about to

  • expire, so it's converging.

  • And this is what we call the price of oil.

  • When you hear oil prices quoted on TV or on magazines,

  • they're quoting the front month futures.

  • Let me be clear about that.

  • Oil is mostly sold on long-term contracts.

  • So, just like our rice merchant, buyers of oil are

  • typically --

  • who buys crude oil?

  • It's some refinery.

  • They've got a big operation and they refine oil.

  • And they care about, what kind of oil do I get?

  • And when is it going to be delivered?

  • And what are you going to do for me, if it's not

  • delivered on time?

  • They have complicated delivery contracts.

  • Almost all oil is sold through that.

  • So, what is the price of oil?

  • You can't figure it out.

  • There's just too many contracts

  • and they're all different.

  • There is a spot market for oil, but that's just overflow.

  • You know what happens?

  • There'll be some mistake.

  • Someone delivered too much oil to the New Haven harbor, or

  • someone reneged on a contract, now I've got this extra oil.

  • It goes on to the spot market, but that market is tiny and is

  • not reliable.

  • You don't know what kind of oil it was, you know, it's all

  • different --

  • what the issues are.

  • So, when you hear oil prices, you're hearing futures prices.

  • So what's happening?

  • How can it be that the futures price in 2015 is lower than

  • the price today?

  • Well, there is something funny going on.

  • I'll tell you one thing that it does mean to me, is that

  • nobody is planning to store oil between now and 2015, at

  • least not as a storage business.

  • Because I'm going to lose money.

  • I'm going to be selling at less, unless I have negative

  • storage costs.

  • I'm not going to store oil between now and then.

  • I'll store it for now.

  • So, that means that people are kind of trying to store a lot

  • of it now, because the contango is there, but it's

  • going to end in December, and then they're going to empty

  • their storage tanks.

  • That must be what storers are thinking.

  • So, this thing doesn't always hold.

  • This only holds when there's commodity in storage.

  • Or you could say, well, it still holds even when you have

  • backwardation, because, in some sense, storage costs can

  • get negative.

  • And so let me just talk about, there's a term that they use

  • called convenience yield.

  • When the futures curve is in backwardation, somebody is

  • still going to be storing oil.

  • So, suppose I have a factory, and my factory depends on oil,

  • because I use it to burn, to produce whatever we make.

  • Am I going to let my warehouse, my storage tank of

  • oil go dry?

  • No, I'm going to need some, just because we might need

  • more than we think.

  • We might have a buffer stock.

  • So, that means, I actually have negative storage costs.

  • I always want oil.

  • I don't want ever to let my tanks go dry.

  • So, the only people who are storing oil, when you have a

  • backwardated futures market, are the people who want

  • convenience yield.

  • Now, I'm omitting some subtleties here.

  • I'm sorry, but I'm trying to make the basic point, that

  • this equation holds when the commodity

  • underlying is in storage.

  • But it doesn't always hold.

  • So, now I wanted to talk about oil a little bit more, because

  • it's so important.

  • I have here the price of oil.

  • I like history.

  • I like to give you long history.

  • I wanted to give you the price of oil back to 1871.

  • And this is, well, U.S. oil price in U.S. dollars.

  • But I've corrected for inflation, so it's real oil

  • prices from 1871 until just a short while ago, last week

  • [addition: data ends on March 18, 2011].

  • And now, in recent years this is the

  • front month oil contract.

  • The oil futures market started in the 1970s, so this is all

  • the front month futures contract.

  • Before that, this is someone's guess as to what the price of

  • oil was, because there weren't such well-developed markets.

  • We didn't have oil futures until the 1970s.

  • So, I wanted to think about what was happening at these

  • various dates.

  • These early swings in the 1870s were due to discoveries

  • of oil, and discoveries of uses for oil.

  • Pennsylvania oil was discovered somewhere around

  • this time in the United States.

  • Texas oil was discovered somewhere around this time in

  • the United States.

  • Our economy wasn't so dependent on petroleum.

  • Actually, if you look up ''oil'' on ProQuest, back in

  • 1870 they didn't even call it oil.

  • They called it petroleum, because what was oil?

  • What did they think oil was in 1870?

  • Whale oil, OK.

  • It was a different world.

  • So, we see a lot of jumping around of oil prices.

  • But we see a big surge going into the 1890s.

  • And there was a big scandal about Standard Oil.

  • Remember that?

  • And the government eventually busted up

  • Standard Oil as a monopoly.

  • So, they were starting to get concerned about oil.

  • But then, if you go forward in time, you see this interesting

  • pattern here.

  • What was going on here?

  • The price of oil became very stable, until, bang, there was

  • this huge upswing in oil.

  • Well, what was happening in this interval of time?

  • In the '40s to 60's, the U.S. was a big producer of oil.

  • It kind of got started here, oil production, with Drake's

  • invention of the oil rig.

  • And the U.S. was the biggest producer of oil.

  • And during this period, when you see oil prices were very

  • stable, the oil prices were actually stabilized by the --

  • it was produced mostly in Texas --

  • Texas Railroad Commission.

  • It says railroad, but it was a government agency in the state

  • of Texas, which worked to stabilize oil prices.

  • But during this period of time, the U.S. was depleting

  • its oil, and other oil discoveries were coming in.

  • And so, this whole period -- this is before there were any

  • futures markets, because there was no reason

  • for a futures market.

  • Oil prices were very stable.

  • And then, you see, here, a sudden jump up in oil prices.

  • And this point right here is called the first oil crisis.

  • So, the first oil crisis, it kind of stands out on a

  • diagram, right?

  • Looking at the whole history, if you exclude those early

  • fluctuations in oil that you see in the 1870s, which were

  • not really so important, because people were really so

  • dependent on oil.

  • So, the first oil crisis was 1973 to '74.

  • And this prompted the creation of the futures market.

  • Because what happened was --

  • it was actually coincided with the Yom Kippur War in Israel.

  • And it was created by a blockade against oil in

  • oil-producing countries.

  • The U.S. was no longer, by this time, the

  • major producer of oil.

  • We had something called OPEC, which is the Organization of

  • Petroleum Exporting Countries.

  • It actually goes back to 1961 with Qatar.

  • 1962, Libya, Indonesia.

  • And then, we added the Abu Dhabi in '67, the United Arab

  • Emirates, '74, Algeria in 1969, Nigeria in 1971, Ecuador

  • in 1973, Gabon in 1975.

  • So what happened was, although the U.S. broke the Standard

  • Oil monopoly around the turn of the century, a new monopoly

  • developed, and it was outside the U.S. And so, there was no

  • trustbusters to break this monopoly.

  • And so, what happened was, the oil exporting countries who

  • belonged to OPEC, who wanted to use oil prices as a

  • strategy to deal with Israel, they restricted

  • their supply of oil.

  • And it caused the first oil crisis right here.

  • I was going to mention another historical fact that, I think,

  • precedes this, but it's part of the story.

  • And that is nationalizations of oil.

  • It used to be that big oil companies went around the

  • world and found oil deposits.

  • And then, they would buy the land, and they wouldn't tell

  • anybody what they were doing.

  • They'd buy the land that had the oil under it.

  • So, the oil companies were very rich.

  • But there was discontent in the less developed countries,

  • who sold them the land and thought, why did we

  • get gypped like that?

  • And so, they started a process.

  • It started with Mexico in 1938.

  • So, oil used to be owned by the oil companies.

  • Mexico said, no, not any longer.

  • It's our national heritage.

  • We never should have sold it to you.

  • We're just taking it back.

  • This was considered outrageous at the time.

  • No country should violate property rights like that.

  • But it was kind of a leftist --

  • the word nationalization was a new word.

  • It was kind of like the people expressing their heritage.

  • It started to take.

  • Then, Iran in 1951.

  • And then, other countries followed.

  • So, oil got taken away from international companies and

  • put under government control of less developed countries.

  • And then, there was a monopoly called OPEC, and that produced

  • this crisis right here.

  • There was a second oil crisis in 1979-80.

  • And this one, again, was associated with trouble in the

  • Middle East. So, in '79-80, we had the Iranian revolution,

  • which again disrupted oil supply.

  • So, 1979-80 is the second oil crisis.

  • And that is due to the fall of the Shah of Iran, and the

  • arrival of the Ayatollah Khomeini, and

  • the Iran-Iraq War.

  • And so, you can see the huge increase in oil prices.

  • These were real panic situations at the time,

  • because people were not used to these --

  • people were used to the stable oil prices, and it was just

  • something taken for granted.

  • But this put the world in a state of shock, because oil

  • prices really jumped up almost sixfold, about sixfold, in a

  • matter of --

  • how many years is that? --

  • six, seven years.

  • So, this left a lot of interest and enthusiasm for

  • oil futures, and it became a major market of the kind we

  • know about today.

  • You know, what happened here?

  • This mark.

  • This is another --

  • This is the second Iraq War, when Saddam Hussein was

  • overthrown.

  • And the U.S. and other countries

  • were involved in that.

  • But what it did is, it cut off the supply of oil briefly,

  • because the Persian Gulf was shut down because of a war.

  • You can bet that the futures market was heavily

  • backwardated right then, for oil.

  • Because everyone knew that the oil prices were not --

  • we weren't running out of oil, we couldn't get at it because

  • of the war.

  • And so, this was another oil-induced spike.

  • Every one of these spikes produced a major worldwide

  • recession, because the world wasn't ready for

  • these spikes enough.

  • So, we see this huge spike in oil in '73,

  • and a worldwide recession.

  • Again, another worldwide recession.

  • This one was called The Great Recession, people forgot that

  • they called it that, and they use that

  • term again more recently.

  • And then there was another worldwide recession --

  • every one of these did it.

  • And so, you can see the fundamental importance of oil,

  • and of oil futures, because oil futures is

  • managing the risk.

  • If you bought an oil futures contract, you

  • weren't impacted by this.

  • If you bought a contract just before this, then the oil

  • crisis doesn't mean anything to me.

  • It's not my problem, because I've already

  • locked in my price.

  • And it's really safe, because the way the futures markets

  • work, they've got this daily settlement process.

  • So, you don't have to worry about your

  • counterparty reneging.

  • It's very civilized.

  • It's a tough world out there, where they're fighting wars,

  • but in Chicago, where the futures markets are --

  • or it was in New York back then --

  • it's a very civilized market.

  • And so, look here, we have the latest spike.

  • It's even bigger.

  • So, oil got to --

  • I can't even reach up there --

  • oil got up to over $140 a barrel in 2008.

  • That's just a short time ago.

  • Now, what did that?

  • That is kind of a puzzle.

  • It has something to do with the world financial crisis.

  • But it's not as well understood as a reaction to

  • any military situation.

  • So, it seems like there's some speculative

  • element that took place.

  • See ultimately, oil is stored in the ground, and it's owned

  • by people, and they have to decide how to develop it and

  • how fast to produce it and sell it.

  • And there were some quick changes of thinking around

  • then, that surprised everyone, I think.

  • And oil is, again, up above $100 a barrel right now.

  • Just we saw in the futures curve.

  • So, actually the futures curve that we saw would look kind of

  • unimpressive on this diagram, right?

  • It would be just going up a little more and a little down,

  • not big swings that are predicted.

  • I just want to finally conclude with financial

  • futures, which I didn't emphasize in this lecture.

  • But we also have futures markets in financial

  • commodities, and I'm just going to tell you

  • about one of them.

  • It's called the S&P 500 futures market, index futures.

  • And now, in effect, you have to deliver not oil, or rice,

  • or wheat, but you have to deliver the S&P 500 index.

  • How do you do that, by the way?

  • How do I deliver 500 stocks?

  • Well, there's a procedure, and it's called cash settlement.

  • It's different.

  • Instead of showing up at warehouse with your trucks

  • full of wheat, you only show up with the money, because

  • they don't expect you to do that with stocks.

  • What is the storage cost for stocks?

  • Well, you know, it's actually negative.

  • It doesn't cost me anything to buy.

  • If I buy a share in a company and store it, it

  • doesn't cost --

  • it's a negative cost, because they pay a dividend.

  • So, the fair value, and this is what you'll see quoted all

  • the time on CNBC, or any of these business --

  • Bloomberg --

  • these business networks is --

  • So, the futures price is equal to 1 plus r minus y, times the

  • spot price.

  • Same formula.

  • This is the interest rate.

  • And this is the dividend yield.

  • So now, whether the futures price is above or below the

  • spot price, is less clear here, because it depends on

  • whether the interest rate is higher than the

  • dividend rate or lower.

  • At this point in history, for short time horizons, the

  • interest rate is less than the dividend rate.

  • We have about a 2% dividend yield on stocks, and we have

  • essentially a 0% interest rate.

  • So, for short horizons, we'd expect to see the futures

  • price less than the spot price in stock index futures.

  • But at longer horizons, I think that would be reversed.

  • But this market is very clear.

  • The fair value relationship is highly predictive of futures

  • prices in the S&P 500 index futures, because there's

  • always storage of stocks.

  • We never deplete the warehouses of stocks, so

  • they're always there.

  • And so, that means that the futures curve is less

  • interesting for stocks than it is for oil.

  • All it does is reflect fair value.

  • And so, it's not like oil, where the storage situation is

  • very complicated, and it's constantly changing.

  • So in a sense, the S&P 500 index futures is not so much

  • about the future.

  • The futures curve is not so much about the future of the

  • stock market.

  • So, don't make the mistake of looking at the futures curve

  • for the S&P 500, and thinking I'm going to forecast the

  • market using this curve.

  • You can't.

  • Basically, the S&P 500 is very hard to forecast. And the

  • futures curve doesn't do you anything, because all it

  • reflects is fair value.

  • So, some futures markets, like gold futures is like this

  • also, there's always gold in storage, it never gets

  • depleted to zero.

  • It's always being stored, so the gold futures curve is not

  • so interesting, either.

  • Next, after the midterm exam, which you have coming up on

  • Wednesday, we will come to options pricing.

  • And that's another fascinating market that we'll talk about.

PROFESSOR ROBERT SHILLER: OK, good morning.

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A2 初級

15.遠期和期貨市場 (15. Forward and Futures Markets)

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    Hhart Budha 發佈於 2021 年 01 月 14 日
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