Lecture 1 why finance

Everybody should be an investor, they felt. A monkey throwing darts at a dart board would do as well as any of the greatest experts. Now, their own theory was basically contradicted by their own experience because all of them seemed to go out into the world and invest, and almost all of them made extraordinary returns and made a huge amount of money all of which made them even less popular in the faculty of arts and sciences.

So, a critical part of their theory was that the markets were so efficient, driven by people like them who are competing to exploit every advantage, and therefore compete away every advantage, and by doing that put all the information they have into the prices. One striking thing is that the people they studied, the business people and the investment bankers they studied adopted their language.

So this had never happened in academia before. I mean, anthropologists study primitive tribes and different kinds of people all the time and not one of them, I venture to say, has ever taken over all the language invented by anthropologists to behave themselves in their own societies, but the business people that these professors were studying ended up using exactly the language created in academia.

Now, Yale was very different. There was no divide between economists and finance people, the business school finance people. Maybe they were financial economists to begin with. So the greatest Yale economist of the first half of the twentieth century was Irving Fisher who you hear a lot about.

He wrote, possibly, the first economics PhD at Yale. There was no economist to teach him so he had to write his PhD with Gibbs, maybe the greatest American physicist of the time. The most famous Yale economist of the second half of the twentieth century was James Tobin, a famous macroeconomist, the most famous macroeconomist, possibly, of the second half of the twentieth century after Keynes, a great Keynesian.

But he got the Nobel Prize for work he did on finance in economics. Finance was incredibly interesting to him. So as you know Shiller has been very critical of the business efficient markets tradition. He feels that these finance professors left something essential out of the whole story. What they left out was psychology. They left out the idea of fads, and rumors, and narratives, which he thinks has as big an effect on prices as the hard information about profits that the business school professors imagined drove profits.

I myself have been quite critical of the financial theory. I started off as a straight pure mathematical economist. To me economics was almost a branch of logic and philosophy that happened to tell you something about the world. Well, I decided around that since I did mathematical economics, and there were all these finance people doing all kinds of mathematical things on Wall Street and doing it very successfully, I thought I might just check out what they were doing. So it might be fun to see what they were up to.

There was a famous finance professor, who I had mentioned before, named Fischer Black who was there at the time and he attracted a lot of people. And so that was the traditional thing to do, but I decided to go to a littler firm called Kidder Peabody, and it was the seventh biggest investment bank at the time. And one thing led to another, and they decided that they wanted to reorganize their research department in fixed income.

So I did, and ultimately there were seventy-five people in the department. All the time I was a professor at Yale. And after five years Kidder Peabody, even though it was a hundred thirty-five years old, formed by a famous family, the name should sound—Peabody—familiar to you, it closed down after a hundred thirty-five years, five years after I got there. It started after the Kidder closing as a rather small hedge fund, but it grew into a very big mortgage hedge fund, in fact the biggest mortgage hedge fund in the country.

Although recently we found out that practically everybody who trades mortgages is basically a hedge fund. So these experiences, of course, have colored my understanding of Wall Street and my approach to the subject. So I took on, in my theoretical work, finance and economic theory on its own terms.

And what I found was that there are two things missing in the Standard Theory. One is that it implicitly assumes you can buy insurance for everything.

Those two things were missing from the Standard Theory, so I built a theory around incomplete markets and leverage, which is a critique of the Standard Theory. So in a way Shiller and I have been vindicated by the crash.

I mean, so let me just show you a picture here. Well, maybe I will, you know, how bad the crash was. The Dow Jones is an average of thirty stocks and what their value is.

Look at that. And that was the only way, according to the old theory, to explain what happened. They changed their mind again. A whole thing down would be the square root of ten or a third. It went down less than two thirds.

It went down fifty percent, so the actual percentage drop was much worse in the Depression than it is now. What else can we get out of these numbers? I just want you to notice a couple other things. So these numbers are all very interesting. So these efficient markets guys, they looked at the change in price every month. It seems to be random. You never get these gigantic outliers if things are normally distributed.

We just looked at the Dow. So you see here that there are these four cycles. Things seemed low in They go up and they go down. Four times the same thing has happened. So let me show you another picture. So this is a second way in which Shiller became famous.

And nobody thought to gather all this information together and take the average and write down an index until Shiller did it. So Shiller says this is irrational exuberance. People just went crazy. Psychology—eventually a new narrative is going to start. Look at the mortgage rates. This is the interest rate you have to pay if you get a mortgage. If you take the present value of your expenditures you just have to pay less.

So, again, this seems like a vindication for Shiller. Now, it also, in a way, is a vindication for my theory which is non-psychological. So my theory is when you take a loan you have to negotiate two things, the interest rate and how much collateral you put up.

Borrow eighty percent of the value of a house. Why is it twenty percent that you have to put down? Maybe it should be ten percent or forty percent. Well, in fact, that number changes all the time. These are non-agency loans. You could put down three percent of the value of the house and borrow the other ninety-seven percent of the value of the house to buy it. So why is it called leverage? So anyway, the point is that leverage went way up.

And now from to you see the margins spiking up. They used to put down only five percent to buy it. Now they have to put down seventy percent to buy it on average. Well, what happened to prices? Prices—this is the inverse of prices—in they started to collapse. So this going up means prices are collapsing. So once again, the margins—tougher margins means lower prices and as the margins came down recently the prices have gone up recently.

So what else do I want to show you? After all, I helped run a hedge fund. And where is this? Okay, so Dow. Where was the peak of the Dow?

It was right over here. Now what was the date? Until then nothing bad seemed to be happening in the world, but suppose that you look not at the Dow, suppose you looked—sorry. The stock market is still going up here. A month later, this is April , a month later the sub-prime index starts to collapse. You see it goes from a hundred to sixty. So that means the people, those experts trading mortgages, already realized there was a calamity about to happen.

This was long before anyone else perceived anything happening, long before the stock market moved, long before the government did anything to correct the problem. So just as financial theory says if you pay attention to the prices you can learn a lot about the world.

The people trading those things—their life depends on fixing the right prices. The prices are going to reflect their opinion. If the price collapsed part of the reason it collapsed, maybe margins and something had something to do with it, but part of the reason it collapsed was because they knew something bad was happening.

To go from a hundred to sixty and since to twenty is a total calamity. So you know that there are one point seven million people who have already been thrown out of their houses.

Probably all of them will be thrown out of their houses, and another four or five million after them might default and have to be thrown out of their houses.

I just think it has to be supplemented by a more general and richer theory. Oh dear, where is my returns? So Kidder Peabody went out of business in There was a tremendous crash in the market, a low of the leverage cycle.

Emerging markets is the blue one, and high yield is the green one, and then there are bunch of other things like treasuries, and this is Libor which is what banks lend to each other at. So you see there was a crash here. Look what happened. Overnight, practically, we lost a huge amount of money. We almost went out of business. Long Term Capital, which, by the way, was run partly by two Nobel Prize winners, Merton Miller, not Merton Miller, Myron Scholes and Robert Merton, two of the guys I mentioned who were the leaders of the financial crisis [correction: leading finance academics], they bankrupted their company and they went out of business.

And why did they go out of business? Anyway, so the prices collapsed. Everything plummets all together this time and then everything is going up again. You promised not to change the margins on us for six months. We have great bonds. So we survived.

We survived that, no thanks to Warren Buffett, although he had a pretty good idea, and then we survived the last crash. So we survived all these crashes, but the fact is things go up, they crash, they go up, they crash, they go up. Could it all be my fault? So the course is going to be divided in the following way.

And part of that argument and part of the sort of hazy knowledge of that argument is what drives resistance to a lot of government programs.

I mean, the government can only screw things up is what people generally believe. Is it a prejudice or is there some actual argument behind that?.

And then, I want to talk about Social Security. So I want to talk about Social Security and should it be privatized and should it be reformed and why did it go bankrupt. Each generation the young are paying for the old. Nobody would do that if they thought they were going to be the last generation paying to the old, and when they got old nobody would help them.

So Social Security rests on this world going on forever which makes it mathematically interesting. Anyway, so I got interested in it from a theoretical point of view and then I got put on all these National Academy panels on Social Security and privatizing.

So let me just give you a few examples. Now they always give you the choice. Do you want to take five million a year over twenty years or just get forty million dollars right now? Which would you do and how do you think about what to do? So now you get tenure at Yale at the age of 50, say. Yale was going to weather it, but Yale had lost twenty-five percent, probably, of its endowment. So how much should he choose to cut? How much should Yale reduce spending every year? The total spending at Yale is a little over two-billion.

So the endowment goes down by five-billion what cuts should you take to the budget. Should faculty salaries be cut, be frozen, should you get three TAs instead of four TAs? What should you do? How big a cut should you take? Now, the same question faced Yale in or so. Ten or twelve years ago the previous president, Benno Schmidt, he suddenly noticed that there was deferred maintenance, as he called it, a billion dollars to fix the Yale buildings.

They decided there was deferred maintenance of a billion dollars. A hundred million dollars every year for ten years had to be spent.

The whole endowment then was three billion, and now we had a one billion dollar deferred maintenance problem. The budget was about one billion then. So how much should you cut the Yale budget at that time? Well, did he make the right decision? Rick Levin took over as president three months later, so probably not.

What mistake did he make in his calculations? What should he have done? What was the right response? The World Series is coming up. So if the Yankees win he gets two hundred thousand, but if the Yankees lose he loses three hundred thousand. I can take big advantage of him. So what can you do? You promise to deliver him five hundred back if the Yankees win and to keep it if the Yankees lose.

What should you do with your friends? Should you bet on the Yankees with your friends? Should you bet on the Dodgers with your friends and how much should you bet at even odds the first night? How do you know how much that is? Somebody offers to play a game with you.

It looks like an even chance of winning or losing. So now the deck is stacked against you. Should you pick another card? But you should pick another card and I can even tell you how many cards to pick.

Even if you keep getting blacks you should keep picking and picking. So how could that be? It sounds kind of shocking. So, a more basic question. There are thirty year mortgages now you can get for five and three-quarter percent interest.

There are fifteen-year mortgages you can get for less, like five point three percent interest. Should you take the fifteen-year mortgage or the thirty year mortgage? How do you even think about that? Why do they offer one at a lower price than the other? And you value all those mortgages at a hundred million dollars. The interest rates go down.

The government lowers the interest rates. Half of them take advantage to refinance. They pay you back what they owe and they refinance into a new mortgage. Half the people are left. That shrunken pool, half as big as the original pool, is that worth fifty-million, half of what it was before, or more than fifty-million, or less than fifty-million? How would you decide that? They see interest rates went down. A bunch of people acted. The people who are left in the pool are different from the people who started in the pool.

Look at all the money you lost for me last year. You could lose money. So, three more short ones. A scientist discovers a potential cure for AIDS. He started a company. So another question, suppose you believed in this efficient market stuff and you rank all the stocks at the end of this year from top to bottom of which stock had the highest return over the year. All the stocks the highest return to the lowest return. Now, suppose you did the same thing in with the same stocks?

Would you expect to get the same order, or the reverse order, or random order? One last one, the Yale endowment over the last fifteen years has gotten something like a fifteen percent annualized return. So is it obvious that the Yale endowment has done better than the hedge fund? Would you say that the Yale manager is better than the hedge fund manager? Its return was fifteen percent. The hedge fund only got eleven percent. So suppose I even told you that the Yale hedge fund had lower volatility—the Yale hedge fund?

So I want to talk about the crisis of It started as a mortgage crisis. Now, how could it be that everything goes wrong in mortgages? The Babylonians invented mortgages. What is a mortgage? You lend somebody money. They put up collateral. How many of you are engineering majors? A few. How many of you actually are from other universities? Great, because last year we had quite a few, so I want to specifically tell you that you're very welcome to attend the classes here.

So it's open door. And last year I remember we had a couple of students from Harvard. That's where I actually work right now. I forgot to mention that, but I'm affiliated with both the math department and the Sloan school here. So anyway, thanks for that. We will be doing a bit more polling along the way, mainly to get feedback of how you feel about the class. Last year we had it online, so if you feel the class is going too fast, or the maths part is going too slow, or the finance part is a bit confusing, the easiest way is really just to send us emails, which you will find from the class website.

So anyway, today We all have MIT emails, which are listed on the website. You can easily stop by Peter and Choongbum's offices. And Vasily and I probably will be less often on campus, but we'll be here quite often and definitely love to be more. So anyway, I will start today's lecture with a story, and a quiz at the end. Don't worry, it's not a real quiz.

Just going to ask you some questions you can raise your hand and give your answer. But let me start with my story. This is actually my personal story. I want to tell you why I tell the story later. But the story actually was in the mid '90s. I just left Salomon Brothers-- that was my first financial industry job-- to go to Morgan Stanley in New York to join the options trading desk. So the first day, I sat down, I opened the trading book, I found something was missing.

So, I turned around, I asked my Desk Quant. I said, where is the Vega report? So, let me show you. So that's the story. So I'm obviously not going to tell you the story of Pi or "Life of Pi. So I'm going to talk about Vega. So by the way, before I tell you the story, what's unique about Vega on this list? That's right. But how many of you actually know what a Vega is? OK, lot of people know. So anyway, I'm not going to-- just for the people who haven't heard about it before, it's a measurement about a book or portfolio or position's sensitivity to volativity.

So, what is volatility? Which again, you will learn more in rigorous terms what has defined in mathematics. But the meaning of it is really a measurement or indication of how volatile, or what's the standard deviation of a price can change over time. That's all you need to know right now. I'm not going to ask you questions later. So my Desk Quant look at me, said-- this is supposed to be options trading desk, so he look at me puzzled.

So instead of answering my question, he handed over me a training manual for new employees and new analysts. So I opened the training manual and looked it through. I actually found my answer. So actually, at Morgan Stanley this is not called Vega, it's called Kappa. So now, I remember to call it Kappa. Kappa is actually a Greek letter. So further, I look on the same page there was actually a footnote, which I copied down. So the footnote about why it's called Kappa at Morgan Stanley.

Kappa is also called Vega by some uneducated traders at the Salomon Brothers. That's where I came from. I just joined. They have mistaken Vega as a Greek letter after gambling at Vegas. So anyway, so that was my first day. So obviously, I learned how to call kappa very quickly, because I came from Salomon Brothers. And I call it Kappa in the last 17 years, but you will hear people calling it Vega. Obviously, I have probably more people calling it the vega. But anyway, so that's my first day at Morgan Stanley.

But why did I tell you the story? What point I try to make? So this story is actually-- when you think about it, mathematical or quantitative finance is a rather new field. A lot of these terms were newly introduced. And the pricing model of options, as you know, was introduced in the black shows in the '70s, or some of the ground work may be done a bit earlier.

But it's not like finance was a quantitative profession to start with. So what we witness in the last 30 years was really a transformation of the trading profession coming from mostly under-educated traders. Some of them typically joined the firms in the mail room and became trader later on. That's typical career path.

And to nowadays, if you walk on the trading floor, you talk to the traders, most of them have advanced degrees and quite a few of them have very high training in mathematics and computer science.

So what has changed over the last 20 or 30 years? I myself, personally, was probably one of the data point experiencing this change. 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 the right or wrong in mathematics, is it right or wrong in physics? So, how the concepts are established and defined and verified. Because this is a field the transformation about the participants, products, models, methodology, everything are changing very rapidly.

Even nowadays, they're still changing. So with that, I will give you some background on how the financial markets actually started, and that's really the history part of this industry. So, when we talk about markets, we know in early days people need to exchange goods. You have something I don't have, I have something you don't have, so there's exchanges. Then it becomes centralized.

There are stock exchanges, futures exchanges all over the world where these products will be listed as securities on these exchanges. That's one way of trading, which is centralized. Obviously, in the last 10, 15 years, now we have ECS, electronic platforms. Trade over even larger volume of those trades. So, financial products is really just one form of trading. There are many other ways of trading aside from exchanges.

One of them, which is called OTC, is over-the-counter, meaning two counterparties agree to do a trade without really subject to the exchange rules, or the underlying trading agreement does not have to be a securitized product, or standardized, or whatever ways you define it.

And the different regions have different exchanges and markets, as well. And they typically specialize in local products, local company stocks, local bonds, and local currencies. So, there are many different forms. So again, what's in common? That's the question you need to ask.

Also, you don't know the specifics. And the currencies, money itself, are also traded. And that's where different currencies issued by different countries. So, when we talk about trading stocks-- there are also people trade baskets of stocks, trade groups of stocks together, and that's stock index or indices.

So, there are different types products. How the stock get listed on the stock exchange? So, when a company changes from private to public, it goes through this IPO process. It's called primary market, primary listing.

And once the stock is listed on the exchange and it becomes traded in the market, we call it secondary trading. So, that's after the primary market.

And equity or stock is one form of trading or one form of financial products. What are other forms? Actually, debt products are more generic than equity products. When you started thinking about it, what is really finance is about? It's really about someone has money, someone doesn't. Someone has money to lend out, someone needs to borrow money. So, that's loan. Loan is really a private agreement between two counterparties or multiple counterparties.

When you securitize them, they become bonds. And when you look at bonds, every government will issue large sovereign debt.

And corporates have issued a lot of debt product, as well. They borrow money when they need to build a new factory or expand. Universities borrow money. When MIT needs to build a new building, some of the money will come from the endowment support, some will come from some other form of research budget, or some will come from debt financing.

Just borrow from the public-- local governments, states, counties, even. So, they have various forms. So, that's product. Commodities, actually, you know.

Metal, energy, agriculture products are traded, mostly in the futures format and some in physical format, meaning you take deliveries. When you actually buying and sell, you build a warehouse to take them. You ship a tank to store above the ocean. And the real estate, you're buying and sell houses.

So, I'm not trying to give you all the definition, dumping the information on you. But I like you at least hearing it once today, and then you have more interest, you can read on the side.

So asset-backed securities is when you have an asset, you basically issue a debt with the asset backing it. And how do you rate the asset's risk level and what's the income stream, cash flow? And before financial crisis, as you heard, large amount of CMBS-- basically, it's a commercial real estate backed securities, mortgage securities, and the residential, as well.

And further of all of these, you heard probably a lot about the derivative products. So, that started with swaps, options. And the structure of the products, it become more tailor-made for either investors or borrowers to structure the products in a way to suit their needs.

And some of the complexity of those structured products become quite high, and the mathematics involved in pricing them and the risk management become rather challenging. So coming back to the players in the market, one large type of player is really bank. Essentially, after Glass-Steagall legislation, there were two main types of banks.

One is called commercial bank, the other is investment bank. Commercial bank is supposedly, you're taking deposits and lend out the money, and doing more commercial services. Investment bank supposed to focus on the capital markets, raising capital, trading, and asset management. But obviously, after , the Glass-Steagall was repealed. There's no longer that. Some people blame that, and probably for a very good reason, for the cause of financial crisis.

But I want to tell you how currently investment banks are organized. Vasily just mentioned he works in the fixed income. So banks typically organized by institutional business and asset management.

So, within the institutional client business, it has typically three main parts. Fixed income, which trade the debt and the derivative products. Equity, trade stocks and the derivative products. So that's how banks are organized. Outside banks, other players, basically, the asset managers, are obviously a very big force in the financial markets.

So the question a lot of people ask is, is this a zero sum game? I'm sure you've heard this many times. So, in the financial markets, some people win, some people lose. A lot of times, it depends on the specific products you trade, the market you're in. It is, lot of times, pretty net zero. But why do we need financial markets?

This comes back to what I described before. Because something existed-- actually, there's a need for it. It's really the need to bridge between the lenders and the borrowers.

That's really coming down to the essential relationship. So, investors who have money need to have better yield or better return, better interest. In the current environment, when you have a savings account, you don't really earn much at all. And so you would have to take more risk to generate more return, or you have longer horizon CDs, other type of products, or trade the stocks.

So, when somebody has money, when you trade stocks, you're essentially-- you're buying a stock, you give the money somewhere. Supposedly, it will go to the company. Company use the money to generate a better return. And for the borrowers, whoever needs money, they need to have access to the capital.

So obviously, different borrowers have different risks. Some people borrow money, never return. So, never generate any returns, or never even return the principal. And so the trade between lenders and the borrowers, is again, essentially the main driver of the financial markets.

So, a few more words about the market participants. So, banks and so-called dealers play the role of market making. What is market making? So, when you or some end user go to the market, wants to buy or sell, typically, if there's no market, you don't really find the match. And some of the products you want to buy or sell may not necessarily be liquid.

So, the dealers step in the middle, make you a price. Say, OK, you want to buy or sell. I can tell you the stock. I make you price. So, that's the price I'm willing to buy or sell. But what the result of the trade-- the dealer actually takes the other side of your trade. So, they take principal risk, in this case. So, that's the difference between dealers and the brokers. So, brokers don't really take principal risks.

If you want to buy something or sell something, if I'm a broker, I don't make you a price. I go to the market makers. I actually put two people together, matchmaking, make that trade happen. So, I earn the commission. So, that's a broker's role. So obviously, there are individual investors, retail investors, same meaning.

Mutual funds, who actually manage public investors' money, typically in the long only format. Long means you buy something. So, you don't really short sell a particular security.

Insurance companies has large asset. They need to generate a return, generate cash flow to meet their liability needs. So, they need to invest. And the pension funds, same thing. As inflation goes higher, they need to pay out more to the retirees, so where do you get the return? Sovereign wealth fund, similarly, endowment funds-- they all have this same situation, have capital and needs to deploy and to make better return.

So this other type of players, hedge funds. So, how many of you have heard hedge funds? OK, good. Almost everyone. And Peter mentioned that he used to work at a hedge fund. And so, there are different types of strategies, which I will dive into a bit more, but hedge fund play the role in the market-- they basically find opportunities to profit from inefficient market positioning or pricing, so they have different strategies.

And the private equity is different type of funds. They basically look to invest in companies and either take them private or investing the private equity form to hopefully improve the company's profitability, and then catch up. And governments obviously have a huge impact on the market.

So, we know in the financial crisis, government intervened. And not only that, at the normal market condition, government always have a very large impact on the market, because they are the policymakers. They decide the interest rate and interest rate curve. And the different policies they push out, obviously, will generate different outlook for the future markets, therefore, profitability.

Then the corporate hedges and the liabilities. When corporates borrow money, they create some risk, so they need to be sensitive to the market, it changes. So, to summarize the types of trading. The first type is really just hedging. That means you're not proactively adding risk to what you have. You already have some exposure. Just give you an example. Let's say you borrow money, you bought a house, so you have mortgage. So, let's say it's a floating rate mortgage payments.

And you're worried about interest rates going higher, so you can lock that rate in into the fixed rate format. Or you can find ways to hedge your exposure. Or your corporate has a large income coming from Europe.

So, you have euros coming in, but you're not sure if euro would trade stronger to the US dollar in the future, or trade weaker. If you think it will be stronger, you just leave it. But if you think it will trade weaker, so you may want to hedge it, meaning you want to sell euro and buy US dollars. And so that's the hedging type. The second type, as I mentioned, is a market maker. So, market maker also takes principal risk, but the main source of profit is really to earn the bid offer.

So, that's what the market maker is trying to profit from. But obviously, they have residual risks sitting on the book. Not every trade is matched. So, how to optimize those group of trades, that's what market maker is doing. Most of the bank's dealers are market makers. And so the third type is really the proprietary trader, the risk taker. So, these are the hedge funds or some portfolio managers.

They need to focus on generating return and control the risk. So, that's where the beta and alpha, the concept comes in. So, if you're a portfolio manager, some people say, don't worry.

Don't go pick any stocks. Very cheap. You can pay very little cost to do it. That's true. So, the return of that, R of the b. That's a return of that index. Now, you have a portfolio A. Your time series of return of your asset A, obviously, you can do linear regression. Lot of you are math major here, and you can find a correlation between those two time series. So, how the two returns are related in a simplified form. So you can say, this actually-- somehow it came out.

It's supposed to be alpha and a beta, but it turned out to be the letters. So, in a short description, beta is really-- just think as a correlated move with the other asset. Alpha is really the difference in the return. It's a format. So let me just go in bit of details of how each type of trade actually occurs.

So, when we talk about hedging, I mentioned the currency example. Let me give you another example. There are a lot of people issue bonds, or issue a debt. So this example I'm going to give you is, let's think about Australian corporate. Because interest rate in Australia is higher than in Japan, so typically, people like to borrow money in Japan, because you pay smaller interest.

And they invest it in Australia. You earn higher interest rate. So let me ask you a question. Who can tell me, why don't people just do that all day long, just borrow from Japan and invest it in Australia? Yeah, go ahead. Because you invest in the Australia Ozzie, Australian dollar. The Australian dollar may become weaker to the yen. You may lose all your profit, or even more. And further, if everybody plays the same game, then when you try to exit, you have the adverse impact of your trade.

So, let's say you think that's the right time to do it, but then at one time, you wake up, you said, huh, I think too many people are doing this. I want to hedge myself.

So, what do you do? So, you try to lock in, right? So basically, you sell the Australian dollars, buy the Japanese yen. Or on the interest rate terms, you say you'll basically pay the Australian dollar in the swap leg, and the receive yen. This involves foreign exchange trade, interest rate swap, and the cross-currency swap.

So, your answer about currency forward is roughly right, but obviously involves a bit more in actual execution. So that's just to give you example. Even if you are not a finance guy, you work in the corporate, you just do you import, export, or building a factory, you have to know, actually, what the exposure is.

So, risk management, nowadays, becomes pretty widespread responsibility. It's not just the corporate treasury's responsibility. So, that's on the hedging side. Obviously, if you are Intel, for example, you sell a lot of chips overseas. And your income-- actually, Intel does have lot of overseas income sitting outside the states.

So, the exposure to them is if the exchange rate fluctuates, dollar becomes a lot stronger, they actually lose money. So, they need to think about how to hedge the revenue produced overseas. And obviously, for import exporters, that's even more apparent. And if you're entering in a merger deal, and one company is buying another, you need to hedge your potential currency exposure and your interest rate exposure.

And whatever is on the assets, or the liability, or the balance sheet, you need to hedge your exposure. So we talked about hedging activity. Let's talk about market making. So if it's a simple transparent product, everybody pretty much knows where the price. So, if you buy Apple stock, I think a lot of people know pretty much where it is. You may even have it on your cellphone, know where that stock is.

But if it's not transparent, so what do you do? But if I asked you instead, what is the core option on Apple stock in two month's time?

I'll give you a strike, let's say, So you're probably less transparent. So that market maker comes in to provide that liquidity, and then takes the risk. They manage the book by balancing those Greeks, which I mentioned earlier. That's called a Delta. Gamma is really the change of the portfolio.

Take the derivative to the delta, or to the underlying spot. So, that's second order derivative. Delta is the first order. So Gamma, now you have curvature or convexity coming in. And Theta is really-- nothing changes in the market.