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By JEREMY BERNSTEIN
“Financial crisis is by definition something that had not been anticipated. If it had been anticipated it could have been arbitraged away.” - Alan Greenspan
At the outset you need to know that I am a theoretical physicist and not a stock broker or commodities trader. But I have been trying to follow the news. It is full of terms such as “mark to market” and “credit default swaps” which at first meant about as much to me as “Bell’s Inequality” might mean to most of you. But I am stubborn and decided that if these things are going to determine my financial future I better know what they mean.
The first thing that becomes clear when you look into the matter is that these concepts are part of a virtual economy. They are not like the “real economy” where, after you go into a grocery store to buy eggs and milk, you come out of the store with eggs and milk and not an option to buy eggs and milk at an agreed price at a later time. If you buy a “credit default swap” you come out of the transaction with a piece of paper-or more likely a computer file-which has no intrinsic value. If you imagine a situation in which you are confronting an aboriginal tribe you might get somewhere if you have beads to swap, but not if you have a credit default swap. These financial instruments are rather new. The commodity they trade in is money. They are very clever devices that were thought up by very smart people to make money from money and they are in the process of doing us all in. I am somehow reminded of something that the great German mathematician David Hilbert said about astrology. If the ten smartest people in the world got together they could not think of anything as stupid as astrology. Now to the glossary.[prebreak][/prebreak]
DERIVATIVES 101
This is such a complex subject, and so fundamental, that I am dividing this entry in the primer in three parts. This one,101, gives the basics.
A derivative is a financial instrument whose value is derived from the values of other financial instruments that do have value.[1] For example if I buy an option to buy some stock in the future at some present price, what determines the value of the option depends on the future value of the stock. The question is, what is such an option worth to me now? To understand this better let us consider a specific example.
Suppose you are given the following information-in reality you are never given this much information but that is for Derivatives 201. You are told that the Horse Feather company, whose stock is presently worth 100$ a share, will in six months be worth $120 with a probability ¾ or $80 with a probability ¼. You are offered an option to buy this stock in six months at $100 a share. What should you pay for this option? This form of option is called a “European” option since it can be exercised only after six months. A so called “American” option can be exercised any time. Your expectation for a gain after six months is, in dollars,
3/4x20+1/4x0 =15 which reflects that fact if the stock drops to $80, the option is worth nothing. This calculation appears to show that the option is worth $15. But never underestimate the ingenuity of people interested in making money. In this case there is the concept of “arbitrage.”
Let us suppose you are willing to buy the option from me for $15.I will take the $15 and pocket $5 which you will never see again. I then go to my friendly bank and borrow $40. This is the “leverage”. In all these transactions I am assuming that there are no stock commissions and no bank interest. Since the people who thought these things up often had a background in physics they called these transactions “frictionless.” It is not difficult to take the “frictions” into account. I take the $40 and the $10 and buy a half share of the Horse Feather company.( If you object to half shares I can modify my example to make it full shares. ) This purchase of the half share is known as the “hedge.” This sort of thing raised to many powers is what “hedge funds” do. I will now show you that I can’t lose.
There are two cases the final price is $120 or the final price is $80. In the former case you will exercise your option which was our agreement.But you are not interested in owning the stock, but simply pocketing the twenty dollar profit which I owe you. I will now sell my half share for $60. Forty of this I will give back to the bank and the remaining twenty I give to you . Note two things. In the first place I get to keep the five dollars. In the second place the true cost of the option was ten dollars since the rest was money borrowed from the bank. You overpaid for the option by five dollars. Now take the second case. The stock has dropped to $80. You do not exercise your option so I owe you nothing. But I sell my half share for $40 which I give back to the bank still pocketing the five dollars.
This seems too good to be true and it is. In Derivatives 201 I will begin to discuss the real world.
DERIVATIVES 201
In 101 I presented a “toy model” to illustrate the basics. I ignored the “friction” of such inconveniences as broker commissions and bank interest. But, by somewhat complicating the mathematics ,these can readily be taken into account. What makes the model a “toy” is the assumption that we know the possible future values of the stock and the probabilities of the stock having one of these values by some sort of clairvoyance. In the real world one replaces clairvoyance by mathematical modeling, although the way things have turned ,out one often longs for a spirit medium.
The idea of such a mathematical model goes back to the year 1900 when the French mathematician Jean Louis Baptiste Alphonse Bachelier published his PhD thesis Théorie de la Spéculation. Bachelier was already thirty years old and had spent time working at the Bourse-the French stock exchange. The question he asked was precisely the one that interests us; How can we predict the future probable values of a stock given our present information? To answer this he proposed the idea that stocks follow a “random walk.” As far as I know he never later connected this to a problem in physics solved in 1905 by Einstein. Einstein surely had never heard of Bachelier. Very few people had until he was rediscovered in the 1950s by mathematical economists like Paul Samuelson.
The problem in question was stimulated by a discovery that the Scottish botanist Robert Brown made in 1827. He noticed that if microscopic pollen grains were suspended in water then these grains performed an odd random movement which is now fittingly called “Brownian motion.” At first Brown reasonably thought that these grains might be alive which explained the motion. But he tried all sorts of other suspended particles including soot from London and all of them exhibited the same motions. Throughout the 19th century this remained a puzzle although the correct solution was conjectured; namely that the suspended particles were being bombarded from all sides by the agitated and invisible molecules belonging to the liquid in which the particles were suspended. It is amusing that one objection to this is one that people first exposed to this idea often make. Such people argue that if the particle is being bombarded from all sides how does it get anywhere? But after the first lurch in some direction it is infinitesimally probable that the second one will reverse the first. The particle will go off in a new direction. It was Einstein who in 1905 made all of this quantitative. He was able to show that the average distance such a particle would travel from its origin in a time t was proportional to the square root of t which could and was tested experimentally.[2] As I mentioned, I find no reference to Brownian motion in anything that Bachelier wrote.
The problem that Bachelier posed was suppose you know the price of some stock now, what is the probability that the stock will have some given price at a later time? He did this by supposing that the later probability was achieved with a number of steps in which any motion of the stock was equally likely to be up or down. This random walk implies an “efficient market”. In this kind of market prices are set by market conditions and that fluctuations do not matter. No scheme will help you to beat the market. In fact all market speculation is based on the assumption that at least in the short run this is false. As a student of probability theory, Bachelier understood that with his assumptions the probability, as the number of ups and downs increased, would approach a “normal” distribution-a bell-shaped curve. From this he could predict the most likely future price. Here we must mention something crucial for what has happened. A property of the bell-shaped curve is that it has “wings”. No matter how far you are away from the most likely there is always a non-zero probability for something that is very unlikely. You may say that it is irrational to worry about the unlikely but keep in mind what Lord Keynes noted,” The market can remain irrational longer than you can remain solvent.”
Bachelier applied his methodology to derivatives-options, but one thing did not seem to have occurred to him-arbitrage-beating the system by hedging.
This was corrected in the 1970s primarily by three mathematical economists, Myron Scholes, Fischer Black and Robert Merton. Merton and Scholes were then at MIT. while Black was a consultant for the Arthur D.Little Company. Scholes and Merton shared the 1997 Nobel Memorial Prize in Economics. Black had died two years earlier. The work was done independently by Black and Scholes, and by Merton. The mantra of the quantitative financial analysts-the “quants” as they are called-is the so-called Black--Scholes equation. It is derived in a way that Bachelier would have understood. The same sort of assumptions about Brownian motion are used. The solutions tell you how to price options. For a scientist like myself it is a curious affair. In quantum mechanics, to take an example, using the mathematics of the theory we can predict the probable results of future experiments from present data. Here we use the probable future to retrodict the present. In quantum mechanics we cannot even describe the past. There are several possible pasts with different probabilities.
Merton’s approach was different and it is the one that is most commonly used by people who deal in these things. He showed that the actual option could be replaced by a “synthetic” option consisting of stocks and cash that reproduced the results of the real option. In fact you need never make reference to the real option. We saw this in the toy model. The stock purchased using the borrowed cash along with the ten dollars replicated the option. Once this was understood the quants had a field day. This was especially true since, as market conditions changed, the mixture of stocks and cash had to be continually adjusted. This could not be done by hand. It had to be done by computers. Dealing with derivatives was like dealing with a black hole. Moreover there was no a priori check on the model. You only knew that it didn’t work when it led to a financial disaster. This happened in 1987 and again in 1998 and now again in 2008. It is the subject of the next entry-301.
DERIVATIVES 301
John Meriwether was born in Chicago in 1947. In his teens he won a caddie scholarship-a scholarship only open to caddies-which he used to attend Northwestern University. After a year of postgraduate teaching he went to the University of Chicago to study business. One of his classmates was Jon Corzine. In 1973, Meriwether took a job at Solomon in New York. This was just before the financial engineering revolution. After it took over, Meriwether formed the arbitrage group at Solomon. His modus operandi was always the same. He looked for the smartest people he could find even if they were smarter than he was. It did not matter how gooky they were. My feeling about Meriwether was while he certainly liked to make money he was much more interested in showing that he and his people we smarter than anyone.
In 1994 Meriwether founded a hedge fund named Long Term Capital Management-LTCM-in Greenwich, Connecticut. He hired, among others, Merton and Scholes. They don’t get any smarter than that. They brought to bear every bit of wizardry you could get out of computer models. For awhile it worked marvels. It was scoring returns of 40% for its investors. It had a trillion dollars under management. This was more than any of the large investment banks. But by four years later the bubble had burst and in less than four months in 1998 they lost close to five billion dollars. What was worse was that they were not playing with their own money. They were leveraged to the hilt which might have been all right if the institutions that had lent them money had not wanted it back once they saw that the ship had hit an iceberg. In the event, LTCM did not have the money to repay these loans. In fact Meriwether tried to borrow more on the theory that, given a bit more time, the hole in the side of the ship would repair itself. What happened?
In the three disasters I mentioned there is a common element. Some financial instrument was created that could not fail so long as the market functioned rationally. The wings of the bell curves didn’t matter. As a physicist I think of these things in terms of thermal equilibrium. If you have a gas at some temperature you can predict what the average energy of the molecules that compose it has. But there are fluctuations-deviations from the average. Under most circumstances these fluctuations dissipate. If there was a circumstance in which they didn’t we would be in hot water at least for awhile. In the case of LTCM the instrument was what is known as “convergent trades.” I will discuss the ones that characterize the other debacles in due course. First convergent trades.
Let us take a simple example. Suppose you have two treasury bonds, one that matures in thirty years and one that matures in twenty-nine years. Let us further suppose that we spot the fact that the second bond is trading for somewhat less than the first. It is reasonable to assume that this is a temporary fluctuation and that the spread between the two bonds will approach zero as the bonds mature and the price of the cheaper bond rises and that of the more expensive bond declines. Here is how we play the game. We “short” the expensive bond. We borrow the shorted bonds from some willing bank, or what have you, and then immediately sell them. If, as expected, the price of this bond drops as the two converge we can then replace the bonds we borrowed at less cost. But suppose instead the price of this bond rises and the cost of covering the short then increases. If this is a brief fluctuation then we can sit tight until things sort themselves out and behave as they are supposed to. But suppose they don’t and the spread gets wider and wider? Then, not to put too fine a point on it, our goose is cooked. This is what happened to LTCM.
The first intimation of trouble was in Thailand in the summer of 1997 with the collapse of the currency which caused people in the Pacific rim countries to look for investments such as our treasury bonds that seemed more secure. This turned into a panic when Russia stopped payment on its debt payments in August of 1998. There was a flight for safety everywhere. LTCM had been using its convergent trade strategy everywhere. They had even opened an office in Japan. The spreads kept getting wider and LTCM more desperate. The obvious response would normally have been tough nuggets. But LTCM was in hock to the tune of about a hundred and twenty billion to its lenders-some of the most prestigious and important financial institutions in the country. In light of what has happened it is interesting to recall the role of Bear Stearns in this. Bear Stearns was the broker of record for LTCM. They kept a reserve of LTCM assets-“cash in the box”. The condition was that if this reserve fell below 500 million Bear Stearns would no longer trade for LTCM and the party would be over. By September when it became clear to Bear Sterns that the assets of LTCM were declining they asked for an additional 500 million. Meriwether tried to borrow more money from everyone including his old class mate Jon Corzine at Goldman Sachs all to no avail. One problem was that as an unregulated enterprise LTCM’s books were closed and no one from the outside could find out the details.
The dénouement began on Sunday, September 20 when representative of the New York Fed along with bankers from Goldman Sachs and JPMorgan made the short trip from New York to Greenwich to examine the condition of LTCM first-hand. It turned out that these bankers had no inkling of LTCM’s off-book trading strategies even though they were counterparties to billions of dollars in loans. It was also clear that LTCM was too big to fail. That would bring down a number of other major financial institutions and the financial structure might collapse like a house of cards. The portfolio of LTCM had to be bought out in a fire sale. One of the bidders was none other than Warren Buffet who attached very stiff conditions such as the firing of the entire management team of LTCM. Meriwether rejected this offer and in the end ,13 banks bought LTCM out and closed the fund.
Before I turn to the other two cases-1987 and the present-it will be helpful if I add a few more primer entries. They will come up later.
LIBOR
Some years ago I made a small investment in a fund offered by Merrill Lynch. I was informed that the returns were adjusted to something called LIBOR. When I asked what that was I was told that it was short for London Interbank Offered Rate. How you get “LIBOR” out of this I am not sure. Though I had no idea why a London offered bank rate should have anything to do with much of anything, I did not at the time have the intellectual curiosity to inquire further. I contented myself by going around and saying that I was in Libor-which would have been marginally more funny if I had been Australian. I have long ago sold the fund and would have given it no more thought except that LIBOR has come back big time in the present economic crisis. This has motivated me to look into the matter.
I was surprised to learn that LIBOR is a fairly recent institution. It had begun informally in 1984 but only became official on January 1,1986. It was a response to the fact that a variety of new financial instruments had appeared with a variety of different interest rate policies. It was thought that it would be a good idea to bring some uniformity to the process. In essence there are sixteen London banks which supply by 11 a.m. London time to a central office the rate at which they could borrow money, based only on their own assets as collateral, from other banks at that time. How this is determined is as much an art as a science because the banks in question do not have to have made such a transaction.
To a suspicious mind like my own, the first question that occurs is that if these rates are used to set a variety of other rates all over the world, would not some of these sixteen banks be tempted to put a little “body English” on their numbers. The tiny staff that receives these numbers at an office in London’s Docklands looks for anomalies. Moreover when it averages them to produce the daily LIBOR it throws out the highest and lowest number it has gotten from the banks. Nonetheless. Why has the LIBOR come to special prominence now? This has to do with its relation to the federal funds rate. This is a rate that is set monthly by the Federal Reserve Open Market Committee. It determines the rates at which American banks in the system will lend money to each other and the rate at which the fed will lend to member banks. Its purpose is normative. Raising the rate will cool the economy while lowering it will in principle do the opposite. The LIBOR, like the canary in the mine shaft, simply reports. When things are normal the federal funds rate and the LIBOR track each other with the funds rate being a percent or so lower than the LIBOR. But recently the two have gotten out of alignment. The funds rate, is as of this writing %1.5, while the LIBOR is over four. This reflects the reluctance of these London banks to lend to each other. It is a signal that something is seriously wrong.
CREDIT DEFAULT SWAP
A “credit default swap” is a form of insurance pure and simple-well impure and not so simple. It is called a “swap” rather than an insurance policy because that way it is exempt from regulation unlike an insurance sale. To understand the magnitude of these transactions note that world-wide the value of the loss that is covered is estimated to be some fifty five trillion dollars! This is about equal to the gross domestic product of the world! But they do not add a scintilla of productivity to anyone. They are simply financial instruments for making or losing huge sums of money fast. The buyer of a credit default swap pays the seller an amount of money to insure against the default of something like a mortgage-or a sliced and diced bundle of mortgages. But these swaps are themselves tradable. Since the whole market is unregulated no one knows who owns what until there is a default and someone has to pay up. Since the market is unregulated there is no specified amount that the sellers of these swaps have to keep on hand to pay the piper in case of default. A run on the swaps such as what is occurring in the mortgage market can put the counterparties into bankruptcy. This is what was about to happen to the American International Group-A.I.G.-which had about $440 billion in outstanding swaps for which they were responsible. The government bailed them out and several executives of the company celebrated by going on a very expensive partridge hunt in England. Let them eat partridge.
MARK TO MARKET
“Mark to market” sometimes called “mark to the market” is an accounting protocol that seeks to apply the same accounting methods to other financial instruments that are routinely applied to stocks. If you own a stock you know that after the market closes its value is posted. This is marking the value of the stock to the market. If someone wanted to know your net worth and you wanted to include this stock this is the value you would give and not some possible value six months from now. But what if the value of the stock were undefined or ambiguous? Then if you were a clever and not particularly ethical accountant you could mark to the market of expected future earnings and inflate the present value of your enterprise. This is something that was done by Enron in spades. Conversely suppose that you held instruments that you were sure would increase in value in the future, but were distressed now, then mark to the market accounting might show that you were going bankrupt even though at some future time you might recover. This sort of thing was one of the elements that put Lehman Brothers out of business.
THE CRASH OF 1987
The 1987 stock market crash, with its Black Monday on October 19th in which the Dow lost 22.6% of its value, is a perfect model of what can go wrong when very smart people do not think things out clearly. In this case the proximate cause was what is known as “portfolio insurance.” To illustrate this let us return to the toy model. Suppose I own a share of Horse Feather which is now worth $100 and is paying a very nice dividend. I want a scheme by which I can hold the stock for awhile with absolutely no risk of loss. Here is what I can do. I can short one share. I borrow a share from my friendly broker and sell it for $100. Now after the time of interest there are two possibilities; either the share will be worth $120 or it will be worth $80. Let us consider the first case first. I have to return one share to the friendly broker. I can if I want to be a little long-winded, sell my share for $120. Take the $100 I have and add $20 and buy a new share to give back or I can just give the broker the share I have. Now let us analyze the second case. I take my $100 and use 80 of it to buy a new share which I give to the broker. I now have $20 plus one share worth $80. In either case I have lost nothing. The insurance worked marvels. What could possibly go wrong?
The underlying assumption in the scheme is that the short selling people have to do to cover their positions, will not influence the market. But so many people had jumped on this insurance that once the market began to fall, and they had to sell into this depressed market, they depressed the market further-a text book example of negative feed back. It seems never to have occurred to geniuses that thought up this scheme that such a thing would be possible.
THE CRISIS OF 2008
We are still too close to this to see how it is going to end. There is no doubt that it began with the collapse of the housing bubble. There is a point I would like to make that I have not seen much discussed. Suppose instead of housing we were talking about, say, a collapse in the price of tulip bulbs. Then if the normal laws of supply and demand are followed, then as the number of tulip bulbs decreases, assuming that people still want them, the price will start to go up. But housing is different. As the prices go down people get into more and more trouble with their mortgages. Hence there are more foreclosures and the stock of available housing increases depressing the prices still further-again a case of negative feedback. As I write this I do not see when this is going to end.
About the Author:
Jeremy Bernstein was a professor emeritus of physics at the Stevens Institute of Technology in Hoboken, New Jersey. He was a staff writer for the New Yorker from 1961 to 1995. He was an adjunct professor at the Rockefeller University and a vice president of the board of trustees of the Aspen Center for Physics of which he is now an honorary trustee. He has held appointments at the Institute for Advanced Study, Brookhaven National Laboratory, CERN, Oxford, the University of Islamabad, and the Ecole Polytechnique. Dr. Berstein has written over 50 technical papers as well as many books on popular science and mountain travel including Physicists on Wall Street and Other Essays on Science and Society and Plutonium: A History of the World's Most Dangerous Element.
[1] Emanuel Derman made the point to me that money itself is a kind of derivative. It used to be linked to gold and now to other material things.
[2] For the fastidious reader I note that what I have called the “distance” here is the square root of the mean square distance and that Einstein’s reasoning was somewhat different. The Polish physicist Marian Smoluchowski at about the same time analyzed Brownian motion as a random walk.
