Sunday, 27 July 2008

Mission Accomplished: The Destruction of Fannie Mae and Freddie Mac (Part 1 of 2)

Speculative capital is inherently self destructive; it eliminates the opportunities that give rise to it. What is the real life manifestation of this characteristic? In other words, how does the self-destructive tendency manifest itself in practice?

On example I used in Speculative Capital and the Credit Woes series was the shrinkage of spreads. Speculative capital is capital engaged in arbitrage. Arbitrage, by definition, tends to bring the price of two arbitraged positions together, eventually making them equal. In such a state of equality, the arbitrage possibility vanishes, and with it, the condition for the existence of speculative capital.

Shrinkage of spreads is a technical example. As the influence of speculative capital permeates beyond the markets to the various segments of social life, does this self-destructive tendency manifest itself in a larger context with more far-reaching social ramifications? The answer is yes. One outstanding example in that regard is the premeditated destruction of Fannie Mae and Freddie Mac.

In the past couple of weeks, the distress at Fannie Mae and Freddie Mac has dominated the business headlines. True to norm, the extensive coverage has left the readers in a state of utter ignorance. What a bond trader, a finance professor or a corporate treasurer knows from reading the New York Times or Wall Street Journal is that two somehow government related mortgage companies are going to lose billions of dollars and need be rescued by the government. That is how the story is framed, confirming the prejudices of the run-of-the-mill consumer of the news, built over the years by equally one-sided reporting, that the government “cannot do anything right” and the politicians “screw up” every time and big government is bad, and so on.

In reality, what we are witnessing is coming to fruition of a deliberate plan – a conspiracy, really – by a group of men in power to destroy Fannie Mae and Freddie Mac so that their institutions could reap larger profits. The success of the plan and the consequences of that success is the subject of today’s posting that will appear in two parts. Part I deals with the details of the operation of the two agencies and is at times slightly technical. So, pay attention!

The Role and Function of Fannie and Freddie

Fannie Mae and Freddie Mac were created by the US Congress to facilitate home ownership in the US. They were to do that by purchasing mortgages from banks.

For reasons that do no concern us here, the price of a house in general is many times above the average yearly income of a worker. The median home price in the US, for example, is about $200,000, while the median household income is about $50,000. If homes were bought and sold for cash only, as they are in many counties around the world, it would require years of saving – well into the middle age – for the average working person to save enough to purchase a house.

Credit circumvents that need. (I discuss the subject of credit – vulgarized beyond recognition to “trust” and “credit worthiness” – in Vol. 4 of Speculative Capital.) Our average worker could borrow the $200,000 asking price of the house from a bank and make only small monthly payments – small because the payment is stretched over 30 years. With 6% interest rate, for example, the monthly principal and interest payment on a $200,000, 30-year loan would be about $1200. (By virtue of this extension, the borrower would pay more in interest than the original sum, but that is the nature of the beast in the system we are investigating.)

Historically, this extension of credit has had two constraints, one at the borrower’s end, the other, at the lender’s.

The constraint on the borrower’s end was his wherewithal; he had to demonstrate his ability to make the monthly mortgage payments. The house that was being purchased was pledged as the collateral for the loan, so in the case of the borrower’s default the bank would repossess the house and sell it to recover the loan. To protect itself further, the bank demanded an initial payment, equal to 20% of the purchase price. This forced the borrower to have a “skin in the game”, which acted as a disincentive for him to walk away from his obligation in the case of a drop in property values. These requirements limited the universe of qualified home buyers.

The second constraint was the banks’ lending capacity. After setting aside 10% for the regulatory capital with Federal Reserve, a bank with $100 million in deposits would only have $90 million to lend. Assuming $200,000 for the average loan, that would translate to 45 mortgages. To lend to the 46th applicant, the bank would have to grow its deposits, a slow process that remains vulnerable to many parameters including the state of local economy.
Fannie Mae and Freddie Mac were created to eliminate this latter constraint. They did it by offering to buy all the banks’ mortgages. In our example, they offered to buy 45 mortgages for, say, $91 million.

The bank happily accepted the offer. By receiving $91 million, it: i) realized a profit of $1 million immediately; and ii) had its $90 million returned to it which it could lend to the second batch, another 45 qualified applicants.

That was the sole function of Fannie Mae and Freddie Mac: to make it possible for banks to lend to more home buyers. They did not lend to individuals or otherwise engaged in banking activities.

What about Fannie Mae and Freddie Mac, how did they get $90 million to buy the mortgages? They borrowed the money in the capital markets. Both entities were created as “government sponsored enterprises” or GSEs, meaning that the US government implicitly guaranteed their debt. As a result, they could borrow at very low rates, almost comparable to the US treasuries. As the mortgage rates were about 2% above the yield of the treasuries, it is easy to see how the two GSE’s made money: they borrowed at 4% and earned 6% on the newly acquired mortgage asset. On a $90 million pool of mortgage, that would translate to $1.8 million annual revenue.

This method of financing, however, ran against the same constraint that had limited the banks’ mortgage lending. The two agencies could not, ad infinitum, borrow in capital markets and buy mortgages because they also had regulatory capital constraints. So they came upon the idea of creating mortgage-backed securities (MBS), a landmark event in capital markets.

The idea behind MBS is a simple one. Pool a group of mortgages and, on the strength of the pool and its monthly payment, issue fixed income securities whose coupon would be paid by the home owners. An MBS is a bond whose coupon, instead of being paid by one borrower, is paid by many borrowers.

Suppose in our example Fannie Mae purchased mortgages from two banks, one for $90 million that we saw and the other for $110 million. The combined mortgage pool would then be $200 million. The agency could issue – sell to capital market investors – 200 thousand MBSs, each with the face value of $1000. (The structure of MBS is more complex than in this example. It involves “tranches” with different loss exposure and credit ratings. That technicality does not concern us here.)

The mortgage pool was vulnerable to the borrowers’ default. If a few borrowers defaulted, the monthly payment to the pool, and thus, the amount of money available to the MBS holders would be reduced. To address this eventuality, Fannie Mae and Freddie Mac guaranteed the payment of MBSs.

That guarantee, offered by two GSEs whose obligations were in turn implicitly guaranteed by the US government, made MBSs tremendously valuable. Note that in our example the yield of US treasuries is assumed to be 4%. A purchaser of a MBS would receive 6% annual coupon. That yield was 2% above the yield of the treasuries but for all intents and purposes, the MBS had the default protection of the treasuries.

Little wonder then, that Fannie Mae and Freddie Mac became tremendously successful. Their asset size, the amount of mortgages they purchased and kept on their balance sheet, the amount of MBS they issued, together with the home ownership, grew tremendously. It was the proverbial American success story.

Monday, 21 July 2008

Why Are We "Digging Deeper Into Debt"?

This past Sunday (July 20, '08) The New York Times had another front page story about the ravages of indebtedness. The heading, “Given the Shovel, Digging Deeper Into Debt” signaled the usual way the story was to be framed: irresponsible borrowers, greedy and unscrupulous lenders. The story’s “human face” was a perfect setup: a slightly overweight divorcee who likes “handbags and knickknacks” and was a “dream customer for lenders” until everything went bad. Serves her right, was the message. But even she was recruited to chastise the fellow borrowers. Her observation made the paper’s “quote of the day”:
I think a lot of people in this country have a lot more debt than they let the outside world know. I worked in retail for five years. And men, women would open up their wallets to pay and the credit cards that were in some of the wallets just amazed me.
Left unmentioned in the article was the cause of the indebtedness, the reason that the US population has suddenly turned irresponsible, unscrupulous and greedy. Yet, the cause is there in plain view for everyone to see. It is the declining income of the workers that has not kept pace with the inflation since the early 1970s. Bloomberg News:
The current U.S. economic expansion is the first in 60 years that may end before many Americans have recovered from the last slowdown. Annual family incomes adjusted for inflation have grown just 0.8 percent since the end of 2001 even as the economy expanded an average 2.7 percent a year, leaving households little cushion to absorb higher food and fuel prices.
That is why the US households borrow, overstretch themselves and then go bankrupt. Irresponsibility and greed play very little role in this march towards pauperism. By way of a comparison, in 2006, five largest investment banks – Goldman, Merrill, Morgan Stanley, Lehman and Bear Stearns – paid $35 billion in bonus. That was more than the gain of 39 million US workers in the period 2001-06. There is vast data on the subject. Google it and see for yourself.

Tuesday, 15 July 2008

Snapshots From Traders' Family Album

In more than one occasion in this blog I have written about the consequences of the genuflection of theorists to businessmen. The root of the problem is an improbably philosophical one, pertaining to the validation of theory. As a theory is a conceptual explanation of the working of the real world, it must coherently and consistently explain and foretell the real world event that it aims to explain. There is no other way to judge the accuracy of a theory.

For reasons well outside the scope of this blog, this self-evident truth was gradually turned on its head by a group of philosophers and economists in the West. Milton Friedman was the most outspoken proponent of this school (hence his fame). He elaborated his ideas in a small pamphlet called The Methodology of Positive Economics. In Vol. 1 of Speculative Capital, I spent some time on this subject:
The Methodology is a manifesto of superficiality which has cast aside its self-conscious defensiveness and assumed an aggressive posture. It is an in-your-face crudeness of unthinking, pushing to impose itself on the unsuspecting reader under the guise of philosophical thought. In it, Friedman strove to create a theoretical framework for a “pure economics,” or an economics for its own sake. The new discipline had to be independent of social constraints: He wrote: “Positive economics is in principle independent of any particular ethical position or normative judgments.”

But if ethical positions and normative judgments were to be set aside, how was one to construct or test economic theories? Economics had always been a social science. Normative issues, ethical positions and social aspects could not simply be ignored. For that, too, Friedman had an answer. He wrote:
Complete “realism” is clearly unattainable, and the question whether a theory is realistic “enough” can be settled only by seeing whether it yields predictions that are good enough for the purpose at hand or that are better than predictions from alternative theories. Yet the belief that a theory can be tested by the realism of its assumptions independently of the accuracy of its predictions is widespread and the source of much of the perennial criticism of economic theory as unrealistic.
By saying that the realism of assumptions did not matter in a theory, Friedman granted economists carte blanche to assume anything they wished as long as their theory produced “accurate predictions.” But how was one to know that the predictions of a theory were accurate? Well, the prediction could be checked against what was observed, i.e., what was given–the status quo. In the highly charged ideological atmosphere of the Postwar era, the implications of this reasoning went far beyond economics. Instead of starting from the observed evidence and arriving at a conclusion which could be unpleasant and controversial, Friedman espoused starting from the accepted system and then making whatever assumptions were needed to justify it.

In subordinating the realism of assumptions to predictions, Friedman turned scientific inquiry on its head. What he said, in essence, was that anything was permissible in economic theory as long as the theory produced acceptable results. The acceptable result was the confirmation of what was already in place. But if the assumptions of a theory did not matter, one could assume ghouls, ghosts and angels to explain economic phenomena. And in a way, that is what happened in the following years.
Friedman’s reasoning put the test of the validity of a model on a slippery slope. Little wonder, then, that the process went downhill immediately until it reached its logic nadir in the hand of theorists of Modern Finance who made the trade as the proxy for the "real world" and proceeded to weave a theory around his actions. The cult of trader worship which was the domain of financial journalist, spread to Modern Finance, a development that set the stage of its demise.

I remembered this history partly because I was working on Vol. 4 of Speculative Capital but also because in the past couple of weeks four traders came into my ken who were in the news under very different circumstances. Ordinarily, in the financial publications, I only come across stories about the Sage of Omaha and the Man Who Broke The Bank of England. Both these gentleman leave me strangely unmoved, as I know one is the cut-throat businessman behind the Geico business model, his folksy pretenses notwithstanding, and the other is the author of George Soros on Globalization, his intellectual pretenses notwithstanding!

Of the four traders, two were on their way to prison. One was dead, and one is alive and well in the pinnacle of his career. Yet, they all have something in common that we will be well advised to understand. Let us first meet the characters.

Sam Israel: Failed Faker

Sam Israel co-founded a hedge fund and from the get-go looted it to finance a lavish life style. He was not a good investor either and soon began losing money. To cover the losses, he produced fake audits and fake report. When the dust was settled, he had swindled $450 million from his investors. Convicted of fraud and sentenced to 20 years in prison, he jumped bail by faking his suicide. After a month of being a fugitive from justice, he turned himself in on the advice of his mother and also because he realized “that God didn’t want me to do that”.

What grabbed my attention more than Israel’s communication with God was his mental capacity as revealed in planning the fake suicide. He parked his car on a bridge, wrote "suicide is painless" in the dust on the hood and got away in his girlfriend's car that was waiting nearby.

I don’t have great expectations. I did not expect Sam Israel to plot like a character from a pre Berlin Wall Le Carre novel or hint at his suicide by drawing the first bar of Chopin’s Funeral March. But even accounting for his duress, the plan was downright embarrassing; a 12-year old with interest in crime stories could have done better. What is more, in post 9/11, post FISA world, he thought he could run and hide.

This man raised $450 million from investors.

Sir John Templeton: The Man Who Understood the True Character of Stock Markets

Sir John Templeton created the Templeton Fund in 1954 and sold it in 1992 for $400 million. In between, he delivered average annual return of 15% to his investors.

Sir John was a religious man. He started his business meetings with prayer “to clear the minds”. He engaged in philanthropy, created a fund to expand the frontiers of religion and started a foundation to support spirituality, giving money to spirituals like Mother Teresa and Billy Graham.

Iranian king gives a pile of gold to his vizir to distribute among the capital’s spiritual men. Sometime later, the vizir returns the gold, saying that he had not been able to find one. “How could it be?” asks a perplexed king, “I am told there are 10,000 spiritual men in this city.” “Your Majesty,” answers the vizir, “the spiritual men refused the money. And those who did not were not spiritual men.”

Money Magazine had called Sir John “arguably the greatest global stock picker of the century”.

Financial Times obituary described him as “the renowned investor and philanthropist who is credited with some of the best-known investment adages”. The paper went on to give an example of those adages:

  • Bull markets are born on pessimism, grow on scepticism, mature on optimism and die on euphoria. (This, according to Financial Times, was the proof that Sir John “understood the true character of stock markets”.)
  • ‘It’s different this time’ are the most expensive words in the English language, has become a maxim for investors.
  • To buy when others are despondently selling and to sell when others are greedily buying requires the greatest fortitude and pays the greatest reward”.
Sir John said and did all those things before he died of pneumonia at age of 95.

Jeffrey Epstein: Multi-talented Jew

Jeffrey Epstein is not nearly as famous as Sir John. In fact his “angle” was to promote himself as a low key operator, of the kind you have to look hard and be somebody to find. He was in the news in relation with his conviction for prostitution involving an underage girl. The venerable Alan Dershowitz of Harvard Law School is being paid to represent him.

If Sir John started the meetings with a prayer, Jeffrey Epstein “starts his mornings with a secret-ingredient bran muffin prepared by his chef,” The New York Times informed its readers. Some like to clear their minds; some, their bodies.

The paper also said the following about “Mr. Epstein”:
His business is something of a mystery. He says he manages money for billionaires, but the only client he is willing to disclose is Leslie H. Wexner, the founder of Limited Brands.

As Mr. Epstein explains it, he provides a specialized form of superelite financial advice. He counsels people on everything from taxes and trusts to prenuptial agreements and paternity suits, and even provides interior decorating tips for private jets. Industry sources say he charges flat annual fees ranging from $25 million to more than $100 million.

As it became clear that he was headed for jail, Mr. Epstein has tried to put on a brave face. “Your body can be confined, but not your mind,” he said in a recent interview by phone.
Rumi himself could not have said it better.

Mohamed El-Erian: Greenspan-inspired Asinine

You cannot get more successful than John Templeton in fund management business, and you cannot get more successful than Mohamed El-Erian in both, practical fund management and markets analysis. For years, he was the president and chief executive of the Harvard Management Company, as well as a faculty member at the Harvard Business School and deputy treasurer of the university, where he delivered outstanding results to Harvard endowment fund. Last year, he left for Pimco, where he is now the co-CEO and co chief investment officer. Hardly a month goes by without him writing or talking about grave financial matters in some major publication.

I remembered him because there he was again, in today’s Financial Times, offering opinion about the current crisis in financial markets.

To say that it is difficult to understand what El-Erian is saying is to be charitable. The man has a knack for making the darkness opaque. Here is an entirely typical sample quote from the Financial Times (with the British spelling preserved):
The price shock will serve to undermine real incomes in the US and lower imports. On the policy front, it will accentuate the tug of war that the Federal Reserve faces on account of its now conflicting inflation and employment objectives. Emerging economies face greater inflation in the context of their buoyant liquidity conditions. Several will see their real effective exchange rates appreciate, by means including measures to allow the nominal exchange rate to appreciate markedly against the dollar. In Europe, growing demands for wage increases may force companies to step up structural reforms and will cause the European Central Bank to increase its hawkish rhetoric.
No fortuneteller ever spawned so much general nonsense. But even in this short paragraph he manages to show his ignorance of a critical point about the working of the Fed when he talks of “conflicting inflation and employment objectives” of the Federal Reserve. He is referring to Humphrey-Hawkins Act that mandates the Fed “to translate into practical reality the right of all Americans who are able, willing, and seeking to work to full opportunity for useful paid employment at fair rates of compensation.”

El-Erian probably heard of it back in school days precisely because then it was a topic of discussion. The Act is still on the books but the Fed simply ignores the part pertaining to the employment. The chief investment officer of a bond fund company, of all places, should know that.

This was not a one-time slippage. Here is El-Erian on the Fannie Mae and Freddie Mac crisis:
“The key is to stop the equity price debacle … from morphing into a full funding crisis for the two institutions,” Mohamed El-Erian, co-chief executive at Pimco, the bond fund manager, told the Financial Times.
It is astounding how a well-educated fund manager who, by virtue of his job, has his fingers on the pulse of the market, can get something so obvious about Fannie Made and Freddie Mac so fundamentally wrong. The equity price debacles is the consequence of the funding crisis, not the other way around. That is true for all corporations and not just financials: first the company runs into trouble, then the stock price drops.

The point here is not to critique El-Erian. I mention him precisely because he is among the best and brightest the real-life finance offers. Yet, this successful trader/fund manager/educator has nothing to offer us by way of insight into markets. That is what he has in common with the other characters in this story. A downright crook in communication with God, a multi-talented Mr. Epstein offering superelite advice for $25–$100 million a year and a knight who imagined the stock market as nothing but the result of the psychological state of investors (and dispensed banalities to that effect), all these men are the blind agents of a force that remains hidden from them. Their experiences are valuable as the instances of the manifestation of that force and its false reflection in the human mind. But that is the extent of the utility of such experience. Afterwards, abstract reasoning must carry us forward.

In unquestioningly and uncritically taking the actions of these men as its foundation and the starting point, the way the Times unquestioningly accepts the claim of $100 million a year superelite advice, Modern Finance set itself up for failure.

Sunday, 6 July 2008

Revisiting Continuous-time Finance (Part 2 of 2)

I don’t know what finance textbooks say about arbitrage these days; I haven’t read one in years. But in the 1980s and well into the 1990s, they had only one example of arbitrage: buying IBM at New York Stock Exchange for, say, $120 and simultaneously selling it in the Pacific Stock Exchange for $120.5 and thus pocketing 50 cents profit. Just like that!

To say that the example flew in the face of the reality and insulted the reader would be an understatement. But I understand why the nonsense stayed around for so long. To really analyze arbitrage, to even define it, one has to know the Theory of Speculative Capital.

Arbitrage is a category in finance. It means buying low and selling high simultaneously. Obviously, that cannot be done with the same commodity or security; that would entail an infinite supply of rich fools. An arbitrageur, rather, must buy (or go long) one position and simultaneously sell (short) an equivalent position.

Equivalent means the equality of certain aspects of two qualitatively different things. In geometry, for example, a circle and a square are said to be equivalent if they have equal areas.

What makes two securities or positions equivalent in finance is the equality of their cash flows, Modern Finance declared. The equivalent positions, furthermore – securities or portfolios with equal cash flows – must trade at the same price. If they did not, an arbitrageur could buy the cheaper position, sell the more expensive position and secure a riskless profit – riskless because the equivalent positions hedged one another and profit because the two positions had to eventually trade at the same price.

That is the Contingent Asset Argument, the boldest and most important theory of modern finance.

Under strict conditions, the reasoning behind CAA is valid. But emboldened by the success of the Black Scholes model, the cheerleader of Modern Finance espoused it with an in-your-face aggressiveness that turned the “argument” into the inevitability of a natural law. “Greed is good,” the memorable line of “risk arbitrageur” Ivan Boesky perfectly captured this belief and attitude.

The focus on the cash flow is the view of a deal maker. It is finance as understood by Brooklyn business brokers. From the get-go, then, the arrogant pioneers of Modern Finance were in fact mouthpieces of half-educated traders and businessmen. The theoretical poverty helped set the stage for the rise of speculative capital and, from there, the systemic crisis in finance that we are witnessing. That is why Continuous-Time Finance merits a revisit.

I have shown in Vols. 2 and 3 of Speculative Capital and then briefly in Credit Woes series how, in blindly following traders, Black, Scholes and Merton entirely misunderstood options. But the reach of CAA goes beyond option valuation and touches all parts of markets.

The equivalency of positions and the deviation of their difference from the “norm” is established through either CAA or statistical analysis. Both methods are utterly unsuitable for the business in hand. In these methods, we have before us the fundamental contradiction between an arbitrageur’s business and his tools of trade. His business is quantifying qualitative differences. His tools of trade are purely mathematical, void of any qualitative content. It is that incompatibility which brings him to the gallows. There would never be an arbitrage-related loss, much less systemic risk, if the relation between the markets were purely mathematical and could be determined as such.

Defining equivalent positions in terms of cash flows is an egregious oversimplification. I will show in Vol. 4 of Speculative Capital how two positions with equal cash flows could have different prices with the difference remaining and even widening because of the impact of various factors.

The empirical evidence refuting the synchronous movement of equivalent positions was there even in the early days. Here is a Wall Street Journal story from 1996.

A Morgan Stanley trader took a $25 million loss on a position in Office Depot Inc. convertible bonds … [The trader] tried to hedge the … bond position by selling short...a mix of Office Depot common stock and call options...Office Depot reported worse-than-expected … earnings, sending its common stock tumbling 23% the next day. The trouble was that the convertible bonds fell more than expected, amid mounting concerns about the company.
The equivalent positions going the opposite way, the hedges behaving badly, is the main theme of the current crisis that has resulted in over $300 billion in losses with no end in sight. The latest victim was Lehman that lost $2.8 in June. The firm’s CFO, before she was let go, blamed the loss on the “divergence between the cash and derivatives market” and “ineffective hedges”.

The saga continues.

That is where Modern Finance now stands, with its intellectual palaces exemplified by Continuous-time Finance in ruins. Having faded, the insubstantial pageant leaves a wreck behind.

Revisiting Continuous-time Finance (Part 1 of 2)

If classic is the description of a work that stands the test of time, Robert Merton’s 700-page Continuous-time Finance is an apt example of unclassic. A mere 18 years after its publication, the book has fallen by the wayside, a colossal Ozymandias statue of ideas that lies in the ruins.

At the time of its publication in 1990, the book was meant as a celebration of the rise of “modern finance”. In a laudatory spirit, Merton elaborates, reworks and chronicles the ideas whose sum total defined the new discipline. The book’s size and heavily mathematical content is intended to show, if only unconsciously, that the foundation of modern finance was built on solid, scientific grounds.

All that is evident in Paul Samuelson’s Foreword to the book:

A great economist of an earlier generation said that, useful though economic theory is for understanding the world, no one would go to an economic theorist for advice on how to run a brewery or produce a mousetrap. Today, that sage would have to change his tune: economic principles really do apply and woe to the accountant or marketer who runs counter to economic law. Paradoxically, one of our most elegant and complex sectors of economic analysis – the modern theory of finance -- is confirmed daily by millions of statistical observations. When today's associate professor of security analysis is asked, “Young man, if you’re so smart, why ain’t you rich?”, he replies by laughing all the way to the bank or to his appointment as a high-paid consultant to Wall Street.
Yet, look closely, by which I mean actually read the book, and you would be struck by the shallowness of its content. What comes through is a Beckettian clerk who labors to formalize what has taken place around him without understanding the forces that drive the events. But Merton is no mere scribe. Like the general discipline he helped create, his formalization gives theoretical cover to the pragmatically crude action of traders. He validates and legitimizes them, making them acceptable and reputable. That is why Continuous-time Finance merits a revisit. An analysis of the current rot in the market cannot be complete without a look at the ideological cheerleaders who paved the way for it.

(This subjugation of theory to practice, the intellectual standing in awe of the ill-educated trader, is in plain view in Samuelson's foreword. Note his ideal of the relevance of modern finance: going to a “high-paid” consulting job on Wall Street, say, to Bear Stearns or Lehman. From Adam Smith to David Ricardo to Karl Marx to Samuelson. What a falling off was there.)

The pride of the place in Continuous-time Finance, as in “modern finance” itself, belongs to option valuation theory, or the contingent claims argument (CCA) in general, as Merton calls it. What is CCA? Simply this, that a riskless position must earn the riskless rate of return. In describing how he and his colleagues came up with the option valuation formula, Fischer Black wrote:

As the hedged position will be close to riskless, it should return an amount equal to the short-term interest rate on close-to-riskless securities. This one principle gives us the option formula.
The idea and the definition of hedging comes from the general accounting relation:

Assets = Liabilities + Owners' Equity

or

A = L + OE

If you have $100 in your pocket, either all of it is yours (OE = $100), or all of its is borrowed (L = $100), or a combination, say $40 borrowed and $60 your own so that $100 = $40 + $60. $100 in your pocket cannot have any other source.

The objective of hedging is to protect OE, the individual’s “net worth” so that its value would not change, no matter what happens in the markets. In mathematical terms, that means that the change in the value of OE must be zero:

change (OE) = 0
Since OE = A – L, for that condition to hold, we must have:
change(A) – change (L) = 0
or

change(A) = change(L)
The above equation is the necessary and sufficient condition for the hedge. It says that the change in the value of assets must be equal to the change in the value of liabilities. Students of finance know this condition under various names and guises, such as matching assets and liabilities or creating a riskless portfolio. The different names merely express the particular viewpoint of the person or entity engaged in the act; treasurers would speak of asset-liability matching, traders of creating a riskless portfolio.

The most consequential development here is the transformation of hedging to arbitrage. No better or more convincing example of a dialectical movement exists anywhere.

The purpose of hedging is preserving the owners’ equity. The hedger begins with an existing asset (liability) and seeks to find a liability (asset) which will offset its adverse price changes.

The purpose of arbitrage, by contrast, is profit. The arbitrageur has neither an asset nor a liability. He uses the hedge relation above to search for any two positions which will enable him to “lock in” a spread.

The difference between hedging and arbitrage, therefore, boils down to the purpose behind the trades, which translates itself to the sequence of execution of trades. When done sequentially, the act is defensive hedging. When done simultaneously, it is aggressive arbitrage. On the after-the-fact basis, an observer will only see a long and a short position.

Hedge fund managers and prop traders took the idea and ran with it. Speculative capital, capital engaged in arbitrage, was thus born.

One practical problem remained: how to create a “close to riskless” position? No one understood the significance of this question in theory or the implications of its execution in practice. It was left to hedge fund managers and prop traders and their quantitative underlings to find the answer.

They did.

I will return tomorrow with the second and final part.