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Showing posts with label derivative. Show all posts
Showing posts with label derivative. Show all posts

Wednesday, 13 April 2016

I'm the real-life Gordon Gekko and I support Bernie Sanders

Asher Edelman in The Guardian


The potential for a depression looms on the horizon. The Vermont senator is the only candidate who can stop banks from spiraling out of control again

 
‘Bernie Sanders is the only independent candidate who escapes the malaise of being bought.’ Photograph: Allstar Picture Library

Banking is the least understood, and possibly most lethal, of all the myriad issues at stake in this election. No candidate other than Bernie Sanders is capable of taking the steps necessary to protect the American people from a repeat of the recent debacle that plunged the nation into a recession from which we have not recovered.

The potential for a depression looms heavily on the horizon. As a trained economist who has spent more than 20 years on Wall Street – and one of the models for Gordon Gekko’s character – I know the financial system is in urgent need of regulation and responsibility. Yet Hillary Clinton is beholden to the banks for their largesse in funding her campaign and lining her pockets. The likelihood of any Republican candidate taking on this key issue is not even worthy of discussion.

The recession of 2007-2016, and the persistent transfer of wealth from the 80% to the 1% is, mostly the result of banking irresponsibility precipitated by the repeal of the Glass-Steagall Act in 1999. The law separated commercial banking (responsible for gathering and conservatively lending out funds) from investment banking (more speculative activities).

A new culture emerged that rewarded bankers for return on equity rather than sound lending practices. The wild west of risk-taking, staked on depositors’ money, became the best sport in town. Why not? If management won, they got rich. When they lost, the taxpayer took on the responsibility. If that sounds like a good wager, it was (and is).

The only problem is what happens when the music ends. Debt-to-capital ratios for investment banking functions rose from 12:1 to 30:1. Options on derivatives on other derivatives increased that leverage many fold. Self-regulation became the rule and, lo and behold, in 2008: crash. America and the world were nailed by a fastball from which the bottom 80% of the American population has yet to recover.

Remarkably, today the derivatives positions held by the large banks approach 10 times those of 2007-2008. In four banks alone, they exceed the GDP of the entire world. This is the interesting consequence when unchecked risk management rests in bankers’ hands.

When Clinton repealed Glass-Steagall, it was the culmination of the largest ever lobbying effort by the banking community to that date, $300m spent to convince Congress that Clinton, aided by Robert Rubin (US treasurer, previously with Goldman Sachs) and Alan Greenspan, a Milton Friedman-style supply-side economist, that the restraints on speculation should be removed. The banking community’s gratitude was and is unending. Who can blame them?

Wait, there’s more. After the collapse of 2008, the Federal Reserve invested more than $15tn to save the banks under the guise of monetary stimulation. At the same time, little or no funds were channeled to the needs of the American people. Yet today we face another crisis of liquidity. This time Europe will break first, followed by their highly leveraged US colleagues. Meanwhile, the bottom 80% of Americans remain mired in a recession, having seen no increase in their incomes during the last 20 years.

Poverty is at its highest level since the 1930s (in some areas of the country, higher). More than 30% of all children live with families subsisting below the poverty level. Employment is at a new all-time low (the percentage of employed persons is at about 49%, having been at more than 52% prior to 2008).

The average American is entitled to more. Only Bernie Sanders is committed to honest solutions to these problems. The way to avert the next banking crisis is the most clear. Assuming a Republican Congress, which would prevent the reinstatement of Glass-Steagall, Bernie has only to turn to regulation and responsibility.

Dodd-Frank provides the necessary structure with which to begin. Enforce it. Put teeth into bank regulation. Determine the acceptable level of risk at which banks can operate. Make management, not underlings or stockholders, responsible for violating the law. Encourage the Justice Department to be clear in seeking appropriate penalties for financial crimes in large institutions, not by fines alone but by the prosecution of those executives responsible.
Split up the banks that are speculating with depositor and government funds. Investment banks are supposed to risk investors’ money but commercial banks should return to lending fairly and carefully to help create a foundation for future growth. Bernie Sanders is the only independent candidate who escapes the malaise of being bought. He is paid for by the people and represents their interests. And you can take that to the bank.

Saturday, 28 April 2012

The maths formula linked to the financial crash

Black-Scholes: The maths formula linked to the financial crash



It's not every day that someone writes down an equation that ends up changing the world. But it does happen sometimes, and the world doesn't always change for the better. It has been argued that one formula known as Black-Scholes, along with its descendants, helped to blow up the financial world.
Black-Scholes was first written down in the early 1970s but its story starts earlier than that, in the Dojima Rice Exchange in 17th Century Japan where futures contracts were written for rice traders. A simple futures contract says that I will agree to buy rice from you in one year's time, at a price that we agree right now.

By the 20th Century the Chicago Board of Trade was providing a marketplace for traders to deal not only in futures but in options contracts. An example of an option is a contract where we agree that I can buy rice from you at any time over the next year, at a price that we agree right now - but I don't have to if I don't want to.

You can imagine why this kind of contract might be useful. If I am running a big chain of hamburger restaurants, but I don't know how much beef I'll need to buy next year, and I am nervous that the price of beef might rise, well - all I need is to buy some options on beef.

But then that leads to a very ticklish problem. How much should I be paying for those beef options? What are they worth? And that's where this world-changing equation, the Black-Scholes formula, can help.

"The problem it's trying to solve is to define the value of the right, but not the obligation, to buy a particular asset at a specified price, within or at the end of a specified time period," says Professor Myron Scholes, professor of finance at the Stanford University Graduate School of Business and - of course - co-inventor of the Black-Scholes formula.

The young Scholes was fascinated by finance. As a teenager, he persuaded his mother to set up an account so that he could trade on the stock market. One of the amazing things about Scholes is that throughout his time as an undergraduate and then a doctoral student, he was half-blind. And so, he says, he got very good at listening and at thinking.

When he was 26, an operation largely restored his sight. The next year, he became an assistant professor at MIT, and it was there that he stumbled upon the option-pricing puzzle.

One part of the puzzle was this question of risk: the value of an option to buy beef at a price of - say - $2 (£1.23) a kilogram presumably depends on what the price of beef is, and how the price of beef is moving around.

But the connection between the price of beef and the value of the beef option doesn't vary in a straightforward way - it depends how likely the option is to actually be used. That in turn depends on the option price and the beef price. All the variables seem to be tangled up in an impenetrable way.
Scholes worked on the problem with his colleague, Fischer Black, and figured out that if I own just the right portfolio of beef, plus options to buy and sell beef, I have a delicious and totally risk-free portfolio. Since I already know the price of beef and the price of risk-free assets, by looking at the difference between them I can work out the price of these beef options. That's the basic idea. The details are hugely complicated.

"It might have taken us a year, a year and a half to be able to solve and get the simple Black-Scholes formula," says Scholes. "But we had the actual underlying dynamics way before."

The Black-Scholes method turned out to be a way not only to calculate value of options but all kinds of other financial assets. "We were like kids in a candy story in the sense that we described options everywhere, options were embedded in everything that we did in life," says Scholes.

But Black and Scholes weren't the only kids in the candy store, says Ian Stewart, whose book argues that Black-Scholes was a dangerous invention.

"What the equation did was give everyone the confidence to trade options and very quickly, much more complicated financial options known as derivatives," he says.

Scholes thought his equation would be useful. He didn't expect it to transform the face of finance. But it quickly became obvious that it would.

"About the time we had published this article, that's 1973, simultaneously or approximately a month thereafter, the Chicago Board Options Exchange started to trade call options on 16 stocks," he recalls.
Scholes had just moved to the University of Chicago. He and his colleagues had already been teaching the Black-Scholes formula and methodology to students for several years.

"There were many young traders who either had taken courses at MIT or Chicago in using the option pricing technology. On the other hand, there was a group of traders who had only intuition and previous experience. And in a very short period of time, the intuitive players were essentially eliminated by the more systematic players who had this pricing technology."

That was just the beginning.

"By 2007 the trade in derivatives worldwide was one quadrillion (thousand million million) US dollars - this is 10 times the total production of goods on the planet over its entire history," says Stewart. "OK, we're talking about the totals in a two-way trade, people are buying and people are selling and you're adding it all up as if it doesn't cancel out, but it was a huge trade."

The Black-Scholes formula had passed the market test. But as banks and hedge funds relied more and more on their equations, they became more and more vulnerable to mistakes or over-simplifications in the mathematics.

"The equation is based on the idea that big movements are actually very, very rare. The problem is that real markets have these big changes much more often that this model predicts," says Stewart. "And the other problem is that everyone's following the same mathematical principles, so they're all going to get the same answer."

Now these were known problems. What was not clear was whether the problems were small enough to ignore, or well enough understood to fix. And then in the late 1990s, two remarkable things happened.

"The inventors got the Nobel Prize for Economics," says Stewart. "I would argue they thoroughly deserved to get it."

Fischer Black died young, in 1995. When in 1997 Scholes won the Nobel memorial prize, he shared it not with Black but with Robert Merton, another option-pricing expert.

Scholes' work had inspired a generation of mathematical wizards on Wall Street, and by this stage both he and Merton were players in the world of finance, as partners of a hedge fund called Long-Term Capital Management.

"The whole idea of this company was that it was going to base its trading on mathematical principles such as the Black-Scholes equation. And it actually was amazingly successful to begin with," says Stewart. "It was outperforming the traditional companies quite noticeably and everything looked great."

But it didn't end well. Long-Term Capital Management ran into, among other things, the Russian financial crisis. The firm lost $4bn (£2.5bn) in the course of six weeks. It was bailed out by a consortium of banks which had been assembled by the Federal Reserve. And - at the time - it was a very big story indeed. This was all happening in August and September of 1998, less than a year after Scholes had been awarded his Nobel prize.

Stewart says the lessons from Long-Term Capital Management were obvious. "It showed the danger of this kind of algorithmically-based trading if you don't keep an eye on some of the indicators that the more conventional people would use," he says. "They [Long-Term Capital Management] were committed, pretty much, to just ploughing ahead with the system they had. And it went wrong."

Scholes says that's not what happened at all. "It had nothing to do with equations and nothing to do with models," he says. "I was not running the firm, let me be very clear about that. There was not an ability to withstand the shock that occurred in the market in the summer and fall of late 1998. So it was just a matter of risk-taking. It wasn't a matter of modelling."

This is something people were still arguing about a decade later. Was the collapse of Long-Term Capital Management an indictment of mathematical approaches to finance or, as Scholes says, was it simply a case of traders taking too much risk against the better judgement of the mathematical experts?

Ten years after the Long-Term Capital Management bail-out, Lehman Brothers collapsed. And the debate over Black-Scholes and LTCM is now a broader debate over the role of mathematical equations in finance.

Ian Stewart claims that the Black-Scholes equation changed the world. Does he really believe that mathematics caused the financial crisis?

"It was abuse of their equation that caused trouble, and I don't think you can blame the inventors of an equation if somebody else comes along and uses it badly," he says.

"And it wasn't just that equation. It was a whole generation of other mathematical models and all sorts of other techniques that followed on its heels. But it was one of the major discoveries that opened the door to all this."

Black-Scholes changed the culture of Wall Street, from a place where people traded based on common sense, experience and intuition, to a place where the computer said yes or no.

But is it really fair to blame Black-Scholes for what followed it? "The Black-Scholes technology has very specific rules and requirements," says Scholes. "That technology attracted or caused investment banks to hire people who had quantitative or mathematical skills. I accept that. They then developed products or technologies of their own."

Not all of those subsequent technologies, says Scholes, were good enough. "[Some] had assumptions that were wrong, or they used data incorrectly to calibrate their models, or people who used [the] models didn't know how to use them."

Scholes argues there is no going back. "The fundamental issue is that quantitative technologies in finance will survive, and will grow, and will continue to evolve over time," he says.

But for Ian Stewart, the story of Black-Scholes - and of Long-Term Capital Management - is a kind of morality tale. "It's very tempting to see the financial crisis and various things which led up to it as sort of the classic Greek tragedy of hubris begets nemesis," he says.

"You try to fly, you fly too close to the sun, the wax holding your wings on melts and you fall down to the ground. My personal view is that it's not just tempting to do that but there is actually a certain amount of truth in that way of thinking. I think the bankers' hubris did indeed beget nemesis. But the big problem is that it wasn't the bankers on whom the nemesis descended - it was the rest of us."

Additional reporting by Richard Knight

Thursday, 23 February 2012

It's time to start talking to the City


A radical reform of the financial sector can only be achieved if we know what kind of capitalism we want

Last week I delivered a lecture on my latest book to about 150 people from the financial industry at the London Stock Exchange. The event was not organised or endorsed by the LSE itself, but the venue was quite poignant for me, given that a few months ago I did the same thing on the other side of the barricade, so to speak, at the Occupy London Stock Exchange movement.

At the exchange I made two proposals I knew may not be popular with the audience. My first was that we need to completely change the way we run our corporations, especially in the UK and the US. I started from the observation that financial deregulation since the 1980s has greatly increased the power of shareholders by expanding the options open to them, both geographically and in terms of product choice. Such deregulation was particularly advanced in Britain and America, making them the homes of "shareholder capitalism".

With greater abilities to move around, shareholders have begun to adopt increasingly short time horizons. As Prem Sikka wrote in the Guardian in December 2011, the average shareholding period in UK firms fell from about five years in the mid-1960s to 7.5 months in 2007. The figure for UK banks had fallen to three months by 2008 (although it is up to about two years now).
In order to satisfy impatient shareholders, managers have maximised short-term profits by squeezing other "stakeholders", such as workers and suppliers, and by minimising investments, whose costs are immediate but whose returns are remote. Such strategy does long-term damages by demoralising workers, lowering supplier qualities, and making equipment outmoded. But the managers do not care because their pay is linked to short-term equity prices, whose maximisation is what short term-oriented shareholders want.

That is not all. An increasing proportion of profits are distributed to shareholders through dividends and share buybacks (firms buying their own shares to prop up their prices). According to William Lazonick – a leading authority on this issue – between 2001 and 2010, top UK firms (86 companies that are included in the S&P Europe 350 index) distributed 88% of their profits to shareholders in dividends (62%) and share buybacks (26%).

During the same period, top US companies (459 of those in the S&P 500) paid out an even greater proportion to shareholders: 94% (40% in dividends and 54% in buybacks). The figure used to be just over 50% in the early 80s (about 50% in dividends and less than 5% in buybacks).

The resulting depletion in retained profit, traditionally the biggest source of corporate investments, has dramatically undermined these corporations' abilities to invest, further weakening their long-term competitiveness. Therefore, I concluded, unless we significantly restrict the freedom of movement for shareholders, through financial reregulation, and reward managers according to more long term-oriented performance measures than share prices, companies will continue to be managed in a way that undermines their own viability and weakens the national economy in the long run.

My second proposal was that, in order to improve the stability of our financial system, we need to radically simplify it. I argued that financial deregulation in the last 30 years led to the proliferation of complex financial derivatives. This has created a financial system whose complexity has far outstripped our ability to control it, as dramatically demonstrated by the 2008 financial crisis.
Drawing on the works of Herbert Simon, the 1978 Nobel economics laureate and a founding father of the study of artificial intelligence, I pointed out that often the crucial constraint on good decision-making is not the lack of information but our limited mental capability, or what Simon called "bounded rationality". Given our bounded rationality, I asserted, the only way to increase the stability of our financial system is to make it simpler. And the most important action to take is to restrict, or even ban, complex and risky financial instruments through the financial world equivalent of the drugs approval procedure.

The reactions of my audience were rather surprising. Not only did nobody challenge my proposals, but many agreed with me. Yes, they said, "quarterly capitalism" has been destructive. True, they related, we've seen too many derivative products that few people understood. And, yes, many of those products have been socially harmful.

It seems that, as it is wrong to label the Occupy movement as anti-capitalist, it is misleading to characterise the financial industry as being in denial about the need for reform. I am not naive enough to think that the people who came to my lecture are typical of the financial industry. However, a surprisingly large number of them acknowledged the problems of short-termism and excessive complexity that their industry has generated to the detriment of the rest of the economy – and ultimately to its own detriment, as the financial industry cannot thrive alone.

The rest of us need to have a closer dialogue with reform-minded people in the financial industry. They are the ones who can generate greater political acceptance of reforms among their colleagues and who can also help us devise technically competent reform proposals. After all, without a degree of "changes from within", no reform can be truly durable.

Sunday, 12 February 2012

The mathematical equation that caused the banks to crash

 Ian Stewart in The Observer 21-02-12

It was the holy grail of investors. The Black-Scholes equation, brainchild of economists Fischer Black and Myron Scholes, provided a rational way to price a financial contract when it still had time to run. It was like buying or selling a bet on a horse, halfway through the race. It opened up a new world of ever more complex investments, blossoming into a gigantic global industry. But when the sub-prime mortgage market turned sour, the darling of the financial markets became the Black Hole equation, sucking money out of the universe in an unending stream.

Anyone who has followed the crisis will understand that the real economy of businesses and commodities is being upstaged by complicated financial instruments known as derivatives. These are not money or goods. They are investments in investments, bets about bets. Derivatives created a booming global economy, but they also led to turbulent markets, the credit crunch, the near collapse of the banking system and the economic slump. And it was the Black-Scholes equation that opened up the world of derivatives.

The equation itself wasn't the real problem. It was useful, it was precise, and its limitations were clearly stated. It provided an industry-standard method to assess the likely value of a financial derivative. So derivatives could be traded before they matured. The formula was fine if you used it sensibly and abandoned it when market conditions weren't appropriate. The trouble was its potential for abuse. It allowed derivatives to become commodities that could be traded in their own right. The financial sector called it the Midas Formula and saw it as a recipe for making everything turn to gold. But the markets forgot how the story of King Midas ended.

Black-Scholes underpinned massive economic growth. By 2007, the international financial system was trading derivatives valued at one quadrillion dollars per year. This is 10 times the total worth, adjusted for inflation, of all products made by the world's manufacturing industries over the last century. The downside was the invention of ever-more complex financial instruments whose value and risk were increasingly opaque. So companies hired mathematically talented analysts to develop similar formulas, telling them how much those new instruments were worth and how risky they were. Then, disastrously, they forgot to ask how reliable the answers would be if market conditions changed.

Black and Scholes invented their equation in 1973; Robert Merton supplied extra justification soon after. It applies to the simplest and oldest derivatives: options. There are two main kinds. A put option gives its buyer the right to sell a commodity at a specified time for an agreed price. A call option is similar, but it confers the right to buy instead of sell. The equation provides a systematic way to calculate the value of an option before it matures. Then the option can be sold at any time. The equation was so effective that it won Merton and Scholes the 1997 Nobel prize in economics. (Black had died by then, so he was ineligible.)

If everyone knows the correct value of a derivative and they all agree, how can anyone make money? The formula requires the user to estimate several numerical quantities. But the main way to make money on derivatives is to win your bet – to buy a derivative that can later be sold at a higher price, or matures with a higher value than predicted. The winners get their profit from the losers. In any given year, between 75% and 90% of all options traders lose money. The world's banks lost hundreds of billions when the sub-prime mortgage bubble burst. In the ensuing panic, taxpayers were forced to pick up the bill, but that was politics, not mathematical economics.

The Black-Scholes equation relates the recommended price of the option to four other quantities. Three can be measured directly: time, the price of the asset upon which the option is secured and the risk-free interest rate. This is the theoretical interest that could be earned by an investment with zero risk, such as government bonds. The fourth quantity is the volatility of the asset. This is a measure of how erratically its market value changes. The equation assumes that the asset's volatility remains the same for the lifetime of the option, which need not be correct. Volatility can be estimated by statistical analysis of price movements but it can't be measured in a precise, foolproof way, and estimates may not match reality.

The idea behind many financial models goes back to Louis Bachelier in 1900, who suggested that fluctuations of the stock market can be modelled by a random process known as Brownian motion. At each instant, the price of a stock either increases or decreases, and the model assumes fixed probabilities for these events. They may be equally likely, or one may be more probable than the other. It's like someone standing on a street and repeatedly tossing a coin to decide whether to move a small step forwards or backwards, so they zigzag back and forth erratically. Their position corresponds to the price of the stock, moving up or down at random. The most important statistical features of Brownian motion are its mean and its standard deviation. The mean is the short-term average price, which typically drifts in a specific direction, up or down depending on where the market thinks the stock is going. The standard deviation can be thought of as the average amount by which the price differs from the mean, calculated using a standard statistical formula. For stock prices this is called volatility, and it measures how erratically the price fluctuates. On a graph of price against time, volatility corresponds to how jagged the zigzag movements look.

Black-Scholes implements Bachelier's vision. It does not give the value of the option (the price at which it should be sold or bought) directly. It is what mathematicians call a partial differential equation, expressing the rate of change of the price in terms of the rates at which various other quantities are changing. Fortunately, the equation can be solved to provide a specific formula for the value of a put option, with a similar formula for call options.

The early success of Black-Scholes encouraged the financial sector to develop a host of related equations aimed at different financial instruments. Conventional banks could use these equations to justify loans and trades and assess the likely profits, always keeping an eye open for potential trouble. But less conventional businesses weren't so cautious. Soon, the banks followed them into increasingly speculative ventures.

Any mathematical model of reality relies on simplifications and assumptions. The Black-Scholes equation was based on arbitrage pricing theory, in which both drift and volatility are constant. This assumption is common in financial theory, but it is often false for real markets. The equation also assumes that there are no transaction costs, no limits on short-selling and that money can always be lent and borrowed at a known, fixed, risk-free interest rate. Again, reality is often very different.
When these assumptions are valid, risk is usually low, because large stock market fluctuations should be extremely rare. But on 19 October 1987, Black Monday, the world's stock markets lost more than 20% of their value within a few hours. An event this extreme is virtually impossible under the model's assumptions. In his bestseller The Black Swan, Nassim Nicholas Taleb, an expert in mathematical finance, calls extreme events of this kind black swans. In ancient times, all known swans were white and "black swan" was widely used in the same way we now refer to a flying pig. But in 1697, the Dutch explorer Willem de Vlamingh found masses of black swans on what became known as the Swan River in Australia. So the phrase now refers to an assumption that appears to be grounded in fact, but might at any moment turn out to be wildly mistaken.

Large fluctuations in the stock market are far more common than Brownian motion predicts. The reason is unrealistic assumptions – ignoring potential black swans. But usually the model performed very well, so as time passed and confidence grew, many bankers and traders forgot the model had limitations. They used the equation as a kind of talisman, a bit of mathematical magic to protect them against criticism if anything went wrong.

Banks, hedge funds, and other speculators were soon trading complicated derivatives such as credit default swaps – likened to insuring your neighbour's house against fire – in eye-watering quantities. They were priced and considered to be assets in their own right. That meant they could be used as security for other purchases. As everything got more complicated, the models used to assess value and risk deviated ever further from reality. Somewhere underneath it all was real property, and the markets assumed that property values would keep rising for ever, making these investments risk-free.
The Black-Scholes equation has its roots in mathematical physics, where quantities are infinitely divisible, time flows continuously and variables change smoothly. Such models may not be appropriate to the world of finance. Traditional mathematical economics doesn't always match reality, either, and when it fails, it fails badly. Physicists, mathematicians and economists are therefore looking for better models.

At the forefront of these efforts is complexity science, a new branch of mathematics that models the market as a collection of individuals interacting according to specified rules. These models reveal the damaging effects of the herd instinct: market traders copy other market traders. Virtually every financial crisis in the last century has been pushed over the edge by the herd instinct. It makes everything go belly-up at the same time. If engineers took that attitude, and one bridge in the world fell down, so would all the others.

By studying ecological systems, it can be shown that instability is common in economic models, mainly because of the poor design of the financial system. The facility to transfer billions at the click of a mouse may allow ever-quicker profits, but it also makes shocks propagate faster.

Was an equation to blame for the financial crash, then? Yes and no. Black-Scholes may have contributed to the crash, but only because it was abused. In any case, the equation was just one ingredient in a rich stew of financial irresponsibility, political ineptitude, perverse incentives and lax regulation.

Despite its supposed expertise, the financial sector performs no better than random guesswork. The stock market has spent 20 years going nowhere. The system is too complex to be run on error-strewn hunches and gut feelings, but current mathematical models don't represent reality adequately. The entire system is poorly understood and dangerously unstable. The world economy desperately needs a radical overhaul and that requires more mathematics, not less. It may be rocket science, but magic it's not.
Ian Stewart is emeritus professor of mathematics at the University of Warwick.