Just because something has value doesn't mean it has a price

If every last shred of incidental online value is given a price tag, we'll never harvest the full fruits of our ingenuity

• 
• • Cory Doctorow
  • guardian.co.uk, Tuesday 8 January 2013 11.01 GMT

Google is a case-study in harvesting positive externalities. Photograph: Britta Pedersen/EPA

 

When future economists look back on the dawn of the internet era, they will marvel that an age of such technological marvel was attended by a widespread, infantile mania for preventing positive externalities.

"Externalities" are the economist's catchall term for the spillover effects experienced by the people who are affected by others' activities. Most of the 20th century was spent locked in battle with the corporate vice of externalising negative costs. Companies are beholden to their shareholders, and so they are meant to save every penny they can, even when saving that penny might cost the rest of society several pounds. The classic example is toxic waste: processing industrial waste before it leaves the factory is a costly proposition, and so, whenever it is possible to do so, companies have defaulted to dumping their waste into the wider world. This is a much cheaper option — for the company.

For the world, it's vastly more costly. After all, when the offensive sludge is all neatly gathered at the effluent pipe's head-end, it is concentrated and handy, and can be gathered and fed into whatever decontamination or sequestration system is appropriate.

But once the sludge has exited the pipe and is out in the world, it has to be gathered up before it can be dealt with. Contaminated coolant can be sealed in barrels at the factory and sent for secure burial. Once it's dumped in a stream, you have to figure out how to get it out of the stream before you can clean it up – this is notoriously difficult.

What's more, streams feed into rivers, and rivers into oceans, and people drink from them and swim in them and eat the animals that swim in them and rely on them. What started as a waste-containment problem has become a public health emergency and an environmental catastrophe – the company's savings are the world's loss.

So policy wonks have spent a century thinking about creating the carrots and sticks necessary to minimise this externalising behaviour. The idea is to work out a system of fines and punishments that make it economically irrational to dump sludge, because the savings from doing so are offset by the penalties for getting caught. Getting this number right is notoriously hard, because you have to factor in some kind of multiplier of the penalty that accounts for the discount that rational – albeit psychopathically immoral – companies will apply based on the likelihood that they will not get caught.

Virtuous circles

But what about positive externalities? Historically, these have been a lot less contentious, and it's easy to see why. A positive externality arises when you do something you want to do that also makes life better for someone else. For example, if you drive your car slowly and carefully to avoid a wreck, a positive externality is that other users of the road have a safer time of it, too. If you keep up your front garden because it pleases you, your neighbours get the positive externality of slightly buoyed-up property values from living on a nicely kept street.

Positive externalities — virtuous cycles — are all around us. Your kid learns to speak because of all the people around her who carry on conversations and because of the TV shows and radio programmes where speaking occurs (as do immigrants like my grandmother, whose English fluency owes much to daytime TV after she came to Canada from Russia).

My flat – on the top floor, above a commercial building – gets some of the rising heat from the building below, capturing our downstairs neighbour's exhaust heat (on the other hand, we provide a positive externality to them by insulating their roof with our home).

The net is the natural home of positive externalities. Start with the "network effect" – the way that adding people to the network creates more value for existing users of the network (one fax machine is useless, two fax machines are slightly useful, a billion fax machines are indispensable, at least, until the web makes them obsolete). Every website that came along increased the likelihood that new users would find some reason to join the internet. Every new user that came along increased the likelihood that someone would make a website that tried to reach that user.

This is a kind of anti-entropic magic trick, using the exhaust from one process to create fuel for the next one. The most famous example is Google's PageRank algorithm, which began when the company's founders realised that every time a web creator added a link from one site to another, there was a kind of implied vote for the linked-to site – when I link to you, I'm implicitly saying that you have something I think others should see. This citation analysis (a common practice in academia, where journals who are widely cited are considered more valuable than less-cited journals; and where journal-articles that are more widely cited are considered more valuable as well) was wildly successful, and it showed that there was, latent on the web, an invisible mesh of authority that could be made visible with the right kind of analysis.

Google is a case-study in harvesting positive externalities. It offered a free, voice-based directory assistance number, and used the interactions users had with its software to build a corpus of common phrases, expressed in multiple accents and under a wide range of field conditions. Then it used this to train the voice-recognition software that powers its Android-based phone-search. Likewise, it mined all the publicly available translations on the web – EU documents that appeared in multiple languages, fan-based translations for subtitles on cult cartoons, and everything else it could find – and used this to train its automated translation engine, providing it with the context that it needed to figure out the nuance and sense of ambiguous phrases.

There are other companies that do well by harvesting these positive externalities. Facebook provides its users with a handy platform for socialising, and then – notoriously – mines their social graph to figure out how to sell things to them.

However, there's a wide difference between the two companies: much of Google's business revolves around capturing externalities from things you were going to make anyway. In many cases, the resources Google mines are public and remain in place even after Google's finished with them (for example, anyone can index the web and do the same citation analysis as Google).

Both Facebook and Google also try to entice the world into activities that generate externalities. Facebook is a giant behaviourist experiment designed to tempt you into systematically undervaluing your privacy, and it uses game-like mechanics to extract more personal data and more social-graph enumeration from its users. Google's a little less obvious about its enticements, but clearly, offering services such as YouTube and Blogger are mostly about figuring out how to earn money from the exhaust-stream from individual and corporate creativity. Facebook, and to a lesser extent, Google, try to claim ownership over your externalities by locking them up in proprietary walled gardens.

Taking a cut

But back to our era's defining mania: resentment over positive externalities. Many people and companies have concluded that if someone, somewhere, is getting value from their labour, that they should get a cut of that value. Irish newspapers are paying solicitors to demand money from websites that link to them, on the grounds that a website is improved if it contains a reference to the news, and that improvement needs to be paid for. Many people have accused Google of "ripping off" the public by indexing content, or analysing it, or both. Jaron Lanier recently accused Google of misappropriating translators' labour by using online translated documents as a training set for its machine-translation engine – an extreme version of many labour-oriented critiques of online business.

And take DRM – digital rights management – which is used to restrict the way you use the media you buy, such as ebooks, videos, and games.

DRM systems have been deployed to stop people from selling used games, to stop them lending their ebooks, to stop them from taking DVDs from one country to another. This is pure positive-externality resentment.

The reasoning for DRM goes like this: "I sold you this [ebook/game/video] for the following uses. If you figure out a way to get any more value out of it, it belongs to me, and you can't have it, until and unless I decide to sell it to you."

In the pre-digital world, this would have been laughable. "I sold you that book: if you want to use it to keep the table from wobbling, you'll have to pay me extra." Or: "I sold you that game to play in your house. How dare you bring it on holiday with you?! You owe me!" Or: "That TV was sold to you for the purposes of watching programmes, not to be used as a white-noise machine to lull your newborn to sleep, and certainly not to support a pile of knick-knacks!"

Of course, removing positive externalities also removes value. Cars are worth more because of the used-car market. University textbooks command a higher price because of the market for used textbooks. If either sector managed to kill those externalities, it would be selling goods that its customers valued less (and would likely find that they demanded lower prices for them, too).

I was at a TV DRM meeting once where a representative from the US-led Motion Picture Association proposed that broadcasters should be able to selectively block the use of wireless retransmitters – the sort of thing that lets you have a receiver in the sitting-room that fed a TV set in your bedroom – because "watching TV in a room other than the one the show is being received in has value, and if it has value, we need to be able to charge money for it".

That's the crux of this irrational fear of positive externalities: "If something I do has value, I deserve a cut." It's one thing to say that someone who hires you to do a job, or purchases your product, should pay you money. But positive externalities are the waste-product of something we were already going to do. They're things that you have thrown away, that you have thrown off, that you have generated in the process of enjoying yourself and living your life.

The mania to internalise your positive externalities is the essence of cutting off your nose to spite your face. I walk down the street whistling a jaunty tune because I'm in a good mood — but stop as soon as I see someone smiling and enjoying the music. I keep my porchlight on to read by on a warm night, but if I catch you using the light to read your map, I switch it off, because those are my photons — I paid for 'em!

Worse still: the infectious idea of internalising externalities turns its victims into grasping, would-be rentiers. You translate a document because you need it in two languages. I come along and use those translations to teach a computer something about context. You tell me I owe you a slice of all the revenue my software generates. That's just crazy. It's like saying that someone who figures out how to recycle the rubbish you set out at the kerb should give you a piece of their earnings. Harvesting positive externalities involves collecting billions of minute shreds of residual value – snippets of discarded string –and balling them up into something big and useful.

If every shred needs to be accounted for and paid for, then the harvest won't happen. Paying for every link you make, or every link you count, or every document you analyse is a losing game. Forget payment: the process of figuring out who to pay and how much is owed would totally swamp the expected return from whatever it is you're planning on making out of all those unloved scraps.

In other words, if all latent value from our activity has a price-tag attached to it, it won't get us all paid – instead, it will just stop other people from making cool, useful, interesting and valuable things out of our waste-product.

It's not just about the results

More important than the numbers you chalk up as a player is gaining personal mastery of yourself - as a cricketer and a person

Paddy Upton

September 25, 2012

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	Gary Kirsten: "When the heat is on in Test cricket, it's not your skill but your character that is being tested" © PA Photos  Enlarge
Related Links Players/Officials: Hashim Amla | Gary Kirsten | Sachin Tendulkar Teams: South Africa

As cricket advances into the entertainment industry, so the celebrity limelight shines more brightly on the players. Cricketers today enjoy more money, more glamour, more exposure than ever before. It's fun, the party is on, but are they sufficiently prepared for the hangovers that lurks in the shadows?

These come in many forms and manifest themselves in the form of scuffles in nightclubs, drink driving, sexual indiscretions, drug abuse, cheating and match-fixing - sometimes driven by a celebrity's sense of being above the law, invincible, and sometimes even immortal.

Cricket stars are easily seduced into defining themselves, their self-confidence and their happiness, by their name, fame, money and the results they produce: happy when they do well in these regards, grumpy and anti-social when not. A darker shadow of the limelight is where players buy into the image of fame (of being a special person) that fans and the media create for them. As they do this, they become more alienated from themselves, losing touch of who they authentically are. They begin to see themselves as superior to ordinary mortals, not only better at the skill that made them famous but also better and more important as people. They struggle to be alone, uncomfortable in their own company. Yet while surrounding themselves with others, they become incapable of genuine relationships.

A loneliness and creeping discontentment begins to shroud the star. This inner emptiness drives the celebrity to wear their "happy", "tough" or "I'm okay" masks while looking to find temporary happiness out there, in more success, fame, money, sex, drink or drugs.

Cricket has plenty of known instances of depression and substance abuse, one of the highest suicide rates of all sports, and a divorce rate to match.

It's about who you are, not what you do
There is another road, less-travelled by superstars, which leads out of the shadows of the limelight and into the light of personal and professional success, sincere relationships, lasting contentment and an all-round fulfilling life.

Speaking to me in 2004, Gary Kirsten said: "I'm searching for the authentic Gary Kirsten - someone who is accepting of his shortcomings and is confident in the knowledge of who he is. One who is willing to have a positive influence and add value to society in my own unique way. I want to make a difference to people's lives and give them similar opportunities that I have had. My perception of success is not about how much money I can earn in the next ten years but rather what impact I made on people I came into contact with."

Gary spent thousands of hours mastering his strokeplay, which had brought him great success and recognition. To this pursuit of professional mastery, he added personal mastery. He often says that when the heat is on in Test cricket, it's not your skill but your character that is being tested.

In life as in cricket, it's who you are inside, your character and your values, rather than what you do, what results you achieve or possessions you gain, that will determine your contentment, enduring success and how you will ultimately be remembered.

Personal mastery is many things. It is a journey towards living successfully as an all-round human being, a tapping into your full potential. It is a commitment to learning about yourself, your mind and emotions in all situations. It is a strengthening of character and deepening of personal values. It is an increased awareness of self, others and the world around; living from the inside out, not the outside in. Peter Senge, one of the authors of the concept of personal mastery, defines it as "the discipline of personal growth and learning".

This idea may already sound too touchy-feely for the John Rambos and Chuck Norrises out there, but before dismissing the concept, know it translated to Kirsten's most successful international season, that it underpins Hashim Amla's remarkable performances, and grounds Sachin Tendulkar's extraordinary fame.

Conversely, the lack of personal mastery has undermined the personal and professional lives of many celebrities. Have you heard about the guy who was a brilliant batsman but whose peers think he is an idiot, and who after retirement had no mates? Or the one who had great talent and opportunity but never managed to deliver? We will never know the truth about all the cricket failures that may seem to have been caused by technical errors but which were actually caused by a lack in character or strength of mind, causing the player to repeatedly succumb to the fear of failure and how it would reflect on them. We all know how the likes of Hansie Cronje, Mike Tyson, Ben Johnson, Mohammad Azharuddin, Diego Maradona and Tiger Woods might be remembered.

The road to personal mastery

Personal mastery is a shift in attitude that drives a shift in behaviour.

From over-emphasising results to placing importance on the processes that set up the best chance of success; from defining one's contentment by results, to deriving contentment from the effort made in the pursuit of that result.

From worrying about what others think about you, to knowing that what others think about you is none of your business. There are people who don't like Nelson Mandela, Mahatma Gandhi or Mother Teresa, so what makes you so special that everyone should like you?

From focusing on the importance of looking good outwardly, to the importance of inner substance and strength of character. It is not about trying to be a good person but allowing the good person in you to emerge;

Personal mastery is a shift from thinking you have the answers, to knowing you have much to learn. From balancing talking and telling with listening and asking. People who think they're "important" seldom ask questions;

It is a shift from pretending to be strong and in control, and from covering up ignorance, faults and vulnerabilities, to acknowledging these human fallibilities while still remaining self-confident. The current South Africa team now openly acknowledges that they have choked in big tournaments in the past, and they're not choked up by this acknowledgement;

When things go wrong, personal mastery is a shift from pointing fingers and blaming others, to taking responsibility. It is first asking "What was my part in this?" before looking elsewhere. It's a shift from being reactive, to being proactive; from withdrawing or getting pissed off by criticism, to accepting that it's one of the few things that helps us grow.

It is about developing social, emotional and spiritual intelligence, in addition to building muscle and sporting intelligence - in the way that Kirsten added the journey of personal mastery to that of professional mastery.

It is a shift from an attitude of expecting things to come to you, to earning your dues through your own effort; and then being grateful for what does come.

It's a shift from focusing on yourself, to gaining awareness of what is going on for others and the world around you. Not everyone is naturally compassionate, but everyone can be aware.

	When things go wrong, personal mastery is a shift from pointing fingers and blaming others, to taking responsibility. It is first asking "What was my part in this?" before looking elsewhere

Personal mastery is a shift from expecting to be told what to do, to taking responsibility for doing what needs to be done. A shift towards becoming your own best teacher as you learn more deeply about your game, your mind and your life, in a way that works best for you. Kirsten insists that players make decisions for themelves, that bowlers set their own fields, and batters take responsibility for their game plans, decisions and executions. Off the field there are no rules to govern behaviour, no curfews, no eating do's and dont's, and no fines system. Players are asked to take responsibility for making good decisions for themselves, at least most of the time.

Personal mastery is about pursuing success rather than trying to avoid failure. It is an acceptance that failure paves the path towards learning and success. It's important in this regard that leaders are okay with their players' mistakes. Almost every sports coach I have watched display visible signs of disappointment when a player makes a mistake. I wonder if these same coaches tell their players to go and fully express themselves? If they do, then their words and their actions do not line up - and their reactions speaks more loudly than their words. Show me a coach who reacts negatively to mistakes, and I will show you a team that plays with a fear of failure.

It is about knowing and playing to your strengths, rather than dwelling on your weaknesses, knowing that developing strengths builds success far more effectively than fixing weaknesses does. If you're a good listener, it's about being even better, for instance.

It requires an awareness of how you conduct yourself in relation to basic human principles, such as integrity, honesty, humility, respect and doing what is best for all. It means having an awareness of and deliberately living personal values as one goes about one's business. It's about knowing how one day you want to be remembered as a person - and then living that way today.

When you, as a top athlete, do well, it's about receiving the praise fully, and expressing gratitude in equal proportion, knowing that no athlete achieves success without the unseen heroes that support them. Praise plus gratitude equals humility. One only need listen to Amla receiving a Man-of-the-Match award to witness humility.

Personal mastery is a path that leads through all of life, bringing improved performances on the field and a more contented and rewarding life off of it. It's a journey out of the shadows of the ego and into the light of awareness; it's a daily commitment, not a destination. It may not be for John Rambo or Chuck Norris, but it works for most.

The bonus is that while personal mastery leads to a happier and more rewarding existence, it also leads to better sport performance. Kirsten adds: "I spent years fighting a mental battle with my pereived lack of skill. Towards the end of my career I dropped this, as well trying to live up to others expectations. I went on to score five Test centuries and have my best year ever. As a coach, I now know that managing myself and others well, being aware of who I am being and why I do things, is of far more importance than technical knowledge of the game."

Another fairly successful and likeable international cricketer who knows the importance of personal mastery states: "Who I am as a person, my nature, is permanent. My results on the field are temporary - they will go up and go down. It is more important that I am consistent as a person. This I can control, my results I cannot." He adds that "people will criticise me for my results, and will soon forget them, but they will always remember the impact I have on them as a person. This will last forever." His name is Sachin Tendulkar.

Paddy Upton is South Africa's performance director.

The maths formula linked to the financial crash

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

By Tim Harford BBC Radio 4, More or Less
 

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

Billions wiped off Europe's biggest companies as political rebellion rocks eurozone

More than £122.3bn was wiped off the value of Europe's biggest companies on Monday amid fears that the eurozone's commitment to austerity was being swept away by political rebellion - just as its debts hit record levels.

Image 1 of 3

Stockmarkets plunged as traders panicked that Angela Merkel could lose her key allies in France and the Netherlands Photo: AP

By Louise Armitstead

10:20PM BST 23 Apr 2012

139 Comments

 

Stockmarkets plunged as traders panicked that Angela Merkel could lose her key allies in France and the Netherlands and that the debt crisis rescue plans could unravel.

The Dutch prime minister Mark Rutte, who is one of the eurozone's "hardliners" on fiscal discipline, dramatically quit in the wake of his coalition's refusal to accept Europe's debt pact. Snap elections could be called as early as June.

Traders were also rattled by Francois Hollande's victory over Nicolas Sarkozy in the first round of the French presidential election. The socialist Mr Hollande has vowed to renegotiate the fiscal pact that including a 3pc of GDP deficit limit.

The political concerns were compounded by data that showed eurozone debt has hit 87.2pc of GDP - the highest level since the launch of the single currency in 1999. Eurostat said that the 17 eurozone members had reduced their deficits from 6.2pc of GDP in 2010 to 4.1pc in 2011 - but overall debt levels had risen by 1.9pc.

Spain, meanwhile, officially sank back into recession as the economy shrank 0.4pc in the first quarter of the year, and German manufacturing shrank at its fastest rate for three years in March. The French composite PMI also fell, according to Markit.

By the end of the day, the Stoxx Europe 600 index has sunk 2.3pc to its lowest level for three months. The German Dax dropped 3.4pc, while France's CAC and Spain's Ibex were down 2.8pc each. In London, the FTSE 100 closed down 1.9pc. In the US, the Dow closed down 0.8pc, the S&P 500 lost 0.8pc and the Nasdaq shed 1pc.

Borrowing costs for the core "sinner states" of Spain and Italy rose back towards "unsustainable" levels. French borrowing costs also rose, widening the spread between oats and German bunds to a record 146.9 basis points. The euro fell almost 1pc against the dollar.

The ECB's bond-buying programme went unused for the sixth week in a row last week, the central bank said. But Brussels moved to reassure markets that the fiscal pact, which Ms Merkel said would "last forever", was still intact.

The European Commission said the pact was signed by states, not governments. "Governments change but commitments on behalf of states cannot be changed without discussion with European partners," said the Commission.

The Dutch finance minister, Jans Kees de Jager, insisted his country would stand by its austerity plans. "The Netherlands will retain its solid fiscal policy and will also show the market it will lower its deficit and also have a path of sustainable government finances," he said.

Libertarianism and the Leap of Faith – The Origins of a Political Cult

By Philip Pilkington, a journalist and writer living in Dublin, Ireland

You wanted God’s ideas about what was best for you to coincide with your ideas, but you also wanted him to be the almighty Creator of heaven and earth so that he could properly fulfil your wish. And yet, if he were to share your ideas, he would cease to be the almighty Father.

– Søren Kierkegaard

Political cults often have the strangest and most obscure origins. Take Marxism, for example. Today it is well-known that Marxist doctrine essentially sprang out of the obscure 19th century economic debates over the source of ‘value’. By ‘proving’ – that is, lifting the assumption from classical political economy – that all ‘value’ came from labour, Karl Marx went on to show that it was therefore only logical to assume the existence of something called ‘surplus value’ that was sucked out of labourers by a parasitic capitalist class. From out of this obscure debate flowed an awesome political movement – and a tyranny to match.

What is less well-known is that today’s most popular political cult – that is, libertarianism – was born in very similar circumstances; it too, arrived into the world out of the obscure 19th century debates over economic ‘value’. But before we explore this in any detail it might be appropriate to speculate a little on what characterises a political cult and why so many of these find their sustenance in economic theories of value.

What is a Political Cult and Why Do they Often Love Economic Value Theory?

A political cult is characterised by a political or economic doctrine that answers all the ‘big questions’ about life, the world and everything else. The doctrine that is handed down is then to be conceived of as a way to live one’s life – a project, handed down from Mount Sinai, that one is under the moral obligation to spread far and wide. This is why we refer to these movements as cults. And it is this that gives them such an awesome status in the glazed eyes of their devotees.

Under such circumstances, politics becomes a sort of religious calling. In these doctrines there is usually an ‘Evil Being’ who is opposing the spread of the ‘Good’ on earth and it is these that are to blame for all the bad things in the world. In Marxism this Evil Being is the capitalist; in libertarianism it is the figure who is at different times referred to as the ‘collectivist’, the ‘liberal’ or the ‘socialist’. Needless to say that, since these figures are usually ones of Extreme Evil they must be ‘liquidated’ or ‘eliminated’ at the first possible opportunity lest they spread their Demonic Gospel to the masses.

Political cults thus provide their devotees with a firm identity in an otherwise changeable and, let us be frank, confusing world. Like all cults they provide an anchor for their devotees with which they can fasten themselves to a rigid doctrine. They also typically lend their devotees a Holier-Than-Thou attitude as they provide them with ‘secrets’ that those outside of the cult cannot grasp. Not only does this allow the devotees to feel ‘special’, in modern political cults it also gives them practical, albeit ‘secret’ advice about what they should do in their day-to-day lives. (Think of the advice to buy gold or foreign stocks coming out of certain libertarian front men, for example).

Finally, the political cult will usually offer their followers the possibility of a Heaven on Earth. If the follower behaves well and spreads their beliefs to others they will eventually arrive at some sort of Utopia. This is their reward for believing in the doctrines, despite these doctrines being ridiculed by others.

So, why do these cults spring out of economic doctrines based on value? Well, this is a very complex question but there is one key aspect that is absolutely fundamental. In order to understand it a little better we must think for a moment about what economic ‘value’ supposedly is. It is, in fact, when we boil it right down, a moral entity. If we can tell what people ‘value’ and why, then we can make prognostications on what is Good for society as a whole.

In times past organised religions handed down fixed value systems to their adherents. Today people have become disillusioned with religious systems – ostensibly because they conflict with these peoples’ supposedly ‘scientific’ worldview. But the impulse among some for the self-assurance provided by a religion is so strong that they seek out ‘scientific’ systems that operate in an identical manner to religious or cult systems.

This is why the economic doctrine of ‘value’ is such a good foundational stone for such a cult. It provides a pseudo-scientific account about how people attribute value to things and in doing so tells the cult member a ‘Truth’ that they can use to make turn the world into a Utopia in which the optimal amount of ‘value’ is realised by the optimal amount of people.

Karl Marx claimed that ‘value’ was embodied labour and hence his followers concluded with him that all that was Good sprang from labour and that society should thus be based on free labour. The libertarians – together with the neoclassicals that they otherwise scorn – believe that all ‘value’ springs from utility maximisation. While the neoclassicals simply tinker with toy-models of ‘value’ to bolster their pseudo-scientific prestige, the libertarians undertake a leap of faith into the unknown and claim that in the theory of marginal utility they have found a ‘Truth’ that must be brought down from Heaven to Earth.

The Birthing of a Cult

Libertarianism was born out of the late 19th century doctrine of marginalism; a doctrine that went on to gain popularity with those opposed to Marxism. We will not dwell too much on the doctrine of marginalism when applied to the analysis of ‘value’ – having done so elsewhere. Here we will merely note that marginalism provides a moral defence for the supposedly ‘free market’ system that we live under today.

Marginalism, when applied to ‘value’ analysis, holds that it is in Man’s nature to follow a certain path in his consumption habits. These habits are determined by his maximising his utility. Most modern marginalists claim that they can use this concept to show that a ‘free market’ system is the fairest social system possible, since it responds automatically to Man’s marginal utility preference it delivers ‘value’ in a perfect and harmonious manner.

Markets deliver this ‘value’ through the mechanism of price. Prices, which reflect peoples’ desires to maximise their marginal utility, ensure that the most equitable distribution of ‘value-in-the-abstract’ is accommodated for by the ‘free market system’. And this is the point at which marginal value analysis becomes a value judgment in a very real sense.

The neoclassicals held, and continue to hold, that their models could capture this complex dynamic. Such an assertion was and is, of course, absolute rubbish. But the Austrians took a different tack. “Yes,” they said, “marginal utility theory is the correct way to go, but we cannot formulate models that adequately capture the inner workings of this great mechanism.”

In their book Modern Political Economics: Making Sense of the Post-2008 World, the authors provide a good summary of this approach. In the book they discuss what effect the discovery of marginalism’s inherent uselessness had on the Austrians:

Faced with the impossibility of mathematically deriving prices and quantities on the one hand and a metric of social welfare on the other, some Marginalists understood the limitations of their utility calculus. Mainly of an Austrian persuasion (most notably Ludwig von Mises, Friedrich von Hayek and Joseph Schumpeter), they even gallantly tried to use this failure to the advantage of their claims on behalf of untrammelled markets and against the encroachments of collective agencies, trade unions, governments etc.

This was a clever move. While the neoclassicals tinkered with their silly toy-models, trying to show how prices are determined through a sort of grand marginal calculus, the Austrians shrugged their shoulders as to how such a Divine Event could occur. Instead they began to think of price as a sort of Miracle that proved the divinity of the Market mechanism. They then went on deploy this argument to show that anything that encroached upon this Divine Being’s presence was inherently Evil:

If no degree of mathematical sophistication can pin down the ‘right’ prices and quantities, how can a government or any other form of collective agency work them out? How could a socialist economy, or even a national health service, ever price things? Thus, the market mechanism is indispensible because of the radical indeterminacy of prices.

Note what is happening here. The Austrians, like their marginalist brothers and sisters, thought that in marginal utility theory they had found the source from which ‘value’ truly flowed. They never for one moment questioned that. Even when they came to conclude that marginalist analysis could never definitively show anything useful about price determination, they remained confident – indeed, they became even more confident – that such an analysis was Truth.

In short, they postulated a theory and then when confronted with the inconsistencies of the theory when it was applied to any practical ventures they simply threw up their arms and claimed that such inconsistency showed just how true theory was and how much we should respect it. The knowledge that the theory imparted then became, in a very real sense, Divine, in that we meagre humans would never be able to grasp it and instead should simply bow down in front of the Great Being that possessed this knowledge – that is: the Market.

This is what gives the libertarians their religious zeal. In their quest for the Grand Truth they find this Truth to be inaccessible to Man. But in this inaccessibility they find a Higher Truth again; namely, that there is some other entity out there – a benevolent entity called ‘the Market’ – that possesses this Truth and all we have to do is follow the Laws which it has handed down to us and we will eventually reach Utopia. This is, of course, a leap of faith – a truly Kierkegaardian Leap of Faith.

From the Leap of Faith to the Knight of Faith

The Austrians were never quite content with the chicanery and political posturing that they had passed off as scientific debate. As alluded to above, their theories about market prices were forged in the debates with those who advocated a socilialistic planned economy. Being ideological to the core, the Austrians were, for a while at least, perfectly content with saying that while no economist could say anything worthwhile about price determination – and thus, any attempt at a socialist planned economy would be doomed to fail because there could be no perfectly informed coven of evil socialist economists who could administer it – they were still happy with the airy theory of market prices that they had just poked such a large hole in. Yes, they had undertaken a Leap of Faith by admitting that their logical constructions would never be whole but, as Kierkegaard well knew, every Leap of Faith needs a hero, a Knight of Faith – and the Austrians soon found theirs.

The Austrians had, although one suspects that they never fully realised this, essentially proved that their theories were inconsistent. There was always, lurking somewhere, that element that disturbed the calculation of prices in the market models.

Let us emphasise here that this element of disturbance was found, not in reality, but only in their models and in their minds. The fact is that the Austrians, even in out-stepping their neoclassical brethren, were still only exploring their own fantasies. This fact must always be kept in the front of one’s mind when considering their doctrines.

We highlight this because it was precisely at this point that the Austrians could have conceded that they were building castles in the sky – ideologically and emotionally motivated castles in the sky, no less – and that it might be time to grow up and give up on the whole sordid venture of trying to establish a ‘logical’ ‘economic’ basis for ‘value’ that would temper them with the moral certainty they needed to carry on their political crusade. But not so. Instead they found a Kierkegaardian Knight of Faith to fill the gap in their logic. And that Knight of Faith was the entrepreneur.

The Austrian economist Israel Kirzner put it as such in his fine paper ‘The Economic Calculation Debate: Lessons for Austrians’ (which is also an excellent historical overview of much of what we have here been discussing):

[T]he truth is that Hayek opened the door to an entirely new perspective on the “goodness” of economic policies and institutional arrangements. Instead of judging policies or institutional arrangements in terms of the resource-allocation pattern they are expected to produce (in comparison with the hypothetically optimal allocation pattern), we can now understand the possibility of judging them in terms of their ability to promote discovery.

And this ‘discovery’, of course, comes from the entrepreneur who was hereafter identified by the libertarian as the social hero who broke through all barriers in the pursuit of the creation of new ‘values’ – and by that, we mean economic ‘values’ – for the community as a whole. Kizner again:

For Austrians, prices emerge in an open-ended context in which entrepreneurs must grapple with true Knightian uncertainty. This context generates precisely the kind of choice that stimulates the competitive discovery process. In this context, the entrepreneur does not treat prices as parameters out of his control but, on the contrary, represents the very causal force that moves prices in coordinating directions.

In Kierkegaard’s writings which, like the writings of the Austrians sought to establish a theological metaphysic from which an individual could derive principles of moral certitude, it was the Knight of Faith – the true believer with complete faith and certainty in both himself and God – that filled in the logical gaps inherent in even the greatest philosophical systems. For the Austrians the entrepreneur filled the same role – except that this was a great hero that had both full faith in the Market and the ability to find opportunities to inject disequilibrium into the price system through innovation.

By now we are far outside the realm of anything even remotely resembling a science of ‘value’. What we have instead is a vast metaphysical and moral system that is built around a very specific – not to mention very narrow – conception of value, together with a sort of existential appendage in the form of the hero-entrepreneur. The hero veneers over the logical flaws in the metaphysical system, while that system remains in place as a faith-based explanatory schema which can be applied to the world around the libertarian.

Note how fantasy blends into reality almost completely at this point. No longer do we separate our supposedly ‘factual’ ideas about ‘value’ from the mythological figure of the entrepreneur. Fact and fantasy merge to form a sort of continuum the purpose of which is to insulate the devotee from any empirical evidence that might arise to prove them wrong – or, at least, misled – regarding, for example, more fundamental and more pressing macroeconomic questions. They simply know what is what because they have it all worked out – and no silly facts are going to tell them otherwise.

From the fertile source of marginal utility value calculus the Austrians thus constructed a pristine moral and metaphysical system. But in doing so – like all metaphysicians – they allowed their imaginations to run away with them. They never noticed the point at which they crossed that fateful line; that line that separates our attempts to represent the world accurately and dispassionately to ourselves from our attempts to create a fantasy world in which we can live. The Austrians had, at first, attempted to use their imaginations to explain the world around them and, in doing so, had fallen into a dream world of their own creation.

And so the foundations of the political cult we call libertarianism were firmly in place. It is an ingenious creation which even came to include what CG Jung and other mythologists might call a central ‘archetypal’ or mythic figure. Even more specifically, what the Austrians have done is insert into their narrative what the great American mythologist Joseph Campbell called the ‘monomyth’. The monomyth is a recurrent theme in mythologies from all over the world. It is essentially a ‘hero myth’ and, as Campbell argues, can be located in most major religious narratives (Christ, Buddha etc.). In this the Austrians provided the libertarian religion with their very own version of the monomyth.

That most libertarians are ignorant of the source of their beliefs – just as most of them are not very conversant with economic theory generally, their protestations to the contrary notwithstanding – only adds a sociological dimension to their cult. Their cult forms a hierarchy where those who are closer to the Grand Truth are supposed to know more than those who are less conversant. Those who are less conversant then scrutinise the Great Texts – which are largely taken to be Holy Writ – until they can advance up the priestly ranks.

The Malign Consequences of Political Cults

After experiencing what used to be called ‘Bolshevism’ we are well aware of the dangers of political cults if they should ever ascend to power. Indeed, we already had forewarnings of this danger in the cult of Reason that Robespierre erected in revolutionary France upon the intellectual architecture that Jean-Jacques Rousseau had constructed for him. All of these cults espouse liberty and freedom and end up creating regimes of pure tyranny. Why? Because in their violent desire to turn reality into a Utopia, they stamp all over reality as it fails to conform to the images in their minds.

Some have objected to fellow Naked Capitalism writer Andrew Dittmer’s ‘interview’ series as an attempt to misrepresent the libertarian movement by espousing the ideas of an extremist. This is unfair. The views of people like Hoppe may be fringe among libertarians – then again, they may not be – but the zealousness is the same across the whole movement.

Libertarians think that they have unearthed a Truth that no one else can grasp (because, of course, this Truth being so pure, anyone who could possibly grasp it must then by default recognise it as Truth). And they think that if they can get adequate social and political power to enforce this Truth we will all be better off for it. Hoppe’s vision of a totalitarian, corporatist future is thus realistic in that if libertarians were ever truly to get into power they would have to enact an immense violence upon the world to try to get it to conform to their vision of Utopia. In this, they are like every other political cult that has ever existed. And they are just as dangerous.

In fact, the libertarians are the direct heirs to the Marxist-Leninist throne. Even though their motives differ substantially, their Faith is based on very similar principles – which is not surprising given that both movements grew out of the same 19th century debate over economic value. In this regard it is useful to recall John Maynard Keynes’ characterisation of Marxism-Leninism:

[It] is the combination of two things which Europeans have kept for some centuries in different compartments of the soul – religion and business.

Keynes also highlighted an important point about how such cults become influenetial:

[They derive their] power not from the multitude but from a small minority of enthusiastic converts whose zeal and intolerance make each one equal in strength to a hundred indifferentists.

The goal may have changed, but the unswerving faith in pseudo-scientific – or, to be very precise, in the Austrians case, because they tend to eschew ‘scientificity’: pseudo-rational – economic doctrines has not. Let us just hope that such a cult does not deliver to us another era of primitive tyranny and medieval inquisition. It is our democracies that are at stake.

The true value of money – or why you can't fart a crashing plane back into the sky

Banknotes aren't worth the paper they're printed on. The entire economy relies on the suspension of disbelief

• 
• • Charlie Brooker
  • guardian.co.uk, Sunday 12 February 2012

I'm no financial expert. I scarcely know what a coin is. Ask me to explain what a credit default swap is and I'll emit an unbroken 10-minute "um" through the clueless face of a broken puppet. You might as well ask a pantomime horse. But even an idiot such as me can see that money, as a whole, doesn't really seem to be working any more.

Money is broken, and until we admit that, any attempts to fix the economy seem doomed to fail. We're like passengers on a nosediving plane thinking if we all fart hard enough, we can lift it back into the sky. So should we be storming the cockpit or hunting for parachutes instead? I don't know: I ran out of metaphor after the fart gag. You're on your own from hereon in.

Banknotes aren't worth the paper they're printed on. If they were, they'd all have identical value. Money's only worth what the City thinks it's worth. Or, perhaps more accurately, hopes it's worth. Coins should really be called "wish-discs" instead. That name alone would give a truer sense of their value than the speculative number embossed on them.

The entire economy relies on the suspension of disbelief. So does a fairy story, or an animated cartoon. This means that no matter how soberly the financial experts dress, no matter how dry their language, the economy they worship can only ever be as plausible as an episode of SpongeBob SquarePants. It's certainly nowhere near as well thought-out and executed.

No one really understands how it all works: if they did, we wouldn't be in this mess. Banking, as far as I can tell, seems to be almost as precise a science as using a slot machine. You either blindly hope for the best, delude yourself into thinking you've worked out a system, or open it up when no one's looking and rig the settings so it'll pay out illegally.

The chief difference is that slot machines are more familiar and graspable to most of us. When you hear a jackpot being paid out to a gambler, the robotic clunk-clunk-clunk of coin-on-tray, you're aware that he had to go to some kind of effort to get his reward. You know he stood there pushing buttons for hours. You can picture that.

The recent outrage over City bonuses stems from a combination of two factors: the sheer size of the numbers involved coupled with a lack of respect for the work involved in earning them. Like bankers, top footballers are massively overpaid, but at least you comprehend what they're doing for the money. If Wayne Rooney was paid millions to play lacrosse in a closed room in pitch darkness, people would begrudge him his millions far more than they already do. Instead there he is, on live television: he's skilled, no doubt about it.

Similarly, it may be tasteless when a rapper pops up on MTV wearing so much bling he might as well have dipped himself in glue and jumped into a treasure chest full of vajazzling crystals, but at least you understand how he earned it.

RBS boss Stephen Hester, meanwhile, earns more than a million pounds for performing enigmatic actions behind the scenes at a publicly owned bank. And on top of his huge wage, he was in line for a massive bonus. To most people, that's downright cheeky: like a man getting a blowjob from your spouse while asking you to make him a cup of tea.

But Hester earned his wage, we're told, because he does an incredibly difficult job. And maybe he does. Trouble is, no one outside the City understands what his job actually consists of. I find it almost impossible to picture a day in Hester's life, and I once wrote a short story about a pint-sized toy Womble that ran around killing dogs with its dick, so I know I don't lack imagination. Class, yes: imagination, no. If I strain my mind's eye, I can just about picture Hester arriving at work, picture him thanking his driver, picture the receptionist saying "Hello, Mr Hester", and picture him striding confidently into his office – but the moment the door shuts, my feed breaks up and goes fuzzy. What does he do in there? Pull levers? Chase numbers round the room with a broom? God knows.

Maybe if all bankers were forced to work in public, on the pavement, it would help us understand what they actually do. Of course, you'd have to encase them in a Perspex box so they wouldn't be attacked. In fact, if the experience of David Blaine is anything to go by, you'd have to quickly move that Perspex box to somewhere impossibly high up, where people can't pelt it with golf balls and tangerines. On top of the Gherkin, say. If Hester did his job inside a Perspex box on top of the Gherkin for a year, this entire argument might never have happened.

The row over bonuses has led some to mutter darkly about mob rule and the rise of anti-business sentiment. Complain about mobs all you like, but you can't control gut reactions, and you can't dictate the mood. And when you try to fart a crashing plane back into the sky, you only succeed in making the atmosphere unpleasant for everyone. And spoiling the in-flight movie. And making the stewardess cry. Looks like I'm all out of metaphor again. Time to end the article. Article ends.

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.

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