Matemáticas, ecuaciones y los límites de la economía

(La columna de Pablo R. Suanzes en el suplemento económico de El Mundo del 28 de abril de 2013)

Kenneth Rogoff y Carmen Reinhart son dos de los economistas más prestigiosos de la actualidad. O al menos lo eran, hasta que se ha puesto en evidencia (maventrap.es/2013/04/18/se-sustenta-la-austeridad-en-un-fallo-de-los-economistas-con-el-excel/) uno de sus papers más conocidos por un error increíble en una tabla de Excel. Sí, Excel (www.fedeablogs.net/economia/?p=30024). La relación de los economistas con las matemáticas es interesante (http://public.econ.duke.edu/~erw/Preprints/Mathematics%20and%20Economics%20%28New%20Palgrave%29.pdf). Es algo que tiene un rol creciente (http://gregmankiw.blogspot.com.es/2006/09/why-aspiring-economists-need-math.html). 

Según algunos cálculos, «más del 80% de la literatura especializada viene expresada en lenguaje matemático» (www.sheriffasoc.com/publicaciones/economina_matematicas.pdf). Las universidades más prestigiosas sólo aceptan para programas de posgrado a alumnos con muy buenas calificaciones en asignaturas con carga cuantitativa (www.salaimartin.com/randomthoughts/item/159-como-ser-admitido-en-columbia.html). Noah Smith, explica por qué son necesarias (http://noahpinionblog.blogspot.com.es/2012/10/what-is-math-and-why-should-we-use-it.html). D. Rodrik también (http://rodrik.typepad.com/dani_rodriks_weblog/2007/09/why-we-use-math.html). Y no sólo en economía. E. O. Wilson dijo hace poco que un buen científico no tiene que ser especialmente bueno en matemáticas. Las críticas y replicas le llovieron enseguida (http://www.psychologytoday.com/blog/finding-the-next-einstein/201304/e-o-wilson-scientists-definitely-need-high-math-ability). Nassim Taleb, célebre por su libro El Cisne Negro, es un conocido crítico de la falta de «rigor matemático», y tiene abierta una cruzada contra los macrobullshiters, algo así como embaucadores que, para él, dicen solamente tonterías macroeconómicas (www.forbes.com/sites/karlwhelan/2013/04/24/when-nassim-taleb-attacks/).

Desde 1494, cuando Luca Pacioli sentó las bases de la contabilidad moderna, el papel de las matemáticas no ha dejado de evolucionar. Marco Licalzi y Achille Basile repasan algunos de los hitos y la importancia de la revolución marginalista (http://venus.unive.it/licalzi/EconMatem1469.pdf). La escuela austriaca de economía es una de las pocas que recela abiertamente del poder explicativo de las matemáticas (http://amartinoro.wordpress.com/2010/02/14/econometria-matematicas-escuela-austriaca-y-otras-divagaciones/). Deirdre McCloskey tiene críticas interesantísimas al respecto (http://www.deirdremccloskey.com/articles/stats/stats.php). Krugman ha mostrado sus reservas hacia la equiparación de «buenos cálculos y buen trabajo económico» (http://krugman.blogs.nytimes.com/2009/09/11/mathematics-and-economics/). Tim Harford ha analizado si hay demasiado pensamiento analítico en finanzas (http://timharford.com/2013/04/rich-pickings-for-scientists/). Seguramente (http://online.wsj.com/article/SB10001424052748704509704575019032416477138.html) sí que haya algo (http://www.bbc.co.uk/news/magazine-17866646).

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

(An article by Tim Harford in http://www.bbc.co.uk/news)

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."

Amigos y enemigos: la breve historia del capitalismo y sus salvadores

(La columna de Pablo R. Suanzes en el suplemento económico de El Mundo del 5 de mayo de 2013)

Sobre el capitalismo se ha dicho mucho, muchísimo. Sin embargo, sobre su historia, sus orígenes y desarrollo, no se ha escrito tanto. y la mayoría de las veces, de hecho, los que han teorizado han sido sus principales adversarios (mun.do/XrGj52). Al menos hasta ahora. En las universidades estadounidenses el tema está de moda, y hay unas cuantas publicaciones recientes o en camino (www.nytimes.com/2013/04/07/education/in-history-departments-its-up-with-capitalism.html?pagewanted=all&_r=1&). Desde el inicio de la crisis, la Universidad de Harvard tiene un Program on the Study of Capitalism (studyofcapitalism.harvard.edu). Columbia (cup.columbia.edu/series/234) o Georgia ya los tenían (capitalism.uga.edu). 

El principal rival teórico del capitalismo ha sido el socialismo, en cualquiera de sus diferentes variantes. Pero para algunos, además de cosmovisiones diferentes, fueron en algunos momentos complementarias de alguna forma (www.la-razon.com/suplementos/tendencias/cierto-modo-marxismo-salvado-capitalismo_0_1792620863.html). Hace unos días, Eric Rauchway publicaba en el TLS una reseña sobre el último libro de Benn Steil titulada How the Soviets saved capitalism. La obra reflexiona sobre el papel de Harry Dexter White, norteamericano que ayudó a configurar el sistema de Bretton Woods (que «salvó y prolongó el capitalismo») y que fue además un importante espía soviético (arikelman.org/wp-content/uploads/2013/04/How-the-Soviets-saved-capitalism-TLS.pdf). El propio autor tiene en el último número de Foreign Affairs un extraordinario perfil sobre él titulado Red White (www.foreignaffairs.com/articles/138847/benn-steil/red-white). 

Al capitalismo siempre le han salido novias. Lipset y Marks explicaron cómo Rooselvet lo había salvado (www.hoover.org/publications/hoover-digest/article/7076). Quizás fue la democracia (www.eoionline.org/blog/how-democracy-saved-capitalism). O Keynes (www.csub.edu/kej/documents/economic_rsch/2012-03-12.pdf). Otros, más rebuscados, apuntan a la izquierda (mrzine.monthlyreview.org/2008/esteven200708.html), a ¡Lenin! (thecosmicparadigm.blogspot.com.es/2011/05/did-lenin-save-capitalism.html) e incluso a Stalin, por obligar a EEUU a esforzarse e innovar (http://www.algora.com/119/book/details.html). Los clásicos apuestan por Milton Friedman (http://online.wsj.com/article/SB10000872396390444226904577558882802335216.html). Los más originales, dan las gracias al whisky (http://www.diariovasco.com/20081109/economia/whisky-salvo-capitalismo-20081109.html). Sí, whisky.

Se retrasa el día de la liberación fiscal

(La columna de Cristina Berechet en suplemento económico de El Mundo del 12 de mayo de 2013)

Desde el 10 de mayo, todo el dinero que ha ganado el trabajador medio español va a parar a su bolsillo y no al del Estado.

130 días de trabajo para pagar el IVA, las cotizaciones a la Seguridad Social por parte del trabajador, el impuesto sobre la renta, los impuestos especiales y otros impuestos municipales como el IBI o el de circulación. No obstante, si se incluyen las cotizaciones a la Seguridad Social pagadas por el empresario, que representan el 60% de la tributación sobre el trabajo, el Día de la Liberación Fiscal (www.civismo.org/es/investigaciones/informes/dia-de-la-liberacion-fiscal-2013) pasaría a ser el 3 de julio. Así, el trabajador medio estaría empleando más tiempo para el Estado que para sí mismo. Por si fuera poco, por la última subida del IVAy de impuestos autonómicos y municipales, este año estamos trabajando 6 días más que en 2012. 

Analizando únicamente la tributación sobre la renta, sorprende que el trabajador medio español tribute al mismo nivel que en Suecia o Finlandia, en torno a un 40%, con la única diferencia de que el salario de estos países casi duplica al español. Incluso en el Reino Unido, con una renta un 40% superior a la nuestra, el mordisco del Estado a los asalariados no supera el 32%. 

¿A qué se debe? A que nuestros políticos alardean de una falsa progresividad y de que las subidas impositivas las tienen que soportar los ricos. Sin embargo, la realidad es que al final los adinerados son pocos y con mayor movilidad. Por ello, acaban pagando los de siempre: las clases medias. 

La mejor forma de subir los impuestos a toda una sociedad es dividirla en ricos, clase media, mileuristas, pobres, etc. Así hoy se suben los impuestos a unos y mañana a otros. Si todos tributáramos a un tipo único sería muy difícil subir los impuestos a toda la sociedad. Como dice el refrán: divide y vencerás.

High-frequency trading - the rise of the machines

(An article by Dean Carroll, editor of publicserviceeurope.com on 10th July)

In the 17th century, it is said that the Rothschilds were able to balance stock markets in their favour by flying carrier pigeons to relay information before their peers. Today's equivalent is high-frequency trading. It is hard to believe but more stock market deals are now carried out by computers than humans, in a number of areas.

We know that HFT, guided by complicated algorithms, takes place in a millisecond or even a microsecond but the speed and volume of deals allows firms to maximise profits. There is no long-term strategy, no major leverage and only light-touch regulation. In Europe, HFT is estimated to be responsible for around 40 per cent of equity trades. In the United States, the figure is closer to 60 per cent.

What's not to like? I hear you say. Well, HFT creates extreme market volatility and has even resulted in a 'flash crash'. On May 6, 2010, US index the Dow Jones plunged 1,000 points – or 9 per cent of its total - only to recover those losses within minutes. This shock was a direct result of HFT. And the sequence of events was triggered by a single sale of $4.1bn in futures contracts by a mutual, in an aggressive attempt to hedge its investment position. This was quickly magnified by HFTs, creating a snowball effect.

Not only that, the limited uses for such a trading device are simply to pump up pension funds or to create greater wealth for the super-rich. All this without truly investing in a productive asset – a company that might make a difference to wider society. Any integrity markets might have once had now lies in tatters.

Nobel Prize winning economist Michael Spence has already called for HFT to be banned. And Joseph M. Mecane of NYSE Euronext, which operates the New York Stock Exchange, said: "It's become a technological arms race, and what separates winners and losers is how fast they can move."

At this precise moment, the world of HFT is analogous to a frontier town. Only this time, it is not humans displaying wild west-style behaviour but the machines we have created. The flash crash of 2010 was a wake-up call. However, it seems the regulators are still asleep and we all know where that leads – circa the 2008 global economic crisis we are still coming to terms with today. Perhaps, carrier pigeons were not such a bad idea after all.