The formula that changed the world

Summary

More or Less – "The Formula That Changed the World"

BBC Radio 4 | Airdate: April 27, 2012
Host: Tim Harford
Guests: Prof. Ian Stewart (Mathematics, Warwick University), Prof. Myron Scholes (Economist, co-inventor of Black-Scholes formula)

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Episode Overview

This episode delves into the origins, impact, and controversy surrounding the Black-Scholes formula, an equation that revolutionized modern finance by providing a systematic way to price financial options. Host Tim Harford explores how a mathematical insight transitioned Wall Street from the realm of intuition to algorithm-driven decisions—sometimes with disastrous results. The discussion features insights from mathematician Ian Stewart and Nobel laureate Myron Scholes himself.

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Key Discussion Points

The Origins of Black-Scholes (00:12–01:53)

• Tim Harford sets the stage: The focus is the Black-Scholes formula—an equation that “transformed Wall Street” and sparked debate over whether it improved markets or contributed to financial crises.
• Ian Stewart explains the historical context:
  • Futures contracts and options have been around for centuries, but "putting a sensible price" on an option was a longstanding puzzle.
  • Options give the right but not the obligation to buy or sell at a set price—a tricky thing to value (“that’s where this world changing equation... can help” [00:49]).

Cracking the Options Pricing Puzzle (01:34–03:33)

• Myron Scholes:
  • Attempts to value options “bothered” him because they wrongly presumed constant risk while the “risk of the option was changing.”
  • He and Fisher Black realized that through constructing certain “risk-free portfolios” combining options and the underlying asset, one can deduce the fair price of an option from existing risk-free prices ([02:34]).

“We were like kids in a candy store in the sense that we described options everywhere and options were embedded in everything we did in life.” – Myron Scholes [03:33]

• The method soon generalized to valuing all kinds of complex financial instruments, not just options.

The Formula Takes Over Wall Street (03:42–04:36)

• Ian Stewart:
  • The Black-Scholes equation didn’t only provide the confidence to trade options but also “much more complicated financial instruments known as derivatives.”
• Myron Scholes:
  • Traders with technical know-how in options pricing technology quickly superseded those relying on “intuition.”

“In a very short period of time, the intuitive players were essentially eliminated by the more systematic players.” – Myron Scholes [03:51]

• By 2007, derivatives trading ballooned to over $1 trillion—ten times the total historical production of goods worldwide (Ian Stewart [04:21]).

Black-Scholes and the Rise and Fall of Quants (04:43–06:15)

• In the late 1990s, Black-Scholes earns a Nobel Prize; Myron Scholes shares it with Robert Merton (Fisher Black passed away).
• Both became partners at Long-Term Capital Management (LTCM), a hedge fund grounded in mathematical strategies.
• Ian Stewart: LTCM initially outperforms conventional traders but collapses spectacularly after the Russian financial crisis, losing $4 billion in six weeks ([05:17–05:37]).
• Ian Stewart: The episode showed the “danger of this kind of algorithmically based trading” if traditional caution is ignored.
• Myron Scholes: Attempts to distance the formula/model from the collapse:

“It has nothing to do with equations, it has nothing to do with models… It was just a matter of risk taking. It wasn’t a matter of modeling.” – Myron Scholes [06:15]

Blame and the Debate on Mathematical Models (06:15–07:46)

• Tim Harford frames the persistent debate: Was LTCM's downfall and the later global crisis an “indictment of mathematical approaches,” or just bad risk management?
• Ian Stewart:

“It was abuse of their equation that caused trouble... it probably wasn’t that equation as such at all... [it was] a whole generation of other mathematical models.” [07:02]

Technology, Progress, and Hubris (07:26–08:48)

• Tim Harford:
  • The formula fundamentally shifted market culture—intuition gave way to “where the computer said yes or no.”
• Myron Scholes:
  • Financial technology is here to stay; the formula is progress, like nuclear power—misuse or accidents don’t negate the underlying value:

“It’s the same way as saying because we had an explosion at a nuclear power plant, that all use of nuclear forever and a day is not valuable.” – Myron Scholes [07:46]

• Ian Stewart:
  • Sees the financial crisis as a “classic Greek tragedy of hubris begets nemesis”:

“The big problem is it wasn’t the bankers on whom the nemesis descended, it was the rest of us.” [08:14–08:48]

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Notable Quotes & Memorable Moments

• “All the variables seem to be tangled up in an impenetrable way.” – Tim Harford [02:34]
• “We were like kids in a candy store...” – Myron Scholes [03:33]
• “By 2007, the trade in derivatives worldwide was $1,000,000,000,000. This is 10 times the total production of goods on the planet.” – Ian Stewart [04:21]
• “It has nothing to do with equations, it has nothing to do with models... It was just a matter of risk taking.” – Myron Scholes [06:15]
• “It was abuse of their equation that caused trouble... it probably wasn’t that equation as such at all.” – Ian Stewart [07:02]
• “It’s the same way as saying because we had an explosion at a nuclear power plant, that all use of nuclear forever and a day is not valuable.” – Myron Scholes [07:46]
• “The big problem is it wasn’t the bankers on whom the nemesis descended, it was the rest of us.” – Ian Stewart [08:48]

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Key Segments & Timestamps

• Introduction & Overview: [00:12–00:49]
• What are Options? (Ian Stewart explains): [00:49–01:34]
• Myron Scholes describes the pricing puzzle: [01:34–02:34]
• How Black-Scholes works and its implications: [02:34–03:42]
• Options to Derivatives; Culture Shift on Wall Street: [03:42–04:36]
• Nobel Prize & LTCM Overreach: [04:43–05:58]
• LTCM collapse; debate over blame (Scholes vs. Stewart): [05:58–07:26]
• Legacy: technology, responsibility, hubris: [07:26–08:48]

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Summary

This episode of More or Less artfully narrates the creation and aftershocks of the Black-Scholes formula in global finance. While the formula allowed complex risk calculations and invigorated financial markets, its misapplication—and the overreliance on quantitative methods—played pivotal roles in financial shocks such as LTCM's collapse. Ultimately, the episode frames Black-Scholes as both a feat of human ingenuity and a cautionary tale of technological hubris, with consensus that progress comes with responsibility and no easy scapegoats.

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For more details on the impact of financial models or suggestions for future episodes, visit bbcworldservice.com/moreorless.

Transcript

[BBC Announcer]

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[Tim Harford]

this is more or less on the BBC World Service. The theme of this week's programme is the equation that changed finance forever. 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. We're going to hear the story of the equation that transformed Wall street and the arguments over whether it made the world a better place or helped cause the financial mess we've all been dealing with for the past five years. It's called the Black Scholes formula. It was first written down in the early 1970s, but our story starts earlier than that, a lot earlier.

[Ian Stewart]

The Black Scholes equation came from attempts to put a sensible price on a financial option. So financial options go well over 100 years.

[Tim Harford]

This is Ian Stewart, professor of Mathematics at Warwick University in the UK, and the author of 17 Equations that Changed the World. A simple futures contract says, I will agree to buy rice from you in one year's time at a price that we agree right now. 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. But I don't have to if I don't want to. But that then leads to a very ticklish what are they worth? And that's where this world changing equation, the Black Scholes formula, can help.

[Myron Scholes]

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.

[Tim Harford]

That's Myron Scholes. And if you're wondering whether it's a coincidence that Professor Scholes is talking about something called the Black Scholes formula, it's not.

[Myron Scholes]

I came upon the problem because my students at MIT had option data and they were writing a master's thesis and they tried to value the option. And when I looked at the way they were trying to value it, it became curious to me that they had to assume a constant rate to value the option when the risk of the option was changing. So you had this puzzle, and the puzzle bothered me a lot.

[Tim Harford]

Several factors contributed to the puzzle. The value of an option to buy beef 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 on how likely the option is to actually be used. All the variables seem to be tangled up in an impenetrable way. Myron Scholes worked on the problem with his colleague, Fisher Black. Black and Scholes figured out that rather than come at the option pricing formula directly, you could get at it indirectly. It turns out that if I own just the right portfolio of beef plus options to buy and sell beef, I have a delicious but 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. The Black Scholes method turned out to be a way not only to calculate the value of options, but all kinds of other financial assets.

[Myron Scholes]

We were like kids in a candy store in the sense that we described options everywhere and options were embedded in everything we did in life.

[Ian Stewart]

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

[Myron Scholes]

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 in a very short period of time, the intuitive players were essentially eliminated by the more systematic players or the ones who had the option pricing technology.

[Ian Stewart]

By 2007, the trade in derivatives worldwide was US$1,000,000,000,000. This is 10 times the total production of goods on the planet. Over its entire history, the Black Scholes

[Tim Harford]

formula had passed the market test. And then in the late 1990s, two remarkable things happened.

[Ian Stewart]

The inventors got the Nobel Prize for economics, and I would argue they thoroughly deserve to get it.

[Tim Harford]

Fisher Black died Young in 1995. When in 1997, Myron Scholes won the Nobel Prize, he shared it not with Black, but with Robert Merton, another option pricing expert. The Nobel Prize is a big deal in the life of most winners. But Myron Scholes had already made his mark. His work had inspired a generation of mathematical wizards on Wall Street. And both he and Robert Merton were players in the world of finance as partners of a hedge fund called Long Term Capital Management.

[Ian Stewart]

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, it was outperforming the traditional companies quite noticeably. And everything looked great.

[Tim Harford]

You can guess how this ended badly. Long Term Capital Management ran into, among Other things, the Russian financial crisis. The firm lost 4 billion dol in the course of six weeks. It was bailed out by a consortium of banks which had been assembled by the Federal Reserve less than a year after Myron Scholes had been awarded his Nobel Prize.

[Ian Stewart]

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. They were committed pretty much to just ploughing ahead with the system they had. There wasn't a great deal else to do and it went wrong.

[Myron Scholes]

It has nothing to do with equations, it has nothing to do with models. And 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 later in summer and fall of 1998. It was just a matter of risk taking. It wasn't a matter of modeling.

[Tim Harford]

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 Myron Scholl said, was it just traders taking too much risk against the better judgment of the mathematical experts? Ten years after the Long Term Capital Management bailout, 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]

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. And it wasn't just that equation. In fact, it probably wasn't that equation as such at all. When we come to the real financial cris, it was a whole generation of other mathematical models and all sorts of other techniques that followed on its heels.

[Tim Harford]

In other words, the Black Scholes formula 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 Myron Scholes argues there's no going back. His equation is a kind of technological progress, and as with any technology, it needs to be used responsibly.

[Myron Scholes]

The fundamental issue is that quantitative technologies in finance will survive and will grow. And that's what bothers me about the professor's claims. He looked and saw, okay, there was a blow up in certain parts of the market. And from that you make the conclusion that everything's gone amiss. It's the same way as saying because we had an explosion at a nuclear power plant, that all use of nuclear forever and a day is not valuable.

[Ian Stewart]

It's very tempting to see the financial crisis and various things that led up to it, as the sort of classic Greek tragedy of hubris begets nemesis. 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 it's not just tempting to do that, but actually there is a certain amount of truth in that way of thinking. I think the bankers hubris did indeed beget nemesis. The big problem is it wasn't the bankers on whom the nemesis descended, it

[Tim Harford]

was the rest of us, Professor Ian Stewart and Professor Myron Scholes. And that's all we've got time for this week in next week's programme. Well, who knows? If you think you know what should be in it, please drop us a line. More or lessbc co.uk our website is bbcworldservice.com more or less the place to subscribe to our podcast. Or you could just tune in the same time next week. Until then, goodbye. More or Less was presented by me, Tim Harford, the undercover economist at the Financial Times. The producer was Richard Knight and the editor, Richard Varden.

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