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The Most Valuable Formula Ever Created

By Alex Planes – May 9, 2013 at 10:09PM

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Learning from the market's past to understand its present.

On this day in economic and business history...

The Black-Scholes option-pricing model, first published in 1973 in a paper titled "The Pricing of Options and Corporate Liabilities," was delivered in complete form for publication to The Journal of Political Economy on May 9, 1972. PBS' NOVA offers the following explanation of the model, and of its importance to the financial world:

Derived by economists Myron Scholes, Robert Merton, and the late Fischer Black, the Black-Scholes formula is a way to determine how much a call option is worth at any given time. The economist Zvi Bodie likens the impact of its discovery, which earned Scholes and Merton the 1997 Nobel Prize in Economics, to that of the discovery of the structure of DNA. Both gave birth to new fields of immense practical importance: genetic engineering on the one hand and, on the other, financial engineering. The latter relies on risk-management strategies, such as the use of the Black-Scholes formula, to reduce our vulnerability to the financial insecurity generated by a rapidly changing global economy.

Here's the theory behind the formula: When a call option on a stock expires, its value is either zero (if the stock price is less than the exercise price) or the difference between the stock price and the exercise price of the option. For example, say you buy a call option on XYZ stock with an exercise price of $100. If at the option's expiration date the price of XYZ stock is less than $100, the option is worthless. If, however, the stock price is greater than $100 -- say $120, then the call option is worth $20. The higher the stock price, the more the option is worth. The difference between the stock price and the exercise price is the "payoff" to the call option.

The Black-Scholes model helped legitimize the Chicago Board Options Exchange (CBOE 2.17%), which began trading in 1973, around the time that Black and Scholes' paper was first published. In 2012, the CBOE transacted over 575 million call options and 535 million put options, which implied a total dollar volume worth $575 billion.

However, this is only a small slice of the total value of financial derivatives traded around the world. Deutsche Borse estimates that the worldwide derivatives market has grown at an annualized rate of 24% per year for the past quarter-century, but this, too, may understate the staggering scope of the worldwide derivatives market. Prior to the financial crisis, the notional value of this market reached an estimated $600 trillion. Five years after the crash ended, some new estimates place the total value of global derivatives at $1 quadrillion. For a sense of the sheer size of that much money were it ever made manifest, picture a tower of $100 bills, about two-thirds of a mile high. That's $1 billion. A quadrillion dollars in stacked $100 bills would be nearly three times as tall as the distance from the Earth to the moon. In slightly more earth-bound terms, $1 quadrillion is 15 times the size of the entire world's annual gross domestic product. Under this simplistic measure, it's hard not to call the Black-Scholes model the most valuable mathematical model ever created.

Holding back the banks
President Dwight Eisenhower signed the Bank Holding Company Act, or BHCA, into law on May 9, 1956. This is a complex law that has undergone various policy shifts and legislative modifications over time in response to the changing conditions of the financial industry, but it continues to act as a foundational piece of financial-industry regulation to this day.

The Eisenhower era, though somewhat more conservative than the New Deal era it supplanted, retained a fundamental distrust of high finance that had colored national perceptions since the Great Depression. It was in this spirit that the BHCA became law. The BHCA effectively barred bank holding companies from expanding across state lines, and also restricted these institutions from engaging in most non-banking activities. Prior to this, the holding company structure would have allowed banks to evade most geographical or commercial restrictions in a rather blatantly transparent way.

Although the scope of acceptable banking activities was gradually expanded over time, it was not until the Rigele-Neale Act of 1994 that interstate banking restrictions were fully lifted. The Gramm-Leach-Bliley Act of 1999 removed many restrictions on allowable banking activities, leading to a wave of industry consolidation that had already begun with the technically illegal-at-the-time 1998 Citigroup merger. The BHCA remained in force as a barrier between banking and pure commerce.

The BHCA saw renewed interest after the recent financial crisis. Saule Omarova and Margaret Tahyar discuss this revival in "That Which We Call a Bank," an article published in 2011:

The financial crisis of 2007-09 brought the seemingly obsolete statute to the forefront of regulatory reform. The key piece of post-crisis reform legislation, the Dodd-Frank Act, effectively expands the BHCA model of regulation and supervision, with some modifications, to all financial institutions designated as "systemically important" and thus subject to consolidated supervision by the Federal Reserve. ...

[T]he post-crisis reform is reinventing the BHCA, which was originally intended primarily to guard against the perceived dangers of excessive concentration of financial and economic power and the emergence of diversified financial-industrial conglomerates, as the basic infrastructure for systemic risk regulation across the entire financial services sector. In effect, the BHCA regulatory regime is being adopted for a variety of financial institutions other than traditional BHCs. To what extent this approach to systemic risk regulation will be effective in practice remains to be seen.

It's worth noting that the Dow Jones Industrial Average (^DJI) enjoyed a period of impressive growth from the time of the BHCA's passage, to the passage of Gramm-Leach-Bliley, with annual gains of 7.4%. This can't be laid solely at the feet of stringent banking regulations, since plenty of other notable economic events happened during the latter part of the 20th century -- but it's also worth noting that, even after the post-crisis recovery is taken into account, the Dow's annualized growth rate during the Gramm-Leach-Bliley era (to the present day) has been just 2.5%.

Building the brand
A year after incorporating Pacific Aero Products in Seattle, William Boeing (BA -0.03%) changed the name of his aircraft manufacturing company to Boeing Airplane Company on May 9, 1917, to better reflect his high personal stake in building it. The newly rechristened Boeing made its first sale two months later, when the U.S. Navy ordered 50 trainer seaplanes, thus launching what would become the aviation industry's most important and most durable company.

By the end of Boeing's first decade under its new name, the company had gained numerous military contracts and was also expanding into airmail and passenger transport. In the 1930s, Boeing became a near-monopoly in aviation under the United Aircraft and Transport Company, which contained aircraft manufacturing operations of all stripes as well as a national passenger airline. After an act of Congress barred the combination of aircraft manufacturing and air transport under the same corporate umbrella, the company split back into its major components. Boeing assumed manufacturing operations in the west, United Technologies -- originally United Aircraft -- took control of the monopoly's eastern plants, and the national airline became United Air Lines.

Fool contributor Alex Planes has no position in any stocks mentioned. The Motley Fool owns shares of Citigroup Inc. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.

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