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OPINION

Exploiting the world of differences

Exploiting the world of differences
February 17, 2022
Exploiting the world of differences

The economist Fischer Black hardly had a promising start to his academic career. He switched his PhD from physics to mathematics. When he tried flip-flopping again, this time from computing to artificial intelligence, Harvard lost patience and asked him to leave. His eventual doctorate in applied maths helped land him a role at the Massachusetts Institute of Technology, where he met Myron Scholes, whose doctorate was in economics. Until an operation had removed scar tissue from both his corneas, Scholes’s reading had been limited to short bursts, and during 10 difficult years, he’d trained himself both to listen and to solve problems through abstract thinking. Fusing that with Black’s silo-breaking intellect enabled the two to come up with a revolutionary equation. But there was a problem: it was too obscure. Nobody would publish it. 

Robert C Merton, an economist at MIT, shared their fascination with numbers, and he began playing around with the formula. What’s more, he found a publisher. All their work could easily have been attributed to him. But Merton wasn’t like that. He insisted that Black and Scholes publish first, and so the model that could have gone down in history as the Merton formula instead became known as Black-Scholes. 

Like so much of pure maths, its practical use was not immediately obvious.

 

The formula

The three claimed to have identified four financial components that influence market prices. For shares, these were: time, because the more time you have, the greater the chance of the share price hitting a peak; future dividends, because they reduce the value left in the company, which ought to dampen the share price; volatility, because you have a better chance of selling when prices are high with a yo-yo share price rather than a static one; and a “risk-free” anchor point, such as government stock, against which returns can be measured.

But how do these factors influence share prices? Weight their probabilities and relationships in a complex mathematical model and you have a formula that tells you the chances of a price going up or down relative to where it was. That’s what Black, Scholes and Merton published in 1973.

 

The impact

Banking was deregulated in the early 1980s, and that allowed mortgages to be sold to others, for bundling, slicing and dicing – and selling on. Black-Scholes helped price financial contracts when they still had time to run. If you bet on a horse, and then want to sell your bet halfway through the race, the equation indicates how much you should sell it for. It can be used to price share options – in their simplest form, this is when people buy the right to make a future purchase of a share at today’s price. 

The pricing of financial options enabled derivatives – essentially investments of investments, or bets on bets – to be developed, and as they became more complex, the new risks were offset by other complex derivatives. Everything appeared to be self-balancing. That increased credit, which would, for a quarter of a century, make people better off, courtesy of more economic growth than would otherwise have happened. 

Then options became a way of paying people. Cash-strapped US start-ups started ladling share options onto their employees as a substitute for large salaries, and this helped fuel the tech boom of the 1990s. At that time, options came for free, but brakes were put on UK companies via guidelines that limited their issue of new shares to employees to 10 per cent of the shares in issue over a rolling ten-year period. 

Fischer Black died in 1995, but Scholes and Merton became directors of a highly profitable hedge fund, Long Term Capital Management, which sought out pricing mismatches in the market. In 1997, they won the Nobel prize in economic sciences.  A year later, LTCM collapsed. The tech bubble popped in 2001, and in 2004, the accountants reined in employee share options with IFRS 2. 

This international standard requires companies to measure share-based payment awards, and charge them as an expense, thereby hitting profits. It treats the indicative measures of employee share options like employee benefits. Think insurance premiums: if the catastrophic event occurs, the past premium is not increased; and if the event does not happen, the premium is not refunded. So when the actual outcome of the option differs from the calculation that models like Black-Scholes produce, it’s not corrected for. Some companies adjust their earnings and cash flows. That’s controversial. 

In 2008, when the western world’s banking edifice came crashing down, Black-Scholes was the obvious scapegoat, even though many had known that its formula’s assumptions were open to debate. The model assesses price differences through a relative (not an absolute) measure, and its weakness as a tool remains its inability to account for the element of uncertainty – but then if options could be valued accurately, we’d know what share prices were going to do. And that will always be elusive.