Louis Bachelier wanted to become a mathematics professor, but the topic he chose for his doctoral dissertation, ‘The Theory of Speculation’, was considered to be disreputable among scientists and failed to attain the top score he would have needed. He died in 1946, practically unknown. However, his research turned out to be groundbreaking, as it laid the foundation of modern finance.
Reliance on the normal distribution
Mr Bachelier was the first to apply probability theory to capital markets. He used the normal distribution, the ‘bell-shaped curve’, put forward by Carl-Friedrich Gauß, to describe the evolution of stock prices. The distribution is ‘normal’ in that it does not allow for dramatic extremes. Consequently, dramatic price movements are virtually impossible in Mr Bachelier’s world. Given the level of knowledge at that time, the normal assumption was a reasonable assumption. It has since become clear, however, that financial markets are far from ‘normal’.
If the normal assumption was correct, the Dow Jones should experience a daily loss of more than 5% roughly once every 3,500 years. In reality, such a steep drop happens almost every 20 months. On Black Monday in October 1987, the index fell by more than 20% - an unthinkable event according to the normal distribution.
Why do financial professionals rely on such outdated theories?
Mr Bachelier’s additional assumption that ups and downs are completely unrelated over time turned out to be a crude simplification. Over the last 50 years we have learned that, if prices crash today, markets tend to remain turbulent in the following periods. So why do portfolio managers still rely on such antiquated models that ignore such facts?
Understanding what happened to Mr Bachelier’s ideas might help to shed some light on this conundrum. After gathering dust for a few decades, Mr Bachelier’s work began to gain momentum and eventually triumphed across finance. Harry Markowitz, an economist, used it in the 1950s to establish formulas, now referred to as ‘Modern Portfolio Theory’ (MPT). This promised portfolios with optimal risk-return characteristics.
Mr Markowitz wasn’t the only one using Mr Bachelier’s simplifying assumptions. So did Paul Samuelson, when formulating his stock price model in 1956 and Eugene Fama, who postulated the highly-regarded efficient market hypothesis in the seventies. Fischer Black, a physicist and Myron Scholes and Robert Merton, economists, developed a model for evaluating options, again relying on the same assumptions. They all received the Nobel Memorial Prize – except Mr Black, who had passed away by that time.
Providing mathematically elegant and convenient solutions to complex problems, MPT reached milestone after milestone, without ever overcoming the fundamental weaknesses of its assumptions. Professionals throughout the world using MPT to optimise portfolios unwittingly took on risks of an unknown dimension.
The consequences were disastrous. One major catastrophe happened in August 1998 when the US hedge fund Long-Term Capital Management (LTCM) lost more than half a billion dollars in just one day. One major cause was the dependence on Scholes and Merton who were principals at LTCM and whose option-pricing formula was heavily relied upon. The US Federal Reserve had to intervene and arranged a bailout with an injection of $3.6 billion.
The LTCM disaster revealed the deep cracks in the foundation of modern finance. 2008 marked further stunning wake-up calls. The breakdown of Bear-Stearns and the collapse of Lehman Brothers let global financial markets implode by about US$16tn that year. Portfolios constructed along Mr Markowitz’ theory went into freefall.
The bluff still works
Despite those events, the normal assumption continues to play a pivotal role in the financial services industry. It is just too convenient, mathematically. The formulas of Mr Markowitz et al. are good enough to bluff most clients, since few people understand the dangers lurking behind them.
The question remains: What does this imply for the investor? For one, investors should thoroughly scrutinise their investment managers; do they understand the limitations and dangers of their concepts and models? Can they successfully understand and manage market risk? The only way to do this reliably is to perform tens of thousands of risk scenarios on an ongoing basis, using so-called ‘Monte Carlo simulations’ that are based on realistic statistical assumptions. Financial risk simply cannot be assessed analytically using elegant formulas. Instead, a large number of plausible outcomes need to be generated and meaningfully evaluated. This can only be accomplished with smart data analytics and the right technology.
It's a bit like aviation. Would you jump aboard a jet plane designed in the 1950s? Would you trust a pilot who relies on a malfunctioning altimeter when crossing the Alps at night? Probably not. The same scepticism is in order when it comes to investment management.