Dr Austin Gerig believes that by following the approach physicists rely on to describe the workings of the universe, economists may be able to uncover universal principles that explain economic phenomena, and even predict extreme economic events. Perhaps we’ll see the next GFC coming.

‘The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction.’ Albert Einstein, 1918.

When researching the natural world, physicists often search for universal laws to explain the systematic working of things. It is an approach that has served them well, but is it one that can transfer to other disciplines? Are there universal laws, for example, that underlie economic systems, and should economists search for such laws?

I believe the answer is yes. I believe there are regularities in social and economic systems that result from universal underlying principles (if not universal laws) and that one task of the economist – perhaps the most important one – is to find these regularities and understand the principles behind them.

As an example, consider the way that prices move in financial markets.

Over a century ago, French mathematician Louis Bachelier proposed that stock prices move up or down in random increments and that price changes are unpredictable. This is called the random walk model for stock prices.

When tested with economic data – real stock prices over time – the random walk model is surprisingly accurate. It holds not only for stock prices, but also for the prices of many other items: stock indices, derivative instruments, commodities and other economic goods, and even for the prices of contracts traded on prediction markets.

The regularity of this behavior across different items suggests some universal principle is behind it. In fact, many economists believe this is true, and they attribute the randomness of prices to the profit maximization (or loss aversion) of investors.

The theory says that if stock prices weren’t random, but were in some way predictable, this predictability would be quickly removed. After all, who would be willing to sell a stock for $90 if everyone knew the price was going to move up to $100? Wouldn’t sellers try to get something closer to $100 right now, and wouldn’t buyers be willing to pay something closer to $100? When these individuals push the price to $100, the predictability in the price movement is removed. If predictable price movements disappear, then the only way for prices to move is with random increments.

A second interesting regularity found in economic prices is that very large price movements, such as stock market crashes, occur frequently. Again, this is true for many different economic items.

To understand just how large these price movements are, consider what it would mean if human heights behaved in a similar way. Assume for a moment that adult human heights were not as they actually are, but instead varied between individuals in the same way that price movements vary. In your city, someone would probably be over 30 feet tall. In your country, the tallest person would likely reach 150 feet, and the tallest person in the world would stand over 1000 feet.

The distinction between human heights and price movements is important because most financial models assume that the distribution of stock returns is the same as the distribution pattern for human heights – the ubiquitous bell-shaped curve known as the normal (or Gaussian) distribution. If this were the case, very large returns (analogous to a 150 foot person) should never occur. But this is wrong. For reasons we do not fully understand, stock returns are not distributed according to a normal distribution. Instead, they have a much larger peak and the ‘tails’ or extremes of the distribution are thicker. This means that large price movements occur more often than predicted.

 

Figure 1 shows the distribution for the daily returns of the S&P 500 stock index from January 3, 1950 to November 25, 2009. (This plot uses publicly available data and can be replicated by downloading data here). The horizontal axis measures the different sizes of returns (0.02 is a 2% return, 0.04 is a 4% return, etc.). The vertical axis shows the relative likelihood of these price changes – the higher the red bar, the more likely that event is observed. Small returns, close to zero, are the most likely occurrence. A normal distribution is also shown in the figure – it is the blue line.

The inset plot shows the probability that a daily return is above a certain threshold value. It enlarges the tail of the distribution – the area where large price returns are recorded. You can see that the probability of large returns is much higher than what normal distribution predicts, i.e., the red curve is above the blue curve for large values of x. The five highest returns, their values, and the dates they were observed are highlighted. Not surprisingly, the largest return occurred on Black Monday, October 19, 1987, when stock markets crashed around the world.

If you look at the y-axis in the inset plot, the probability for a daily return to exceed 10% is around 10-4. This means it has happened approximately once every 40 years. For comparison, the blue curve – a normal distribution – predicts this to happen once every 7×1018 years, which for all practical purposes means never.

One way to explain the discrepancy between observed stock returns and financial models is to consider large price movements as outliers – surprising events outside of the normal model. There are several reasons to do this. First, there are good underlying reasons to assume a normal distribution for returns as a first guess, and no one has yet developed a theory for why it should be otherwise. Second, we usually explain large price movements in this way – stock markets crashed because computer trading malfunctioned or the global financial crises occurred because banks made large mistakes. With these explanations, we implicitly suggest that they are one-time events – outliers – that can be accounted for and controlled in the future. The problem is, despite our efforts, they keep happening.

An alternative explanation is that something more fundamental is causing these events – perhaps an elementary principle underlies the existence of extreme price movements. There are several reasons to believe this is true. First, these events occur universally across traded items. I’m unaware of any economic price series that does not exhibit this property. Second, the empirical evidence does not show these events as statistical outliers. You can see this for the S&P 500 index in the inset plot where the red curve extends continuously in a uniform way down to the points where extreme price movements are recorded. These points do not exist by themselves but fit nicely where you’d expect them when extrapolating the red curve from smaller price movements. Finally, there is evidence that price returns for different stocks all deviate from the normal distribution in the exact same way.

Figure 2 shows this result for six stocks that are traded on the New York, London, and Madrid stock exchanges. This data is not all from the same time period. By appropriately rescaling the axes for each stock, the distributions collapse on the same non-normal curve. Why would these unrelated price series all behave in the exact same way unless something fundamental was the cause?

As I mentioned, I believe there are regularities in social and economic systems that can be explained by universal principles. The regularity of economic price movements is one example. The reason why prices are random is understood – it occurs because individuals are profit maximizing. The reason prices deviate from a normal distribution is not understood and is currently a matter of much debate. I believe the evidence suggests that some universal mechanism underlies these deviations, and that large price movements are not outliers to an otherwise correct (normal) model. If this is true, the methodologies used in physics can help economists understand what is driving the result. If it is due to something such as human behavior or the way in which markets are structured, then there might be ways to curtail behavior or structure markets differently such that these extreme events do not occur. If it is due to some economic principle, then perhaps it is something we can only understand and better prepare for.

Dr Austin Gerig is a graduate of the University of Illinois at Urbana-Champaign. He joined the UTS School of Finance and Economics in December 2008 as a Post Doctoral Research Fellow. His research interests include theory of market impact, determination of optimal execution strategies, market making, and the origins of clustered volatility and extreme price movements.