How major market crashes around the world can be quantitatively explained.
The Chinese art and calligraphy market has been on fire. Between 2000 and 2011, the market, represented by the Chinese Painting 400 Index, gained more than 700%, or about 21% per year. More impressively, it gained about 353% from June 2009 to June 2011.
Do these kinds of extreme gains seem familiar? We have witnessed many similar asset-price bubbles. The story is the same. Positive feedback and herding among speculative investors produce runaway prices until the deviation from equilibrium is so large that the market becomes unstable, creating a high probability (or an inevitability) of a crash.
This is clearly happening in the Chinese art market. There’s certainly herding behavior and positive feedback among Chinese art investors. The past decade’s economic boom has created new wealth in China and rising demand for Chinese fine art and calligraphy, driving up prices. Increasing prices in turn attract more art investors and speculators, who are desperate to join the party. They see past price apprecia- tions and become very confident that they, too, can sell their art at higher prices than what they paid for them. And so it goes, on and on.
But when will this mania for Chinese art end? More important for us, do the Chinese art-market boom and other asset-price bubbles share the same characteristics, and do all bubbles originate in the same manner? If yes, can we identify these factors beforehand and predict when a bubble will burst?
Herd Behavior and Market Bubbles
A number of studies have considered herd behavior as a possible explanation for the excessive volatility observed in financial markets (such as Bannerjee, 1992; Topol, 1991; and Shiller, 1989).
The thinking behind this approach is simple: Interaction of market participants through herding can lead to large fluctuations in aggregate demand, leading to heavy tails in the distribution of returns. In the popular literature, “crowd effects” often have been associated with large fluctuations in market prices of financial assets.
Shiller (2000) provides massive evidence to support his argument that “irrational exuber- ance” played the role in producing the ups and downs of the stock and real estate markets. He listed 12 precipitating factors that gave rise to the booms in the stock markets and housing markets. These factors are amplified via feedback loops and naturally occurring Ponzi schemes, aided by the media, and can ultimately lead to market crashes.
Shiller also demonstrates that psychological factors, such as herd behavior and epidemics, are exerting their important effects. For example, the influence of authority over people can be enormous; people are ready to believe authorities even when they plainly contradict matter-of-fact judgment.
He cites many other factors, including that people tend to follow other people and choose not to exercise their own judgment about the market and that most people purchase stocks based on direct interpersonal communication instead of independent research.
Cont and Bouchaud (2000) provide a math- ematical model to link two well-known market phenomena: the heavy tails observed in the distribution of stock market returns on one hand and herding behavior in financial markets on the other hand.
In the 1990s, two groups of researchers (Sornette, Johansen, and Bouchaud, 1996; and Feigenbaum and Freund, 1996) independently discovered an apparent tendency of stock prices to exhibit log-periodic power laws before a crash. The fundamental hypothesis of the model is that financial crashes are macroscopic examples of critical phenomena. A critical phenomenon indicates a highly correlated unstable market. In other words, as some traders say, “In a market crisis, all correlations jump to one.”
Collective behaviors in people emerge through the forces of imitation, which leads to herding. Herding behavior of investors can result in a significant deviation of financial prices from their fundamental values. A speculative bubble, which is caused by a positive feedback investing style, also leads to a faster-than- exponential power law growth of prices (Sornette, 2003). The competition between such nonlinear positive feedbacks and negative feedbacks contributes to nonlinear oscillations. For example, technical investors who have a positive view of the market bid up prices at the expense of fundamental investors, who view the market as ridiculously overpriced. The result is that a log-periodic modulation of the price accelerates up to the crash point.
Like any other models, the LPPL model has been debated and challenged, and we will not attempt to discuss them here. Major stock market crashes around the world, however, can be quantitatively explained by this model. These crashes include the 1929 crash, the 1987 crash, the crash of the Russian market in 1998, the 1990 Japanese Nikkei Index crash, several Hong Kong crashes in the 1990s, the Internet bubble crash in 2000, and more than 20 emerging-markets crashes. All of these market bubbles appeared to show the similar LPPL before they crashed.
Chinese Stock Market Crash of 2007
Greed and fear are rooted in human nature, so it’s unlikely people will change anytime soon. Greediness and fear also drive herding and positive feedbacks, so investors should expect these factors to remain in markets. The latest herding example occurred not too long ago, in 2007. In particular, we’ll look at the Chinese stock market crash.
We use the Shanghai Stock Exchange Composite Index to represent the Chinese stock market. The Chinese stock market is dominated by individual investors, unlike equity markets in developed countries where a form of polariza- tion between individual and institutional investors is evident. Millions of new Chinese small investors had been flooding into the booming Chinese stock market from 2005 to 2007, indicating a strong herd behavior. The bubble burst in October 2007. A year after the crash, the Shanghai Composite had lost about 64% of its value. It was a classic example of herd behavior leading to market crash in an emerging market.
Using the LPPL model, Exhibit 1 shows that the Chinese stock market crash in 2007 was predictable. The green line charts the price of the index. The blue line is the calculated curve based on the LPPL model. The out-of-sample test was made on Sept. 25, 2007. The model predicted a crash date of Sept. 5, 2007. The actual crash started Oct. 17, 2007, 42 days later than predicted. The time-series price index is reasonably fitted by the log-periodic power law model; we can see the precursors of log-periodic oscillations before the crash occurred.
Nasdaq Crash of 2000
History provides many examples of bubbles driven by unrealistic expectations of future earnings. These types of bubbles just don’t occur in developing markets. As proof, we have the Nasdaq crash of 2000.
The Nasdaq Composite Index consists mainly of technology stocks, such as Internet, e-com- merce, software, computer hardware, and telecommunications names. When Nasdaq reached its historical high at 5,133 in March 2000, many stocks were trading at fourdigit price/earnings ratios. Brocade Communications Systems BRCD, for example, sported a P/E of 6,185; Trend Micro ADR TMIC had a P/E of 4,350; and SeaChange International SEAC traded at a P/E of 3,765. Investors in these companies undoubtedly expected high future earnings from these stocks and completely ignored their economic fundamentals.
Exhibit 2 shows the bubble phase of the Nasdaq. The orange line stands for the price of the index. The blue line is based on the LPPL model. Again, the model clearly picked up the signals of an impending crash and almost perfectly predicted it.
Chinese Art Crash of 2012
Let’s return to our Chinese art-market bubble. In it, can we identify the same LPPL signature indicating a potential crash that we could see in the two other bubbles we discussed?
The Chinese Painting 400 Index is based on the Chinese art and calligraphy auction market and reflects the prices of the most influential 400 Chinese artists and calligraphers in ancient, modern, and contemporary China. The yellow line in Exhibit 3 shows the growth of the Chinese Painting 400 Index since 2000. The blue line is the calculated curve based on the LPPL model. It predicts the crash date in June 2011. In other words, the Chinese art market already has entered its critical crash stage.
We first ran the model in May using all of the available information up to December 2011. At the point, the index had lost 5.4% in the two prior quarters. The model predicted larger losses in the coming quarters. At the end of June, we received the latest art index data. For the trailing year, the Chinese Painting 400 Index had lost 30.1%. The Chinese art-market bubble has indeed sprung a huge leak. Like with many other market bubbles, the logperiodic power law model successfully predicted the crash of the Chinese Painting 400 Index.
Power of the Model
We showed that three recent market bubbles displayed the same LPPL signature before they crashed. Our analyses indicate that all the bubbles have the same origins and similarly move toward a crash.
Positive feedback and herding produce runaway prices until the deviation from equilibrium is so large that the market is unstable and has a high probability to crash. When the stock price accelerates at a much faster rate than exponential growth rate, the skyrocketing return will always come with an increased crash hazard rate.
Financial markets are complex systems. In such systems, a speculative bubble can easily be created through positive feedback. What is more challenging is that, as complex systems grow, two things happen (Rickards, 2011). These systems require exponentially greater amounts of energy to keep operating, and they become vastly more risky and prone to catastrophic failure.