A statistical analysis of the Chinese stock market bubble


  • Author: Dr John Fry
  • Date: 06 Oct 2015
  • Copyright: Image appears courtesy of Getty Images

The recent Chinese stock market crash began in June earlier this year [1]. Within the space of one month, shares on the Shanghai Stock Exchange had lost a third of their value. During a subsequently lengthy period of market turbulence, there were also large stock market losses as recently as August 24-25th – labelled Black Monday and Black Tuesday respectively [1].

As the world’s second largest economy and the world’s most populous country, China is clearly very important globally. Recent events have raised fears of knock on consequences – especially if recent stock market losses lead to a subsequent devaluation of the Chinese yuan. A major source for concern is that this would then result in significantly reduced Chinese demand for manufactured goods – especially luxury goods [1]. A particular worry in the United Kingdom is how reduced numbers of Chinese students may affect the nation’s internationally renowned Higher Education sector [2]. Though these fears may be well founded, the immediate consequences of stock market falls in China remain unclear.

thumbnail image: A statistical analysis of the Chinese stock market bubble

How might we make a quick assessment of this issue using an elementary statistical analysis? A Granger causality test can be used to see if the stock market price has an effect upon the number of students once the size of the previous year’s cohort has been taken into account. A Granger Causality test gives no evidence (p=0.888) that Chinese stock prices on the opening day in September affects the number of Chinese students studying in the United Kingdom. So it perhaps seems unlikely that the number of Chinese students studying in the United Kingdom will decrease dramatically, at least in the short term.

In the year leading up to the crash and encouraged by a media frenzy, enthusiastic investors flocked to the market and, often using borrowed money, helped to inflate the bubble [1, 3-4]. This reinforces an important social dimension to many financial bubbles [5]. The upsurge in prices far exceeded the rate of economic growth and profits in the underlying companies. The consequences were dramatic. As investors faced margin calls on their stock holdings, many were forced to sell off their shares in droves, precipitating the crash [1].

A plot of the closing prices of the Shanghai Stock Exchange (SSE) Composite Index is shown below in Figure 1 and shows a dramatic increase from the summer of 2014 onwards. Some commentators see the bursting of the Chinese bubble as inevitable. An article by The Independent [4] sees the bursting of the Chinese stock market bubble as inevitable due to the sheer scale of the price rises involved, the lack of education amongst many Chinese investors, the volatility of the market (labelled by [4] as the worst outside of Greece), the disconnection between Chinese stocks and the real economy, and the fact that much of the boom had been fuelled by borrowing. These considerations lead one to ask if there is any statistical basis for assessing whether or a crash was inevitable?

Figure 1: Daily closing prices of the Shanghai Composite Index January 2014-May 2015 inclusive

In line with wider financial and economic contexts a statistical model was developed in [6] to provide a description of unsustainable super-exponential growth in market prices. Approximate exponential growth is common to many financial and economic time series. If a price series grows faster than this, then it is an indication that the observed level of growth is ultimately unsustainable. Under the model in [6], economic risks have the effect of pushing up prices during the bubble. However, under this model the same risks also have the effect of reducing the instantaneous volatility. This means that during a bubble, a naïve statistical analysis of historical data is liable to under-estimate the true level of risk involved.

Several articles (see e.g. [1, 4]) highlight the effects of the speculative frenzy in the year leading up to the crash. As a result using the model in [6] and data from June 2014 to the end of May 2015, we found significant evidence p=0.000 of a speculative bubble. The model in [6] also suggests that the bubble accounts for around 27.5% of the observed historical prices. This compares with a fall of around 1/3 in the month following the onset of the crisis [1] and a fall of 38.9% comparing the market high of 5166 [3] to the current value of 3156.54 (correct at the time of writing).

A study of financial history suggests future crises are inevitable. The evocatively titled book [7] identifies various crises dating as far back as the default of Dionysius of Syracuse in Greece in the Fourth Century BC. During boom periods, over-confident investors over-estimate the true extent of the returns available – neglecting the true level of risk involved. Sadly, these new developments are rarely “as different” as previously thought and the bubble eventually bursts. It is particularly striking to note that the contemporary tales of stock speculation in China using borrowed funds appear to be qualitatively very similar to the 1929 Wall Street crash.

It is particularly striking to note that the contemporary tales of stock speculation in China using borrowed funds appear to be qualitatively very similar to the 1929 Wall Street crash.

Allied to the above China also incorporates some of the classic ingredients of past bubbles and crashes such as rapid technological progress and an influx of new investors into the market [8].

Whilst the historical comparisons are compelling, there are also some China specific factors that are worthy of consideration. China’s stock market has been described as being simultaneously the world’s largest and yet one of the world’s weakest and most volatile [4]. Previous boom-bust episodes have been documented as recently in 2001 and in 2008 [9]. In [9] it is argued that psychological reasons mean that China is especially prone to stock market bubbles. The reasons given include the unique opportunity that the stock markets provide to people who have previously been unable to become rich, too many under-qualified investors taking part for fear of missing out on a unique opportunity to make money, and the relatively few options available to Chinese investors. China thus shares qualities of other stock markets in the region, such as Hong Kong’s Hang Seng, which have been labelled by commentators as especially prone to bubbles and crashes [10].

Additional challenges remain due to China’s sheer size and the increasingly integrated nature of the global economy. This occurs alongside wider uncertainties about political and economic reforms as China’s government seeks to manage the transition from a purely socialist command economy to an economy that is at the same time both partially socialist and partly capitalist [3].

Stock markets are inherently risky. A series of both historical and China-specific factors mean that this is especially true for the Chinese stock market. As they respond to the recent crisis, the Chinese authorities undoubtedly face a very challenging situation. In the short term the global consequences of the bursting of the Chinese stock market bubble are unclear. In the long-term, economic crises in China may prove to be more serious in the future. All that can be certain is that the study of financial history points to one unassailable truth. Globally significant stock market crashes will continue to occur in the future.

[1] 2015 Chinese stock market crash. Wikipedia https://en.wikipedia.org/wiki/2015_Chinese_stock_market_crash  
[2] Matthews, D. (2015) Does China’s crash signal crisis for the UK? Times Higher Education 2219 (3-9 September 2015) 20-21.
[3] Schell, O. (2015) Why China’s stock market bubble was always bound to burst. The Guardian. http://www.theguardian.com/world/2015/jul/16/why-chinas-stock-market-bubble-was-always-bound-burst  
[4] China stock market: Five facts that show how the bubble arose – and why it might be bursting. The Independent.
[5] Kindleberger, C. M. and Aliber, R. (2005). Manias, panics and crashes; A history of financial crises, fifth edition. Hoboken, New Jersey: Wiley.
[6] Fry, J. (2014) Multivariate bubbles and antibubbles. European Physical Journal B 87, 174
[7] Reinhart, C. M., and Rogoff, K., 2009. This time it's different. Eight centuries of financial folly. Princeton: Princeton University Press.
[8] Zeira, J., 1999. Informational overshooting, booms and crashes. Journal of Monetary Economics 43, 237-257
[9] Yao, S. and Luo, D. (2009) The economic psychology of stock market bubbles in China. The World Economy 32, 667-691
[10] Sornette, D. (2003) Why stock markets crash: critical events in complex financial systems. Princeton: Princeton University Press.

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