“Speculative Influence Network” During Financial Bubbles: Application To Chinese Stock Markets

L. Lin

School of Business, East China University of Technology and Science, 200237 Shanghai, China

Research Institute of Financial Engineering, East China University of Technology and Science, 200237 Shanghai, China

D. Sornette

ETH Zurich, Department of Management, Technology and Economics, Scheuchzerstrasse 7, CH-8092 Zurich, Switzerland

Swiss Finance Institute, c/o University of Geneva, 40 blvd. Du Pont d’Arve, CH 1211 Geneva 4, Switzerland

Abstract:

We introduce the Speculative Influence Network (SIN) to decipher the causal relationships between sectors (and/or firms) during financial bubbles. The SIN is constructed in two steps. First, we develop a Hidden Markov Model (HMM) of regime-switching between a normal market phase represented by a geometric Brownian motion (GBM) and a bubble regime represented by the stochastic super-exponential Sornette-Andersen (2002) bubble model. The calibration of the HMM provides the probability at each time for a given security to be in the bubble regime. Conditional on two assets being qualified in the bubble regime, we then use the transfer entropy to quantify the influence of the returns of one asset i onto another asset j, from which we introduce the adjacency matrix of the SIN among securities. We apply our technology to the Chinese stock market during the period 2005-2008, during which a normal phase was followed by a spectacular bubble ending in a massive correction. We introduce the Net Speculative Influence Intensity (NSII) variable as the difference between the transfer entropies from i to j and from j to i, which is used in a series of rank ordered regressions to predict the maximum loss (%MaxLoss) endured during the crash. The sectors that influenced other sectors the most are found to have the largest losses. There is a clear prediction skill obtained by using the transfer entropy involving industrial sectors to explain the %MaxLoss of financial institutions but not vice versa. We also show that the bubble state variable calibrated on the Chinese market data corresponds well to the regimes when the market exhibits a strong price acceleration followed by clear change of price regimes. Our results suggest that SIN may contribute significant skill to the development of general linkage-based systemic risks measures and early warning metrics.

“Speculative Influence Network” During Financial Bubbles: Application To Chinese Stock Markets – Introduction

It is widely recognized that the backdrop of almost every proceeding financial bubble is the prevalence of speculative mania, which causes valuation to drift out of whack, associated with a reinforcing imbalance between the size of unrealized supply and demand intentions, which forms the genesis of the potential market collapse. Speculative mania is by and large embodied in a variety of herding behaviors when investors imitate and follow other investors’ strategies while tending to suppress their own private information and beliefs (Devenow and Welch, 1996; Avery and Zemsky, 1998). Such imitation can be either rational or irrational. Rational herding results from different possible mechanisms, such as (i) the anticipation by rational investors concerning noise trader’s feedback strategies (Long et al., 1990), (ii) Ponzi schemes resulting from agency costs, (iii) monetary incentives given to competing fund managers (Dimitriadi, 2004; Dass et al., 2008) and (iv) rational imitation in the presence of uncertainty (Roehner and Sornette, 2000). In contrast, irrational herding is driven by market sentiment (Banerjee, 1992), fad (Bikhchandani et al., 1992), informational cascades (Barberis et al., 1998), ‘word-of-mouth’ effects from social imitation or influence (Shiller, 2000; Hong et al., 2005) or irrational positive feedback trading from extrapolation of past growth rate (Lakonishok et al., 1994; Nofsinger and Sias, 1999).

The challenge of diagnosing bubbles can thus be reduced to the detection and characterization of the regularities associated with herding effects in real time, with the goal of predicting the potential upcoming regime-shift and possible large sell-off resulting from their evolution. Most existing analyses have emphasized herding of the overall market, considering that investors tend to synchronize their behavior across the whole investment horizon. Accordingly, methods to detect bubbles have been focused mostly on representations of the whole market performance, in general by using market indices. The rationale is that, during bubble regimes when widespread speculative behavior is prevalent, individual stocks tend to become cross-sectionally more tightly correlated in their behavior and follow the general market dynamics. Notwithstanding this fact, the focus on market indices rather than the constituting individual stocks is bound to overlook endogenous structures of herding within the universe of stocks (see e.g. Sias (2004), Choi and Sias (2009)) and could potentially miss useful patterns associated with the dynamics of speculation during the bubble build up. In particular, the financial crisis of 2008 that followed a large bubble regime (Brunnermeier and Oehmke, 2013; Sornette and Cauwels, 2014) suggests that there is important information for the development of systemic risk metrics imbedded in the study of speculative bubble behavior in disaggregated industrial or firm level.

Speculative Influence Network

This paper presents an extension of more conventional bubble diagnosing methods by breaking down the structure of investment herding into its individual firm components. For this, we introduce the novel concept of the Speculative Influence Network (SIN), defined as a directional weighted network representing the causal speculative influencing relationships between all pairs of investment targets. In other words, we quantify how speculative trading in one asset may draw speculative trading in other asset. Here, we will focus on stocks, but the method is more generally applicable to any basket of assets. Specifically, we first estimate in real time the probability of speculative trading in each stock in the basket of interest, using a bubble identifying technique that was introduced for whole market indices but that we now extend to individual stocks. The strength of the bubble at the level of a single stock may increase or fade multiple times during the development of a global market bubble, perhaps due to particular idiosyncratic properties of the firm and of the corresponding industrial sector. The Hidden Markov Modeling (HMM) approach, which is specially designed to calibrate regime-switching processes, is thus a convenient methodology to make our bubble detection approach at the individual stock level more robust. Once we have characterized the subset of stocks being qualified in a bubble regime, we calculate the Transfer Entropy (TE), which is a measure developed in Information Science to quantify the casual relationship between variables. The underlying intuition behind this method is that, if a stock Y exhibits a strong speculative influence on another stock X, then the existence of speculative trading of X can be predicated on the evidence of speculative trading on Y. In the language of Information Science, there is an information flow from Y towards X, which is quantified by the entropy transfer from Y to X.

The essential first step is of course to detect the presence of a bubble. For this, we borrow from the simple and generic prescription that a bubble is a transient regime characterized by faster-than-exponential (or super-exponential) growth (see e.g. (Husler et al., 2013; Kaizoji et al., 2015; Leiss et al., 2015; Sornette and Cauwels, 2015; Ardila-Alvarez et al., 2015) for recent empirical tests and models). The “super-exponential” behavior results from the existence of

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