Log Periodic Power Analysis of Critical Crashes: Evidence from the Portuguese Stock Market

The study of critical phenomena that originated in the natural sciences has been extended to the financial economics’ field, giving researchers new approaches to risk management, forecasting, the study of bubbles and crashes, and many kinds of problems involving complex systems with self-organized criticality (SOC). This study uses the theory of self-similar oscillatory time singularities to analyze stock market crashes. We test the Log Periodic Power Law/Model (LPPM) to analyze the Portuguese stock market, in its crises in 1998, 2007, and 2015. Parameter values are in line with those observed in other markets. This is particularly interesting since if the model performs robustly for Portugal, which is a small market with liquidity issues and the index is only composed of 20 stocks, we provide consistent evidence in favor of the proposed LPPM methodology. The LPPM methodology proposed here would have allowed us to avoid big loses in the 1998 Portuguese crash, and would have permitted us to sell at points near the peak in the 2007 crash. In the case of the 2015 crisis, we would have obtained a good indication of the moment where the lowest data point was going to be achieved.

Does Momentum Trading Generate Extra Downside Risk?

Momentum strategies tend to provide low returns during market crashes, and they crash themselves when the market rebounds after significant crashes. This is reflected by positive downside market betas and negative upside market betas of zero-cost momentum portfolios. Such asymmetry in upside and downside risks is unfavorable for investors and requires a risk premium. It arises mechanically because of momentum portfolio rebalancing based on trailing asset performance. The asymmetry in upside and downside risks is a robust unifying feature of momentum portfolios in various geographical and asset markets. The momentum premium can be rationalized within a standard asset-pricing framework, where upside and downside risks are priced differently.

Crash Diagnosis and Price Rebound Prediction in NYSE Composite Index Based on Visibility Graph and Time-Evolving Stock Correlation Network

This study proposes a framework to diagnose stock market crashes and predict the subsequent price rebounds. Based on the observation of anomalous changes in stock correlation networks during market crashes, we extend the log-periodic power-law model with a metric that is proposed to measure network anomalies. To calculate this metric, we design a prediction-guided anomaly detection algorithm based on the extreme value theory. Finally, we proposed a hybrid indicator to predict price rebounds of the stock index by combining the network anomaly metric and the visibility graph-based log-periodic power-law model. Experiments are conducted based on the New York Stock Exchange Composite Index from 4 January 1991 to 7 May 2021. It is shown that our proposed method outperforms the benchmark log-periodic power-law model on detecting the 12 major crashes and predicting the subsequent price rebounds by reducing the false alarm rate. This study sheds light on combining stock network analysis and financial time series modeling and highlights that anomalous changes of a stock network can be important criteria for detecting crashes and predicting recoveries of the stock market.

Statistical properties of the aftershocks of stock market crashes revisited: Analysis based on the 1987 crash, financial-crisis-2008 and COVID-19 pandemic

During any unique crisis, panic sell-off leads to a massive stock market crash that may continue for more than a day, termed as mainshock. The effect of a mainshock in the form of aftershocks can be felt throughout the recovery phase of stock price. As the market remains in stress during recovery, any small perturbation leads to a relatively smaller aftershock. The duration of the recovery phase has been estimated using structural break analysis. We have carried out statistical analyses of 1987 stock market crash, 2008 financial crisis and 2020 COVID-19 pandemic considering the actual crash times of the mainshock and aftershocks. Earlier, such analyses were done considering absolute one-day return, which cannot capture a crash properly. The results show that the mainshock and aftershock in the stock market follow the Gutenberg–Richter (GR) power law. Further, we obtained higher [Formula: see text] value for the COVID-19 crash compared to the financial-crisis-2008 from the GR law. This implies that the recovery of stock price during COVID-19 may be faster than the financial-crisis-2008. The result is consistent with the present recovery of the market from the COVID-19 pandemic. The analysis shows that the high-magnitude aftershocks are rare, and low-magnitude aftershocks are frequent during the recovery phase. The analysis also shows that the inter-occurrence times of the aftershocks follow the generalized Pareto distribution, i.e. [Formula: see text], where [Formula: see text] and [Formula: see text] are constants and [Formula: see text] is the inter-occurrence time. This analysis may help investors to restructure their portfolio during a market crash.

FINANCIAL RISKS AND STOCK MARKET CRASHES: AN EMPIRICAL ANALYSIS OF THE TUNISIAN STOCK MARKET

This study aims to investigate the effect of financial risks on the stock market crashes occurrence from 1999 to 2020. Using the windows method, we detect two stock market crises in the Tunisian stock market. Based on the probit model, we find evidence that low stock return risk, low EUR/TND exchange rate risk, high interest rate risk, high credit risk and high liquidity risk increase the occurrence probability of stock market crashes. Our results suggest that the decrease in volatility, particularly in equity and exchange market, the increase in volatility in interest rate, the credit rating downgrades issued by Moody’s and the low liquidity market contribute to crashes in the Tunisian stock market. In summary, financial risks, which are the market risks, the credit risk and the liquidity risk could be leading indicators of crashes in the Tunisian stock market. Keywords: Stock market crashes; Liquidity risk; Credit risk; Market risks.

Using Topological Data Analysis (TDA) and Persistent Homology to Analyze the Stock Markets in Singapore and Taiwan

In recent years, persistent homology (PH) and topological data analysis (TDA) have gained increasing attention in the fields of shape recognition, image analysis, data analysis, machine learning, computer vision, computational biology, brain functional networks, financial networks, haze detection, etc. In this article, we will focus on stock markets and demonstrate how TDA can be useful in this regard. We first explain signatures that can be detected using TDA, for three toy models of topological changes. We then showed how to go beyond network concepts like nodes (0-simplex) and links (1-simplex), and the standard minimal spanning tree or planar maximally filtered graph picture of the cross correlations in stock markets, to work with faces (2-simplex) or any k-dim simplex in TDA. By scanning through a full range of correlation thresholds in a procedure called filtration, we were able to examine robust topological features (i.e. less susceptible to random noise) in higher dimensions. To demonstrate the advantages of TDA, we collected time-series data from the Straits Times Index and Taiwan Capitalization Weighted Stock Index (TAIEX), and then computed barcodes, persistence diagrams, persistent entropy, the bottleneck distance, Betti numbers, and Euler characteristic. We found that during the periods of market crashes, the homology groups become less persistent as we vary the characteristic correlation. For both markets, we found consistent signatures associated with market crashes in the Betti numbers, Euler characteristics, and persistent entropy, in agreement with our theoretical expectations.