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Register a new userFat Tails in Financial Return Distributions Revisited: Evidence from the Korean Stock Market
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This study empirically re-examines fat tails in stock return distributions by applying statistical methods to an extensive dataset taken from the Korean stock market. The tails of the return distributions are shown to be much fatter in recent periods than in past periods and much fatter for small-capitalization stocks than for large-capitalization stocks. After controlling for the 1997 Korean foreign currency crisis and using the GARCH filter models to control for volatility clustering in the returns, the fat tails in the distribution of residuals are found to persist. We show that market crashes and volatility clustering may not sufficiently account for the existence of fat tails in return distributions. These findings are robust regardless of period or type of stock group.
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We investigate the statistical properties of the correlation matrix between individual stocks traded in the Korean stock market using the random matrix theory (RMT) and observe how these affect the portfolio weights in the Markowitz portfolio theory. We find that the distribution of the correlation matrix is positively skewed and changes over time. We find that the eigenvalue distribution of original correlation matrix deviates from the eigenvalues predicted by the RMT, and the largest eigenvalue is 52 times larger than the maximum value among the eigenvalues predicted by the RMT. The $beta_{473}$ coefficient, which reflect the largest eigenvalue property, is 0.8, while one of the eigenvalues in the RMT is approximately zero. Notably, we show that the entropy function $E(sigma)$ with the portfolio risk $sigma$ for the original and filtered correlation matrices are consistent with a power-law function, $E(sigma) sim sigma^{-gamma}$, with the exponent $gamma sim 2.92$ and those for Asian currency crisis decreases significantly.
The aim of this study is to investigate quantitatively whether share prices deviated from company fundamentals in the stock market crash of 2008. For this purpose, we use a large database containing the balance sheets and share prices of 7,796 worldwide companies for the period 2004 through 2013. We develop a panel regression model using three financial indicators--dividends per share, cash flow per share, and book value per share--as explanatory variables for share price. We then estimate individual company fundamentals for each year by removing the time fixed effects from the two-way fixed effects model, which we identified as the best of the panel regression models. One merit of our model is that we are able to extract unobservable factors of company fundamentals by using the individual fixed effects. Based on these results, we analyze the market anomaly quantitatively using the divergence rate--the rate of the deviation of share price from a companys fundamentals. We find that share prices on average were overvalued in the period from 2005 to 2007, and were undervalued significantly in 2008, when the global financial crisis occurred. Share prices were equivalent to the fundamentals on average in the subsequent period. Our empirical results clearly demonstrate that the worldwide stock market fluctuated excessively in the time period before and just after the global financial crisis of 2008.
This paper introduces a non-parametric framework to statistically examine how news events, such as company or macroeconomic announcements, contribute to the pre- and post-event jump dynamics of stock prices under the intraday seasonality of the news and jumps. We demonstrate our framework, which has several advantages over the existing methods, by using data for i) the S&P 500 index ETF, SPY, with macroeconomic announcements and ii) Nasdaq Nordic Large-Cap stocks with scheduled and non-scheduled company announcements. We provide strong evidence that non-scheduled company announcements and some macroeconomic announcements contribute jumps that follow the releases and also some evidence for pre-jumps that precede the scheduled arrivals of public information, which may indicate non-gradual information leakage. Especially interim reports of Nordic large-cap companies are found containing important information to yield jumps in stock prices. Additionally, our results show that releases of unexpected information are not reacted to uniformly across Nasdaq Nordic markets, even if they are jointly operated and are based on the same exchange rules.
We study in this paper the time evolution of stock markets using a statistical physics approach. Each agent is represented by a spin having a number of discrete states $q$ or continuous states, describing the tendency of the agent for buying or selling. The market ambiance is represented by a parameter $T$ which plays the role of the temperature in physics. We show that there is a critical value of $T$, say $T_c$, where strong fluctuations between individual states lead to a disordered situation in which there is no majority: the numbers of sellers and buyers are equal, namely the market clearing. We have considered three models: $q=3$ ( sell, buy, wait), $q=5$ (5 states between absolutely buy and absolutely sell), and $q=infty$. The specific measure, by the government or by economic organisms, is parameterized by $H$ applied on the market at the time $t_1$ and removed at the time $t_2$. We have used Monte Carlo simulations to study the time evolution of the price as functions of those parameters. Many striking results are obtained. In particular we show that the price strongly fluctuates near $T_c$ and there exists a critical value $H_c$ above which the boosting effect remains after $H$ is removed. This happens only if $H$ is applied in the critical region. Otherwise, the effect of $H$ lasts only during the time of the application of $H$. The second party of the paper deals with the price variation using a time-dependent mean-field theory. By supposing that the sellers and the buyers belong to two distinct communities with their characteristics different in both intra-group and inter-group interactions, we find the price oscillation with time.
This study investigates the impact of the COVID-19 pandemic on the stock market crash risk in China. For this purpose, we first estimated the conditional skewness of the return distribution from a GARCH with skewness (GARCH-S) model as the proxy for the equity market crash risk of the Shanghai Stock Exchange. We then constructed a fear index for COVID-19 using data from the Baidu Index. Based on the findings, conditional skewness reacts negatively to daily growth in total confirmed cases, indicating that the pandemic increases stock market crash risk. Moreover, the fear sentiment exacerbates such risk, especially with regard to the impact of COVID-19. In other words, when the fear sentiment is high, the stock market crash risk is more strongly affected by the pandemic. Our evidence is robust for the number of daily deaths and global cases.
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