Inferring fundamental value and crash nonlinearity from bubble calibration

Identifying unambiguously the presence of a bubble in an asset price remains an unsolved problem in standard econometric and financial economic approaches. A large part of the problem is that the fundamental value of an asset is, in general, not directly observable and it is poorly constrained to calculate. Further, it is not possible to distinguish between an exponentially growing fundamental price and an exponentially growing bubble price. In this paper, we present a series of new models based on the Johansen–Ledoit–Sornette (JLS) model, which is a flexible tool to detect bubbles and predict changes of regime in financial markets. Our new models identify the fundamental value of an asset price and a crash nonlinearity from a bubble calibration. In addition to forecasting the time of the end of a bubble, the new models can also estimate the fundamental value and the crash nonlinearity, meaning that identifying the presence of a bubble is enabled by these models. In addition, the crash nonlinearity obtained in the new models presents a new approach to possibly identify the dynamics of a crash after a bubble. We test the models using data from three historical bubbles ending in crashes from different markets. They are the Hong Kong Hang Seng index 1997 crash, the S&P 500 index 1987 crash (Black Monday) and the Shanghai Composite index 2009 crash. All results suggest that the new models perform very well in describing bubbles, forecasting their ending times and estimating fundamental value and the crash nonlinearity. The performance of the new models is tested under both the Gaussian residual assumption and non-Gaussian residual assumption. Under the Gaussian residual assumption, nested hypotheses with the Wilks' statistics are used and the p-values suggest that models with more parameters are necessary. Under the non-Gaussian residual assumption, we use a bootstrap method to obtain type I and II errors of the hypotheses. All tests confirm that the generalized JLS models provide useful improvements over the standard JLS model.     

经济政策不确定性、意见分歧与股价崩盘风险

基于中文媒体构建的中国经济政策不确定性指数,研究经济政策不确定性对股价崩盘风险的影响效果和机制。结果显示：经济政策不确定性的提高会显著加剧股价崩盘风险,这表明经济政策不确定性是崩盘风险的诱因之一。通过对影响机制检验发现,经济政策不确定性对股价崩盘风险的正向作用,随着投资者意见分歧的增加而加强。在宏观经济良好时期,非国有股权和规模较大的企业,经济政策不确定性并未明显加剧股价崩盘风险,甚至起到了缓解股价崩盘风险的作用。     

A statistical model of speculative bubbles,with applications to the stock markets of the United States,Japan, and China

It is common knowledge that the more prices deviate from fundamentals, the more likely it is for prices to reverse. Taking this into account, we propose a simple statistical model to identify speculative bubbles in financial markets. Through the estimates of the time varying parameters, including transition probabilities, we can identify when and how newly born bubbles grow and burst over time. The model can be estimated by recursive computations, which require a huge storage capacity for standard computers. For this reason, we introduce an approximation in the computation, maintaining the recursive nature of our estimation technique. We then apply this model to the stock markets of the United States, Japan, and China, estimate its parameters and the probabilities of a bubble crash, and obtain several interesting results: the time series data of the stock price bubble show an inherently non-stationary development and the probability of a bubble crash indeed increases as the stock price becomes too high or too low.     

Super-Exponential RE bubble model with efficient crashes

We propose a dynamic Rational Expectations (RE) bubble model of prices, combining a geometric random walk with separate crash (and rally) discrete jump distributions associated with positive (and negative) bubbles. Crashes tend to efficiently bring back excess bubble prices close to a “normal” process. Then, the RE condition implies that the excess risk premium of the risky asset exposed to crashes is an increasing function of the amplitude of the expected crash, which itself grows with the bubble mispricing: hence, the larger the bubble price, the larger its subsequent growth rate. This positive feedback of price on return is the archetype of super-exponential price dynamics. We use the RE condition to estimate the real-time crash probability dynamically through an accelerating probability function depending on the increasing expected return. After showing how to estimate the model parameters, we obtain a closed-form approximation for the optimal investment that maximizes the expected log of wealth (Kelly criterion) for the risky bubbly asset and a risk-free asset. We demonstrate, on seven historical crashes, the promising outperformance of the method compared to a 60/40 portfolio, the classic Kelly allocation, and the risky asset, and how it mitigates jumps, both positive and negative.     

Market fragility and international market crashes

We extend the Pukthuanthong and Roll (2009) measure of integration to provide an estimate of systemic risk within international equity markets. Our measure indicates an increasing likelihood of market crashes. The conditional probability of market crashes increases substantially following increases of our risk measure. High levels of our risk measure indicate the probability of a global crash is greater than the probability of a local crash. That is, conditional on high levels of systemic risk, the probability of a severe crash across multiple markets is larger than the probability of a crash within a smaller number of markets.     

股吧评论、分析师跟踪与股价崩溃风险——关于模糊信息的信息含量分析

东方财富股吧等股票论坛日渐活跃,反映了投资者对获得上市公司真实、完整、及时信息的强烈需求。尽管股吧有助于促进信息传播,但仍是非正式的信息发布平台,股吧评论本质上是一种模糊信息。为探明股吧评论的信息含量,本文以2012—2017年A股上市公司为研究样本,研究股吧评论对股价崩溃风险的影响,以及同样属于模糊信息的分析师跟踪在这一过程中可能产生的作用。实证结果表明,股吧评论分歧越小,股价崩溃风险越大,并且分析师跟踪人数和研报数量在上述影响过程中发挥中介作用。研究结果有助于厘清股吧评论影响股价崩溃风险的路径和机理,既丰富了股价崩溃风险成因的研究,也揭示了股吧评论、分析师跟踪等模糊信息的信息含量。     

Can the probability of extreme returns be the basis for profitable portfolios? Evidence from China

Based on the generalized logit predicting model from Jang and Kang (2019), this paper estimates the ex-ante probability of extreme returns and finds that the significantly negative (positive) influence of the predicted crash (jackpot) probability is robust, whether based on the traditional portfolio construction, orthogonalized portfolio construction and Fame-Macbeth cross-section regression. Further analyses show both the behavioral speculators' trading and rational investors' arbitrage limits could be the sources of mispricing caused by extreme returns. Overall, this paper applies a predicting model to estimate the probabilities of the future extreme returns, and figures out the significant influence and possible sources of the crash and jackpot probabilities in China. Portfolios based on extreme return probabilities can be profitable and steady bases for uninformed investors in the Chinese stock market.     

Board diversity and stock price crash risk

We show how board diversity influences stock price crash risk. By classifying board diversity into relation-oriented diversity (gender and age) and task-oriented diversity (tenure and education), we find that greater diversity on board can lower the risk of future stock crash. Additional analyses show that the effect of board diversity on future crash risk is stronger for firms with high information opacity and low institutional ownership. Overall, our findings provide new insights and suggest for more diverse boards to improve corporate governance practices.     

The time-varying asymmetry of exchange rate returns: A stochastic volatility – stochastic skewness model

While the time-varying volatility of financial returns has been extensively modelled, most existing stochastic volatility models either assume a constant degree of return shock asymmetry or impose symmetric model innovations. However, accounting for time-varying asymmetry as a measure of crash risk is important for both investors and policy makers. This paper extends a standard stochastic volatility model to allow for time-varying skewness of the return innovations. We estimate the model by extensions of traditional Markov Chain Monte Carlo (MCMC) methods for stochastic volatility models. When applying this model to the returns of four major exchange rates, skewness is found to vary substantially over time. In addition, stochastic skewness can help to improve forecasts of risk measures. Finally, the results support a potential link between carry trading and crash risk.     

Fund trading divergence and performance contribution

Considering that the most distinct trading decisions are crucial to evaluate the ability of fund managers to add value, this paper aims to examine the trading divergence level among mutual funds and to capture its determinants and its performance consequences. We propose a measure that is more informative than the traditional overlap metrics, providing evidence of a positive and significant trend of fund trading divergence over time, especially after the Global Financial Crisis (GFC) of 2008. Our results also show a negative influence of market stress on the trading divergence level. Interestingly, we find greater contribution to subsequent fund performance in the divergent portions of trading decisions.     

Accounting regulations,enforcement, and stock price crash risk: Global evidence in the banking industry

This study uses the banking industry as a unique testing setting to examine the impact of accounting and enforcement regulations on stock price crash risk. We find that stocks are less likely to crash in countries with stricter accounting regulations and enforcement standards. More importantly, we provide evidence that the impact of accounting regulations is more significant in countries with stricter enforcement standards, suggesting that enforcement mechanisms and accounting regulations are complementary. We find that the main channels for accounting regulations and enforcement standards to affect stock price crash risk are regulations that strengthen information disclosure and improve the effects of direct supervision and external auditors. Our findings are robust after we include more control variables, employ regional regulatory developments as instrumental variables, conduct change regressions, use alternative measures of enforcement, and estimate in various subsamples. Our study has policy implications for how to design accounting regulations and enforcement mechanisms in a more effective manner.     

Family firms and crash risk: Alignment and entrenchment effects

Stock price crash risk could be lower in family firms because the controlling family investors have a longer-term interest, hold greater decision rights and are better informed than investors in diffusely owned firms (alignment effect). However, the agency costs between family and nonfamily investors (entrenchment effect) could affect crash risk in two opposing ways. Non-controlling investor skepticism about insider entrenchment limits overvaluation and reduces the crash risk. In contrast, entrenched insiders could hide bad news to exploit private benefits, which could increase the crash risk. We show that family firms exhibit a lower crash risk than similar nonfamily firms after controlling for lower overvaluation, which is consistent with the better alignment effect. Moreover, we show that better governance further reduces the crash risk, which indicates that the substitutive relationship between strong governance and family ownership shown in countries with low investor protection rights does not carry over to the U.S. where investor protection rights are strong.     

Excess perks and stock price crash risk: Evidence from China

We investigate the impact of excess perk consumption on crash risk in state-owned enterprises in China. To enjoy excess perks, executives in state-owned enterprises have an incentive to withhold bad news for extended periods, leading to higher future stock price crash risk. Consistent with this assertion, we find a positive correlation between excess perks and crash risk. The findings are robust to the inclusion of other determinants of crash risk identified in the literature, such as earnings management, conditional conservatism, and firm-level corporate governance mechanisms. The results still hold after accounting for possible endogeneity issues using a two-stage least squares estimation. Earnings management (conditional conservatism) helps amplify (lessen) this impact. Moreover, better external monitoring mitigates the impact of excess perks on firm crash risk. We further find that the impact of excess perks on crash risk is more pronounced in firms whose executives are approaching retirement and persists for at least two years.     

The flash crash: An examination of shareholder wealth and market quality

We investigate stock returns, market quality, and options market activity around the flash crash of May 6, 2010. Abnormal returns are negative on the day of and the day after the flash crash for stocks that had trades that executed during the crash subsequently cancelled by either Nasdaq or NYSE Arca. Consistent with studies that suggest that other sources of liquidity withdrew from the markets during the flash crash, we find that the fraction of trades executed by the NYSE increases during this volatile period. Market quality deteriorates following the flash crash as bid-ask spreads increase and quote depths decrease. Evidence from the options markets indicates that investor uncertainty increased around the time of the crash and remained elevated for several days.     

A new efficient method for estimating the Gerber–Shiu function in the classical risk model

In this paper, we propose a new efficient method for estimating the Gerber–Shiu discounted penalty function in the classical risk model. We develop the Gerber–Shiu function on the Laguerre basis, and then estimate the unknown coefficients based on sample information on claim numbers and individual claim sizes. The convergence rate of the estimate is derived. Some simulation examples are illustrated to show that the estimate performs very well when the sample size is finite. We also show that the proposed estimate outperforms other estimates in the simulation studies.     

Abnormal real operations,real earnings management,and subsequent crashes in stock prices

We study the impact of firms’ abnormal business operations on their future crash risk in stock prices. Computed based on real earnings management (REM) models, firms’ deviation in real operations (DROs) from industry norms is shown to be positively associated with their future crash risk. This association is incremental to that between discretionary accruals (DAs) and crash risk found by prior studies. Moreover, after Sarbanes–Oxley Act (SOX) of 2002, DRO’s predictive power for crash risk strengthens substantially, while DA’s predictive power essentially dissipates. These results are consistent with the prior finding that managers shift from accrual earnings management to REM after SOX. We further develop a suspect-firm approach to capture firms’ use of DRO for REM purposes. This analysis shows that REM-firms experience a significant increase in crash risk in the following year. These findings suggest that the impact of DRO on crash risk is at least partially through REM.     

When stock price crash risk meets fundamentals

We investigate the relationship between fundamental strength and stock price crash risk by analyzing a large sample of Chinese firms. We mainly find that firms with stronger (weaker) total fundamental strength, higher (lower) profitability and higher (lower) operating efficiency have lower (higher) stock price crash risk. Moreover, this negative relationship is more pronounced for firms with a great number of short-term institutional investors and opaque firms. Additional test illustrates that internal control could ameliorate this negative relationship. All these findings are robust to alternative measurements of crash risk and endogeneity correction.     

Economic policy uncertainty and stock price crash risk

We examine the impact of economic policy uncertainty (EPU) on firm-specific crash risk. Based on a large sample of Chinese listed firms over the period from 2000 to 2017, we provide empirical evidence that firms are more likely to experience stock price crashes when EPU increases. Cross-sectionally analysis further reveals that the impact of EPU on stock price crash risk is stronger for firms whose returns are more sensitive to EPU. More specifically, young stocks, small stocks, high volatility stocks, and growth stocks, which have higher valuation uncertainty per se, are more sensitive to EPU and are more affected by EPU in terms of crash risk. We further show that EPU is significantly and positively associated with aggregated stock price crash risk at the market level.     

Compensation peer crash risks and corporate own investments: New evidences from U.S. stock markets

This study, employing US listed firms with compensation peer disclosures, investigates the impact of compensation and industry peer stock price crash risks on firms' own investments. We document three new evidences in the examination. First, we find that firms' own investments are positively affected by compensation peer crash risks but not industry peers. Second, we show that firms' own investments are explained by compensation peer crash risks only. Third, we demonstrate that the compensation peer crash risks and firms' own investments relation is positively moderated by corporate governance. Besides, additional analysis suggests that peers' incentive effect is a possible explanation to the positive compensation peer crash risks and firms' own investments relation.     

A statistical analysis of log-periodic precursors to financial crashes*

Motivated by the hypothesis that financial crashes are macroscopic examples of critical phenomena associated with a discrete scaling symmetry, we reconsider the evidence of log-periodic precursors to financial crashes and test the prediction that log-periodic oscillations in a financial index are embedded in the mean function of this index (conditional upon no crash having yet occurred). In particular, we examine the first differences of the logarithm of the S&P 500 prior to the October 1987 crash and find the log-periodic component of this time series is not statistically significant if we exclude the last year of data before the crash. We also examine the claim that two separate mechanisms are needed to explain the frequency distribution of draw downs in the S&P 500 and find the evidence supporting this claim to be unconvincing.