Fat Tails Research Articles

Anchoring effect, prospect value and stock return

This paper studies the relation between prospect value and stock return under the anchoring effect. Our findings show that high (low) prospect value stocks are overpriced (underpriced) in the Chinese stock market. However, this negative relation only exists in stocks far from the 52-week high, where the long-short portfolio of prospect value earns a significant risk-adjusted return of 0.95% per month, and disappears near the 52-week high. Furthermore, we find the interaction between the 52-week high and prospect value mainly derives from the loss aversion feature. Our findings keep robust after controlling for the effect of stock fat-tail distribution.

Temperature-mediated diffusion of nanoparticles in semidilute polymer solutions.

The temperature is often a critical factor affecting the diffusion of nanoparticles in complex physiological media, but its specific effects are still to be fully understood. Here, we constructed a temperature-regulated model of semidilute polymer solution and experimentally investigated the temperature-mediated diffusion of nanoparticles using the particle tracking method. By examining the ensemble-averaged mean square displacements (MSDs), we found that the MSD grows gradually as the temperature increases while the transition time from sublinear to linear stage in MSD decreases. Meanwhile, the temperature-dependent measured diffusivity of the nanoparticles shows an exponential growth. We revealed that these temperature-mediated changes are determined by the composite effect of the macroscale property of polymer solution and the microscale dynamics of polymer chain as well as nanoparticles. Furthermore, the measured non-Gaussian displacement probability distributions were found to exhibit non-Gaussian fat tails, and the tailed distribution is enhanced as the temperature increases. The non-Gaussianity was calculated and found to vary in the same trend with the tailed distribution, suggesting the occurrence of hopping events. This temperature-mediated non-Gaussian feature validates the recent theory of thermally induced activated hopping. Our results highlight the temperature-mediated changes in diffusive transport of nanoparticles in polymer solutions and may provide the possible strategy to improve drug delivery in physiological media.

Examining the efficiency of stock markets using multifractal detrended fluctuation analysis. Empirical evidence from OIC (Organization of Islamic Cooperation) countries during the GFC and COVID-19 pandemic

PurposeThis study aimed to examine the efficient market hypothesis (EMH) for the stock markets of 12 member countries of the Organization of Islamic Cooperation (OIC), such as Egypt, Indonesia, Jordan, Kuwait, Malaysia, Morocco, Pakistan, Saudi Arabia, Tunisia, Turkey and the United Arab Emirates (UAE), during the global financial crisis (GFC) and the COVID-19 (CV-19) epidemic. The objective was to classify the effects on individual indices.Design/methodology/approachThe study employed the multifractal detrended fluctuation analysis (MF-DFA) on daily returns. After calculation and analysis, the data were then divided into two significant events: the GFC and the CV-19 pandemic. Additionally, the market deficiency measure (MDM) was utilized to assess and rank market efficiency.FindingsThe findings indicate that the average returns series exhibited persistent and non-persistent patterns during the GFC and the CV-19 pandemic, respectively. The study employed MF-DFA to analyze the sequence of normal returns. The results suggest that the average returns series displayed persistent and non-persistent patterns during the GFC and the CV-19 pandemic, respectively. Furthermore, all markets demonstrated efficiency during the two crisis periods, with Turkey and Tunisia exhibiting the highest and deepest levels of efficiency, respectively. The multifractal properties were influenced by long-range correlations and fat-tailed distributions, with the latter being the primary contributor. Moreover, the impact of the fat-tailed distribution on multifractality was found to be more pronounced for indices with lower market efficiency. In conclusion, this study categorizes indices with low market efficiency during both crisis periods, which subsequently affect the distribution of assets among shareholders in the stock markets of OIC member countries.Practical implicationsMultifractal patterns, especially the long memory property observed in stock markets, can assist investors in formulating profitable investment strategies. Additionally, this study will contribute to a better understanding of market trends during similar events should they occur in the future.Originality/valueThis research marks the initial effort to assess the impact of the GFC and the CV19 pandemic on the efficiency of stock markets in OIC countries. This undertaking is of paramount importance due to the potential destabilizing and harmful effects of these events on global financial markets and societal well-being. Furthermore, to the best of the authors’ knowledge, this study represents the first investigation utilizing the MFDFA method to analyze the primary stock markets of OIC countries, encompassing both the GFC and CV19 crises.

Fat tails, serial dependence, and interlinkages of the geopolitical risk and food market during the COVID-19 pandemic and war crisis: an application of Bayesian vector heterogeneous autoregressions.

We investigate fat tails and network interconnections of geopolitical risk index and food prices, including the price of corn, rice, and wheat, using seven Bayesian vector heterogeneous autoregression fashions. This paper differentiates dynamically between network interlinkages between these variables during the short, medium, and long runs. We found some noteworthy results in our study. In the first place, network interlinkages exhibit remarkable differences over time. Interlinkages between variables in our designed networks are increased in the short, medium, and long term due to transient events occurring in markets during the studied period. During the Russia-Ukraine conflict, the long-term ties within the system are more significantly impacted. Additionally, based on net-directional linkages, each market's role shifts (from sending to receiving shock and vice versa) during the pre- and post-Ukraine-Russia conflict, whereas these roles persist during the COVID-19 pandemic. Observations of short- and medium-term trends reveal that the geopolitical risk index is shock receivers transmitted to these markets by the rice and corn markets. The results indicate that the geopolitical risk index persists as shock receivers in terms of long-horizon measures.

The Price Distribution of Consumer Goods in Retail Markets

Derived is an analytic dynamic model of the price distribution of consumer goods in retail markets. The stationary price distribution is established from the conservation equation of offered units and two simplifying assumptions. Under the condition that independent traders make small random price variations around a nearly constant supply price, the stationary price distribution of a good must have the form of a fat-tailed Laplace distribution. The standard deviation of the distribution is determined by the price volatility of the goods. Also, the price distribution of an ensemble of goods is established and applied to empirical data with good quantitative agreement.

Equivalence of information production and generalised entropies in complex processes.

Complex systems with strong correlations and fat-tailed distribution functions have been argued to be incompatible with the Boltzmann-Gibbs entropy framework and alternatives, so-called generalised entropies, were proposed and studied. Here we show, that this perceived incompatibility is actually a misconception. For a broad class of processes, Boltzmann entropy -the log multiplicity- remains the valid entropy concept. However, for non-i.i.d. processes, Boltzmann entropy is not of Shannon form, -k∑ipi log pi, but takes the shape of generalised entropies. We derive this result for all processes that can be asymptotically mapped to adjoint representations reversibly where processes are i.i.d. In these representations the information production is given by the Shannon entropy. Over the original sampling space this yields functionals identical to generalised entropies. The problem of constructing adequate context-sensitive entropy functionals therefore can be translated into the much simpler problem of finding adjoint representations. The method provides a comprehensive framework for a statistical physics of strongly correlated systems and complex processes.

Assessment of algerian interbank interest rate through extreme value theory

This article tries to examine the evolution of interest rates in the Algerian interbank money market which focuses on the behavior of extreme. Empirical results illustrate that data are not distributed normally, exhibiting that their distribution is fat tails. Applying the GEV method on the maxima shows that the distribution law of the maxima changes over time due to the non-stationary data. Subsequent investigations suggest two subsample periods. The first period characterized by a deterioration of the liquidity of Algerian banks following the collapse of oil prices (1997-2000), the distribution law obtained is the law of Fréchet, but during the period characterized by an excess liquidity of the banks resulted from the increase in oil prices (2002-2013), the distribution law found is that of Weibull which is right bounded.

Measuring methane emissions during the installation of residential and commercial natural gas meters in China

Methane is a potent greenhouse gas that accounts for one-quarter of the world's radiative forcing. Methane emissions from the natural gas sector are prevalent throughout the natural gas (NG) chain. Studies have shown that methane emissions from post-meter uses of natural gas are vastly understated. A surge in the number of natural gas users, for example, would amplify the climate impact of methane emissions during the installation of natural gas meters. Thus, quantifying methane emissions during the installation of natural gas meters is critical in light of severe global climate change and urgent reduction targets. In this study, we used a mass balance approach to calculate methane emissions during the separate installation of 1444 residential natural gas meters and 51 commercial natural gas meters. Our results revealed the methane emission had a fat tail distribution. Specifically, the estimated mean methane emissions for household users were 0.008 (0.001–0.022) kg per household and 0.192 (0.013–0.816) kg per commercial user. Extrapolating these statistics to the whole of China, total emissions from 2007 to 2021 were 3.80 million metric tons (MMt) CH4, with an annual average of 0.25 MMt. Notably, in terms of economic development and population size, the provinces with the highest methane emissions were concentrated in the southeast. Our findings close a gap in measuring CH4 emissions in China across the natural gas chain and provide data to support the reduction targets set and the development of reduction technologies.

Hedging longevity risk under non-Gaussian state-space stochastic mortality models: A mean-variance-skewness-kurtosis approach

Longevity risk has recently become a high profile risk among insurers and pension plan sponsors. One way to mitigate longevity risk is to build a hedge using derivatives that are linked to mortality indexes. Longevity hedging methods are often based on the normality assumption, considering only the variance but no other (higher) moments. However, strong empirical evidence suggests that mortality improvement rates are driven by asymmetric and fat-tailed distributions, so that existing longevity hedging methods should be expanded to incorporate higher moments. This paper fills the gap by adopting a mean-variance-skewness-kurtosis approach based on non-Gaussian extensions of commonly-used stochastic mortality models, formulated in a state-space setting. On the basis of a general representation of these models, the authors derive (approximate) analytical expressions for the moments of the present values of the hedging instruments and the liability being hedged. These expressions are then integrated with a polynomial goal programming model, from which the optimal hedge portfolio is identified. Finally, the paper demonstrates the theoretical results with a real mortality data set and a range of hedger preferences.

Transcriptome profiling of differentiating adipose-derived stem cells across species reveals new genes regulating adipogenesis

Adipose-derived stem cells (ADSCs) that are enriched in adipose tissue with multilineage differentiation potential have become an important tool in therapeutic research and tissue engineering. Certain breeds of sheep exhibit a unique fat tail trait such that tail tissue accounts for approximately 10 % of body weight and can provide an excellent source of ADSCs. Here, we describe isolation of primary ADSCs from ovine embryonic fat tail tissues that displayed high self-renewal capacity, multilineage differentiation and excellent adipogenic ability. Through transcriptome analysis covering ADSCs differentiating into adipocytes, 37 transcription factors were involved in early transcriptional events that initiate a regulatory cascade of adipogenesis; the entire adipogenic activity consists of a reduction in proliferation ability and upregulation of genes related to lipid generation and energy metabolism, as well as several genes associated with myogenesis. Furthermore, Comparative transcriptome analysis across species (sheep, human, and mouse) revealed enhanced basal metabolic ability in differentiating ovine ADSCs, which may relate to the excellent adipogenic capability of these cells. We also identified a small evolutionarily conserved gene set, consisting of 21 and 22 genes exhibiting increased and decreased expression, respectively. Almost half (20) of these genes have not previously been reported to regulate adipogenesis in mammals. In this study, we identified important regulators that trigger ovine adipocyte differentiation, main biological pathways involved in adipogenesis as well as the evolutionarily conserved genes governing adipogenic process across species. Our study provides a novel excellent biomaterial and novel genes regulating adipogenesis for cellular transplantation therapy and investigations of fat metabolism.

An Empirical Study on the Logarithmic Return of Securities

Objective: Previous studies have shown that the distribution of security returns has the characteristics of peak and fat tail, and it is not realistic to use logarithmic normal distribution to describe security returns. This paper mainly studies the specific form of security returns distribution and conducts empirical research. Methods: We first assume that the security returns follow a logarithmic t-distribution. Then, the maximum likelihood estimation and moment estimation are used to explore the degree of freedom of the distribution. Finally, the goodness of fit test is used to conduct an empirical analysis about Shanghai Securities Composite Index. Results: The specific expression formulas for the estimator of the degree of freedom are obtained. Empirical testing shows that the security returns follow a logarithmic t-distribution. Conclusion: The probability distribution of security returns is unrealistic to assume that the security returns follow the logarithmic normal distribution. It is more practical to use the logarithmic t-distribution to characterize the distribution of security returns. Our results provide theoretical assistance for exploring the pricing of financial derivatives.

Risk in the cryptocurrency markets: the role of structural breaks and fat-tailed distributions in estimating value-at-risk and expected shortfall

Cryptocurrencies have gained much attention in recent times with investors, speculators, and regulators showing a keen interest in the cryptocurrency markets. However, not much attention has been paid to quantifying their risk measures. This paper estimates the risk in the cryptocurrency markets using Value-at-Risk and Expected Shortfall. We use Johnsons Su distribution to model the innovations in the returns and present a comparative analysis of different fat-tailed and skewed distributions used in modeling the returns. The estimation takes into account endogenously determined structural breaks in the data. We employ several backtesting methodologies to test the efficacy of the forecasts. Empirical results show that the Johnson’s Su distribution gives exceptional results, and outperforms other fat-tailed distributions and the normal distribution, especially at the 1% (for long positions) and 99% levels (for short positions). Furthermore, our results are robust to different subsamples and the methodology employed (recursive or rolling window). Our results have clear policy implications for various market participants, regulators, and the government.

Differences between NZ and U.S. individual investor sentiment: more noise or more information?

In this study, we introduce a newly created sentiment index of individual investors in NZ constructed similar to the well-known sentiment index provided by the American Association of Individual Investors (AAII) in the U.S. This unique setup allows us to compare different aspects of investors’ behaviour in both countries. We show that NZ market participants are less confident about the directional movement of the stock market, their expectations are more volatile and their distributions have fatter tails. By contrast, both bullish and bearish sentiment is more persistent among U.S. investors. Furthermore, our analysis of return predictability reveals that both groups of investors behave as noise traders. However, the results for NZ investors are stronger. Overall, our findings call for better financial education, particularly in the area of equity investing.

Opinion Dynamics Explain Price Formation in Prediction Markets.

Prediction markets are heralded as powerful forecasting tools, but models that describe them often fail to capture the full complexity of the underlying mechanisms that drive price dynamics. To address this issue, we propose a model in which agents belong to a social network, have an opinion about the probability of a particular event to occur, and bet on the prediction market accordingly. Agents update their opinions about the event by interacting with their neighbours in the network, following the Deffuant model of opinion dynamics. Our results suggest that a simple market model that takes into account opinion formation dynamics is capable of replicating the empirical properties of historical prediction market time series, including volatility clustering and fat-tailed distribution of returns. Interestingly, the best results are obtained when there is the right level of variance in the opinions of agents. Moreover, this paper provides a new way to indirectly validate opinion dynamics models against real data by using historical data obtained from PredictIt, which is an exchange platform whose data have never been used before to validate models of opinion diffusion.

Tax progressivity and the Pareto tail of income distributions

In a continuous-time version of the Bewley–Huggett–Aiyagari model, this paper shows theoretically and numerically that the fatness of the Pareto upper tail of the income distribution depends on tax progressivity only through the general equilibrium effect on the interest rate. With confiscatory taxes (marginal income tax rate approaching 100% at the top), the Pareto exponent is independent of tax progressivity.

The Effects of Sheep Tail Fat, Fat Level, and Cooking Time on the Formation of Nε-(carboxymethyl)lysine and Volatile Compounds in Beef Meatballs.

This study aimed to determine the effects of fat type (sheep tail fat (STF) and beef fat (BF)), fat levels (10, 20, or 30%), and cooking time (0, 2, 4, and 6 min, dry heat cooking at 180 °C) on the carboxymethyl lysine (CML) content in meatballs. pH, thiobarbituric acid reactive substance (TBARS), and volatile compound analyses were also performed on the samples. The use of STF and the fat level had no significant effect on the pH value. The highest TBARS value was observed with the combination of a 30% fat level and STF. CML was not affected by the fat level. The highest CML content was determined in meatballs with STF at a cooking time of 6 min. In the samples cooked for 2 min, no significant difference was observed between STF and BF in terms of the CML content. STF generally increased the abundance of aldehydes. Aldehydes were also affected by the fat level and cooking time. A PCA provided a good distinction between groups containing STF and BF regardless of the fat level or cooking time. Pentanal, octanal, 2,4-decadienal, hexanal, and heptanal were positively correlated with CML.

Data-driven statistical reduced-order modeling and quantification of polycrystal mechanics leading to porosity-based ductile damage

Predicting the process of porosity-based ductile damage in polycrystalline metallic materials is an essential practical topic. Ductile damage and its precursors are represented by extreme values in stress and material state quantities, the spatial probability density function (PDF) of which are highly non-Gaussian with strong fat tails. Traditional deterministic forecasts utilizing sophisticated continuum-based physical models generally lack in representing the statistics of structural evolution during material deformation. Computational tools which do represent complex structural evolution are typically expensive. The inevitable model error and the lack of uncertainty quantification may also induce significant forecast biases, especially in predicting the extreme events associated with ductile damage. In this paper, a data-driven statistical reduced-order modeling framework is developed to provide a probabilistic forecast of the deformation process of a polycrystal aggregate leading to porosity-based ductile damage with uncertainty quantification. The framework starts with computing the time evolution of the leading few moments of specific state variables from the spatiotemporal solution of full-field polycrystal simulations. Then a sparse model identification algorithm based on causation entropy, including essential physical constraints, is utilized to discover the governing equations of these moments. An approximate solution of the time evolution of the PDF is obtained from the predicted moments exploiting the maximum entropy principle. Numerical experiments based on polycrystal realizations of a representative body-centered cubic (BCC) tantalum illustrate a skillful reduced-order model in characterizing the time evolution of the non-Gaussian PDF of the von Mises stress and quantifying the probability of extreme events. The learning process also reveals that the mean stress is not simply an additive forcing to drive the higher-order moments and extreme events. Instead, it interacts with the latter in a strongly nonlinear and multiplicative fashion. In addition, the calibrated moment equations provide a reasonably accurate forecast when applied to the realizations outside the training data set, indicating the robustness of the model and the skill for extrapolation. Finally, an information-based measurement is employed to quantitatively justify that the leading four moments are sufficient to characterize the crucial highly non-Gaussian features throughout the entire deformation history considered.

Why the Basic Axioms of Risk Assessment Can Be Problematic to Identify Risk? – The Development of the VUCA Meter

The VUCA world is the epitome of the challenges linked with some of the undercurrents currently shaping businesses in the projectified society. The terms Volatility, Uncertainty, Complexity and Ambiguity (VUCA) are used as descriptive for the continuous flux project managers and project planners are forced to keep at bay. In this article, the authors present an idea to connect the VUCA concept as a risk identification platform to access, identify and isolate low-probability but high-impact events often called black swans or fat tail events. It is argued that the assumptions of conventional risk assessment in the domain of project management can lead to skewed general outcomes due to limitations of the intellect to assess probability. The outline of the VUCA meter is drafted and argued that the meter can augment the conventional risk assessment approach.

How can machine learning be used for accurate representations and predictions of fracture nucleation in zirconium alloys with hydride populations?

Zirconium alloys are critical material components of systems subjected to harsh environments such as high temperatures, irradiation, and corrosion. When exposed to water in high temperature environments, these alloys can thermo-mechanically degrade by forming hydrides that have a crystalline structure that is different from that of zirconium. Cracks can nucleate near these hydrides; hence, these hydrides are a direct link to fracture failure and overall large inelastic strain deformation modes. To fundamentally understand and predict these microstructural failure modes, we interrogated a finite-element database that was deterministically tailored and generated for large strain-dislocation-density crystalline plasticity and fracture modes. A database of 210 simulations was created to randomly sample from a group of microstructural fingerprints that encompass hydride volume fraction, hydride orientation, grain orientation, hydride length, and hydride spacing for a hydride that is physically representative of an aggregate of a hydride population. Machine learning approaches were then used to understand, identify, and characterize the dominant microstructural mechanisms and characteristics. We first used fat-tailed Cauchy distributions to determine the extreme events. A multilayer perceptron was used to learn the mechanistic characteristics of the material response to predefined strain levels and accurately determine the critical fracture stress response and the accumulated shear slips in critical regions. The predictions indicate that hydride volume fraction, a population-level parameter, had a significant effect on localized parameters, such as fracture stress distribution regions, and on the accumulated immobile dislocation densities both within the face centered cubic hydrides and the hexagonal cubic packed h.c.p. matrix.

Size scaling of failure strength at high disorder

We investigate how the macroscopic response and the size scaling of the ultimate strength of materials change when their local strength is sampled from a fat-tailed distribution and the degree of disorder is varied in a broad range. Using equal and localized load sharing in a fiber bundle model, we demonstrate that a transition occurs from a perfectly brittle to a quasi-brittle behavior as the amount of disorder is gradually increased. When the load sharing is localized the high load concentration around failed regions make the system more prone to failure so that a higher degree of disorder is required for stabilization. Increasing the system size at a fixed degree of disorder an astonishing size effect is obtained: at small sizes the ultimate strength of the system increases with its size, the usual decreasing behavior sets on only beyond a characteristic system size. The increasing regime of the size effect prevails even for localized load sharing, however, above the characteristic system size the load concentration results in a substantial strength reduction compared to equal load sharing. We show that an adequate explanation of the results can be obtained based on the extreme order statistics of fibers’ strength.