Left Tail Research Articles

Quantile volatility connectedness among themes and sectors: Novel evidence from China

Against the backdrop of increasing interest in factor investing, this paper explores volatility connectedness among theme factors and sector indices in the Chinese stock market using the Diebold-Yilmaz approach with quantile factor VAR. Our static analysis reveals significant similarities at extreme quantiles, contrasting with the conditional median. We find that higher connectedness measures at extreme quantiles correspond to improved performance of portfolios based on sectors and themes. Additionally, dynamic analysis indicates a strong link between total connectedness and closely tied risk events in China. Moreover, variations in connectedness between the right and left tails serve as a market-level risk proxy, significantly influencing the performance of both themes and sectors. These findings underscore the importance of understanding volatility connectedness for devising effective investment strategies and enhancing risk management practices in the Chinese stock market.

Commodity Market Downturn: Systemic Risk and Spillovers during Left Tail Events

We investigate systemic risk and spillovers in the commodity network during left-tail events using state-of-the-art methodologies: the Component Exponent Shortfall (CES), Quantile-Vector Autoregression (QVAR) and Causality-in-Risk. Our analysis focuses on five commodity groups: Energy (Crude Oil, Heating Oil, Natural Gas, Coal), Base Metals (Aluminum, Copper, Nickel, Zinc), Ferrous Metals (Iron, Steel), Precious Metals (Gold, Palladium, Platinum, Silver), and Others (Rubber). Across the models utilized, we consistently find that energy commodities and precious metals, along with copper as a standalone commodity, represent the most systemically risky group. Thus, portfolios incorporating these commodities are advised to implement more careful diversification to mitigate risks stemming from systemic factors. This may require additional attention to precious metals, as they are often considered safe-haven assets. Expediting the implementation of regulations that promote the replacement of fossil energy sources with green alternatives could be instrumental in managing systemic risk in the commodity market while also facilitating global sustainability. Finally, the results show that the impact of the Israeli-Palestinian conflict on both systemic risk and spillovers has been limited compared to the effects of COVID-19 and the Russia-Ukraine war.

Alterations of subcortical structure volume in pediatric bipolar disorder patients with manic or depressive first-episode

BackgroundBipolar disorder may begin as depression or mania, which can affect the treatment and prognosis. The physiological and pathological differences among pediatric bipolar disorder (PBD) patients with different onset symptoms are not clear. The aims of the present study were to investigate subcortical structural alterations in PBD patients with first-episode depressive (PBD-FED) and first-episode manic (PBD-FEM).MethodsA total of 59 individuals including 28 PBD-FED, 13 PBD-FEM, and 18 healthy controls (HCs) underwent high-resolution structural magnetic resonance scans. FreeSurfer 7.2 was used to detect changes in subcortical volumes. Simultaneously, thalamic, hippocampal, and amygdala subregion volumes were compared between the three groups.ResultsAnalysis of covariance controlling for age, sex, education, and estimated intracranial volume shows third and fourth ventricle enlargement in patients with PBD. Compared with the PBD-FED and HCs, the PBD-FEM group had reduced gray matter volume in the left thalamus, bilateral hippocampus, and right amygdala. Subsequent subregion analyses showed right cortico-amygdaloid transient, bilateral accessory-basal nucleus, left hippocampal tail, right hippocampal head, and body volume reduction in the PBD-FEM group.ConclusionsThe present findings provided evidence of decreased subcortical structure in PBD-FEM patients, which might present its trait feature.

Distributions and Correlation Properties of Offshore Wind Speeds and Wind Speed Increments

We determine distributions and correlation properties of offshore wind speeds and wind speed increments by analyzing wind data sampled with a resolution of one second for 20 months at different heights above sea level in the North Sea. Distributions of horizontal wind speeds can be fitted to Weibull distributions with shape and scale parameters varying weakly with the vertical height separation. Kullback–Leibler divergences between distributions at different heights change with the squared logarithm of the height ratio. Cross-correlations between time derivatives of wind speeds are long-term anticorrelated, and the even parts of their correlation functions satisfy sum rules. Distributions of horizontal wind speed increments change from a tent-like shape to a Gaussian with rising increment lag. A surprising peak occurs in the left tail of the increment distributions for lags in a range 10-200km\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10-200\\,{km}$$\\end{document} after applying the Taylor’s hypothesis locally to transform time lags into distances. The peak is decisive in order to obtain an expected and observed linear scaling of third-order structure functions with distance. This suggests that it is an intrinsic feature of atmospheric turbulence.

Systemic risk in banking, fire sales, and macroeconomic disasters

We develop a dynamic computational network model of the banking system where fire sales provide the amplification mechanism of financial shocks. Each period a finite number of banks offers a large, but finite, number of loans to households. Banks with excess liquidity also offer loans to other banks with insufficient liquidity. Thus, each period an interbank loan market is endogenously formed. Bank assets are hit by idiosyncratic shocks drawn from a thin tailed distribution. The uneven distribution of shocks across banks implies that each period there are banks that become insolvent. If insolvent banks happen also to be heavily indebted to other banks, their liquidation can trigger other bank failures. We find that the distribution across time of the growth rate of banking assets has a ‘fat left tail’ that corresponds to rare economic disasters. We also find that the distribution of initial shocks is not a perfect predictor of economic activity; that is some of the uncertainty is endogenous and related to the structure of the interbank network.

Scaling properties of (2+1) directed polymers in the low-temperature limit

Abstract In terms of the replica method, we consider the low-temperature limit of (2+1) directed polymers in a random potential. The proposed approach allows us to compute the scaling exponent θ of the free energy fluctuations as well as the left tail of its probability distribution function. It is argued that θ = 1 / 4 , which is slightly different to the zero-temperature numerical value that is close to 0.241.

Food-fuel nexus beyond mean-variance: New evidence from a quantile approach

This paper investigates the dynamic relationship between crude oil, ethanol, and corn markets across various quantiles of return distributions, as well as at higher statistical moments. Using a quantile vector autoregression model and data from 2007 to 2022, we find that the cross-market linkages are quantile dependent, with the strongest connections observed in the tails of the distribution. A shock to the oil market significantly impacts ethanol and corn returns under extreme bearish and bullish conditions. Positive shocks to the corn market reduce ethanol returns when the ethanol market is highly bullish, but this effect becomes positive in the left tail of the distribution. We also identify significant co-movement in higher statistical moments between these markets. Extreme excess kurtosis in the food-fuel nexus is more likely to occur with high financial market uncertainty, a bullish stock market, contracting industrial production, and a strong US dollar. In addition to these variables, credit spreads, futures market liquidity, futures term structure, and hedging pressure also influence kurtosis in individual markets within the nexus.

A fast and accurate numerical method for the left tail of sums of independent random variables

We present a flexible, deterministic numerical method for computing left-tail rare events of sums of non-negative, independent random variables. The method is based on iterative numerical integration of linear convolutions by means of Newtons–Cotes rules. The periodicity properties of convoluted densities combined with the Trapezoidal rule are exploited to produce a robust and efficient method, and the method is flexible in the sense that it can be applied to all kinds of non-negative continuous RVs. We present an error analysis and study the benefits of utilizing Newton–Cotes rules versus the fast Fourier transform (FFT) for numerical integration, showing that although there can be efficiency benefits to using FFT, Newton–Cotes rules tend to preserve the relative error better, and indeed do so at an acceptable computational cost. Numerical studies on problems with both known and unknown rare-event probabilities showcase the method’s performance and support our theoretical findings.

The National Trend of Data of the Scale of Attitude Toward Culture of Living with Disaster Risk (SAC-LDR)

In this study, we analyzed data collected from an internet survey targeting Japanese citizens on the Scale of Attitude toward Culture of Living with Disaster Risk (SAC-LDR), which was proposed in our previous study. The scale quantifies respondents’ attitude toword living with nature and its risks, to examine how the SAC-LDR scores are affected by the respondents’ attributes, such as age or lifestyle, and frequency distributions and correlations between variables. We found that: (1) the SAC-LDR scores had a mean value of 41.1 out of 60 and displayed not a completely normal distribution, but a distribution with slightly long left tail; (2) the SAC-LDR scores had a high correlation with the Power to Live with Disasters, which represents individual traits favorable to surviving through disasters; and (3) the SAC-LDR scores displayed regional differences within Japan.

Credit Market Frictions and the Linkage Between Dispersion and Macro Uncertainty

Cross-sectional dispersion and macro uncertainty (volatility of aggregate economic variables) are conceptually distinct. However, empirically, they both comove and are countercyclical. This paper builds a general equilibrium model and demonstrates that credit market frictions allow cross-sectional dispersion to drive time-varying macro uncertainty endogenously. In the model, as firm-level productivity becomes more dispersed, more firms are pushed to the left tail of the productivity distribution, resulting in more defaults and a depletion in aggregate net worth. This mechanism generates countercyclical leverage and aggregate volatility. The model implies that the government can inject equity in economic downturns to stabilize aggregate volatility. This paper was accepted by Lukas Schmid, finance. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.00166 .

Economic Disparities, Life Events, and the Gender Mental Health Gap

This paper studies factors explaining the gender mental health gap using Australian data. We show that men have significantly higher mean outcomes and the left tail of the combined distribution is disproportionately female. Using regression-based decompositions, we examine the degree that both socioeconomic inequalities and life experience account for this phenomenon. We find that disparities in income play a substantial role, and subject to an assumption of exogeneity, would be enough to account for the gender gap amongst individuals with very poor psychological wellbeing. We also examine the mental health effects of various negative life experience, such as the death of a family member or being a victim of violence. At the individual level, these variables have large effect sizes but are not strongly correlated with gender to explain our mental health disparities.

Does US financial uncertainty spill over through the (asymmetric) international credit channel? The role of market expectations

We show that the international credit channel is an important channel through which US financial uncertainty spills over internationally. Moreover, we find the asymmetric responses of domestic and international credit conditions to US financial uncertainty shocks, contingent upon market participants' expectations. During periods of pessimism regarding future economic conditions, the impact of US financial uncertainty on both domestic and international credit conditions intensifies significantly, leading to a severe global economic slowdown. Elevated US financial uncertainty disproportionately affects the left tails of the distribution more than the right tails, heightening the likelihood of negative global output growth. Conversely, in times of optimism, heightened US financial uncertainty exerts modest effects on international credit conditions and global economic conditions. Yet it stretches the conditional distribution substantially, signaling an increasingly uncertain future.

Do firm expectations respond to monetary policy announcements?

This paper investigates whether UK firms’ price growth expectations respond to the Bank of England (BoE) monetary policy announcements and explores the underlying mechanism. Using microdata from the UK Decision Maker Panel survey, we isolate the exogenous component of the monetary policy decisions by comparing firms’ responses filed before and after BoE announcements. Guided by a model of dispersed information, our analysis suggests that firms respond to monetary policy announcements but are, overall, not as informed and sophisticated as financial market participants. Firms’ price expectations respond to actual interest rate changes, as well as to bank rate changes purged from their systematic component, but not to high-frequency surprises. The left tail of their expected price change distribution is particularly sensitive to monetary policy announcements. Furthermore, we unveil significant non-linear effects, with changes in interest rates of 50 basis points being mostly responsible for revisions in expectations. This implies that the recent tightening cycle was effective in shifting firms’ expectations primarily at its peak when a sequence of consecutive large rate hikes was implemented. We also show that UK news coverage of the BoE’s activities increases following policy rate changes, highlighting the media’s crucial role in shaping public expectations.

Capital flows-at-risk: Push, pull and the role of policy

We characterise the probability distributions of various types of gross capital flows conditional on information contained in financial asset prices in a panel of emerging market economies, with a focus on ‘tail’ events. Our framework, based on the quantile regression methodology, allows for a separate role of push- and pull-type factors. We find that both push and pull factors have heterogeneous effects across the distributions of gross capital flows, which are most marked in the left tails. We then explore the role of the pre-existing stance of macroprudential and capital flow management policy in shaping probability distributions of capital flows. Macroprudential and capital flow management measures can both be stabilising, leading to less volatile flows and in particular to lower chances of large portfolio outflows. A tighter macroprudential stance can also reduce the sensitivity of portfolio flows to global financial shocks.

Analysis of eigenvalue condition numbers for a class of randomized numerical methods for singular matrix pencils

The numerical solution of the generalized eigenvalue problem for a singular matrix pencil is challenging due to the discontinuity of its eigenvalues. Classically, such problems are addressed by first extracting the regular part through the staircase form and then applying a standard solver, such as the QZ algorithm, to that regular part. Recently, several novel approaches have been proposed to transform the singular pencil into a regular pencil by relatively simple randomized modifications. In this work, we analyze three such methods by Hochstenbach, Mehl, and Plestenjak that modify, project, or augment the pencil using random matrices. All three methods rely on the normal rank and do not alter the finite eigenvalues of the original pencil. We show that the eigenvalue condition numbers of the transformed pencils are unlikely to be much larger than the δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document}-weak eigenvalue condition numbers, introduced by Lotz and Noferini, of the original pencil. This not only indicates favorable numerical stability but also reconfirms that these condition numbers are a reliable criterion for detecting simple finite eigenvalues. We also provide evidence that, from a numerical stability perspective, the use of complex instead of real random matrices is preferable even for real singular matrix pencils and real eigenvalues. As a side result, we provide sharp left tail bounds for a product of two independent random variables distributed with the generalized beta distribution of the first kind or Kumaraswamy distribution.

Tail risk spillovers between Islamic sectoral equities and bond markets: a time-frequency domain approach

ABSTRACT This study examines the tail risk spillover between Islamic sectoral stock indices and country specific investable Islamic bonds in time and frequency domain and provides useful implications for portfolio management. For the analyses, Conditional Autoregressive ValueatRisk (CAViaR), Quantile Connectedness, and DCCGARCH t-Copula models are estimated utilizing daily data from 15 countries. The findings show that the connectedness and spillover of risks are much stronger at tails than at median, and in the short-term than in long-term. Whereas median risk connectedness surges during COVID-19 pandemic, the connectedness between tail risks is usually elevated even before the COVID-19 pandemic with industrial sector being consistently a significant net transmitter of shocks. Moreover, all the sectoral stock market indices are significant and consistent transmitter of left tail shocks indicating a much stronger role of sectoral stock markets in transmitting large negative shocks. A heightened connectedness is also observed during Russia-Ukraine war mainly in the short-term frequency. The portfolio analysis shows that long positions in sectoral stocks can usually be hedged by taking short positions in Islamic bonds. Hedging effectiveness and optimal portfolio weights are also calculated to provide market participants with further information.

Complete Left Tail Asymptotic for the Density of Branching Processes in the Schröder Case

For the density of Galton-Watson processes in the Schröder case, we derive a complete left tail asymptotic series consisting of power terms multiplied by periodic factors.

Left and right: a tale of two tails of the wealth distribution

We study a model of wealth accumulation in altruistic lineages, in which households face uninsurable risk, investment indivisibilities and borrowing constraints. A thick upper tail of the stationary distribution of wealth is shown to emerge as a robust prediction, irrespective of (1) the presence of multidimensional (wealth and ability) heterogeneity and non-convexities in human capital formation, and (2) the nature of parental bequest motives (joy-of-giving vs. paternalism). Additionally, (3) we identify conditions under which the unique, ergodic wealth distribution exhibits a mass point at the bottom of its support, where credit market imperfections continue to affect, along the convergence process, the structure of wealth transitions at the lineage level. Motivated by these results, we then analyze the sensitivity of the left tail to various frictions and fiscal instruments that affect bequest strategies and the ensuing transmission of wealth across generations. In particular, capital income or bequest taxes with no redistribution may reinforce economic mechanisms underpinning mobility traps in the left tail, thereby increasing the persistence of households in the lowest tiers of the wealth distribution.

The complex elliptic Ginibre ensemble at weak non-Hermiticity: Edge spacing distributions

The focus of this paper is on the distribution function of the rightmost eigenvalue for the complex elliptic Ginibre ensemble in the limit of weak non-Hermiticity. We show how the limiting distribution function can be expressed in terms of an integro-differential Painlevé-II function and how the same captures the nontrivial transition between Poisson and Airy point process extreme value statistics as the degree of non-Hermiticity decreases. Our most explicit new results concern the tail asymptotics of the limiting distribution function. For the right tail we compute the leading order asymptotics uniformly in the degree of non-Hermiticity, for the left tail we compute it close to Hermiticity.

Robust memory of face moral values is encoded in the human caudate tail: a simultaneous EEG-fMRI study

Moral judgements about people based on their actions is a key component that guides social decision making. It is currently unknown how positive or negative moral judgments associated with a person’s face are processed and stored in the brain for a long time. Here, we investigate the long-term memory of moral values associated with human faces using simultaneous EEG-fMRI data acquisition. Results show that only a few exposures to morally charged stories of people are enough to form long-term memories a day later for a relatively large number of new faces. Event related potentials (ERPs) showed a significant differentiation of remembered good vs bad faces over centerofrontal electrode sites (value ERP). EEG-informed fMRI analysis revealed a subcortical cluster centered on the left caudate tail (CDt) as a correlate of the face value ERP. Importantly neither this analysis nor a conventional whole-brain analysis revealed any significant coding of face values in cortical areas, in particular the fusiform face area (FFA). Conversely an fMRI-informed EEG source localization using accurate subject-specific EEG head models also revealed activation in the left caudate tail. Nevertheless, the detected caudate tail region was found to be functionally connected to the FFA, suggesting FFA to be the source of face-specific information to CDt. A further psycho-physiological interaction analysis also revealed task-dependent coupling between CDt and dorsomedial prefrontal cortex (dmPFC), a region previously identified as retaining emotional working memories. These results identify CDt as a main site for encoding the long-term value memories of faces in humans suggesting that moral value of faces activates the same subcortical basal ganglia circuitry involved in processing reward value memory for objects in primates.