Shock-dependent conditional skewness in international aggregate stock markets

This article uses the S_U-normal distribution to model the dynamic behavior of skewness in ten international aggregate stock indices—five indices each from developed and emerging markets. The conditional skewness process is specified as both autoregressive and dependent on lagged return shocks. Our primary result is that a negative return shock skews the time-varying distribution to the right for mature markets but to the left for emerging markets. In addition, we find that the asymmetry in volatility is noticeably larger in developed markets than in emerging markets. Finally, including the skewness process in modeling has no effect on the asymmetry and persistence in volatility obtained. These results are different from those of previous studies, which demonstrate the existence of both effects.     

Risk-neutral skewness and market returns: The role of institutional investor sentiment in the futures market

This paper investigates the effect of index risk-neutral skewness on subsequent market returns and explores whether this effect will vary with various types of institutional investor sentiment in the futures market. Using index futures returns as the proxy of market returns, the empirical results show that the index risk-neutral skewness has a significantly negative effect on subsequent index futures returns. Moreover, the effect of institutional investor sentiment on subsequent index futures returns varies with various types of institutional investor sentiment. Finally, the effect of index risk-neutral skewness on subsequent index futures returns relies on various types of institutional investor sentiment.     

On Testing for the Nullity of Some Skewness Coefficients

Three tests for the skewness of an unknown distribution are derived for iid data. They are based on suitable normalization of estimators of some usual skewness coefficients. Their asymptotic null distributions are derived. The tests are next shown to be consistent and their power under some sequences of local alternatives is investigated. Their finite sample properties are also studied through a simulation experiment, and compared to those of the √ b ₂-test.     

On compensation for risk aversion and skewness affection in wages

This paper presents extensive empirical testing of the hypothesis that greater post-schooling earnings risk requires higher expected returns. Expanding on this notion, on the basis of utility theory, we predict that workers not only care about risk but also about the skewness in the distribution of the compensation paid: workers exhibit risk aversion and skewness affection. To test these hypotheses, this paper carefully develops various measures of risk and skewness by occupational/educational classification of the worker and finds supportive evidence: for men, wages rise with occupational earnings variance and decrease with skewness, for women only the negative effect of skewness is significant.     

Modelling conditional skewness: Heterogeneous beliefs,short sale restrictions and market declines

This paper tests the relationship among heterogeneous beliefs, short sale restrictions and time-varying conditional skewness under different market conditions. The results show that heterogeneous beliefs and short sale restrictions have negative impacts on conditional skewness during periods of market decline but have negative, positive or no impacts during periods of market growth. This evidence reconciles conflicting evidence in recent empirical studies on the relationship among heterogeneous beliefs, short sale restrictions and conditional skewness.     

Regional variation in productivity: a study of the Danish economy

We develop a model of labor productivity as a combination of capital-labour ratio, vintage of capital stock, regional externalities, and total factor productivity (TFP). The skewness of TFP distribution is related to different growth theories. While negative skewness is consistent with the neo-Schumpeterian idea of catching up with leaders, zero skewness supports the neoclassical view that deviations from the frontier reflect only idiosyncratic productivity shocks. We argue that positive skewness is consistent with an economy where exogenous technology is combined with non-transferable knowledge accumulated in specific sectors and regions. This argument provides the framework for an empirical model based on stochastic frontier analysis. The model is used to analyse regional and sectoral inequalities in Denmark.

Extreme risk transmission channels between the stock index futures and spot markets: Evidence from China

We develop a skewness-dependent multivariate conditional autoregressive value at risk model (SDMV-CAViaR) to detect the extreme risk transmission channels between the Chinese stock index futures and spot markets. The proposed SDMV-CAViaR model improves the forecast performance of extreme risk by introducing the high-frequency realized skewness. Specifically, the realized skewness has a significant impact on the spillovers, but the realized volatility and realized kurtosis do not, which implies that the jump component plays an important role in extreme risk spillovers. The empirical results indicate there are bidirectional extreme risk spillovers between the stock index futures and spot markets, the decline of one market has direct and indirect channels to exacerbate the extreme risk of the other market. Firstly, the market decline will directly increase the extreme risk of related markets by decreasing market returns. Besides, the decline will indirectly increase the extreme risk by increasing the negative realized skewness and extreme risk spillovers.     

Liquidity skewness premium

Risk-averse investors may dislike decrease of liquidity rather than increase of liquidity, and thus there can be asymmetric preference in variation of liquidity. In addition, investors are likely to avoid extreme illiquidity. This paper examines whether the skewness of an individual firm’s liquidity capturing asymmetric distribution of liquidity and extreme illiquidity is priced in the US stock market. Using the skewness of the daily price impact, we find that it is positively priced, and this positive relation is significant up to eight months after controlling for other effects. Moreover, we find our results remain significant with the skewness of alternative liquidity measures, i.e., dollar-volume, and turnover.     

The ‘wrong skewness’ problem: a re-specification of stochastic frontiers

In this paper, we study the ‘wrong skewness phenomenon’ in stochastic frontiers (SF), which consists in the observed difference between the expected and estimated sign of the asymmetry of the composite error, and causes the ‘wrong skewness problem’, for which the estimated inefficiency in the whole industry is zero. We propose a more general and flexible specification of the SF model, introducing dependences between the two error components and asymmetry (positive or negative) of the random error. This re-specification allows us to decompose the third moment of the composite error into three components, namely: (i) the asymmetry of the inefficiency term; (ii) the asymmetry of the random error; and (iii) the structure of dependence between the error components. This decomposition suggests that the wrong skewness anomaly is an ill-posed problem, because we cannot establish ex ante the expected sign of the asymmetry of the composite error. We report a relevant special case that allows us to estimate the three components of the asymmetry of the composite error and, consequently, to interpret the estimated sign. We present two empirical applications. In the first dataset, where the classic SF has the wrong skewness, an estimation of our model rejects the dependence hypothesis, but accepts the asymmetry of the random error, thus justifying the sign of the skewness of the composite error. More importantly, we estimate a non-zero inefficiency, thus solving the wrong skewness problem. In the second dataset, where the classic SF does not yield any anomaly, an estimation of our model provides evidence for the presence of dependence. In such situations, we show that there is a remarkable difference in the efficiency distribution between the classic SF and our class of models.     

Retrieving the implicit risk neutral density of WTI options with a semi-nonparametric approach

This paper contributes to the literature on the estimation of the Risk Neutral Density (RND) function by proposing a log-semi-nonparametric (log-SNP) distribution as the implicit RND when the Gram-Charlier model is used for option pricing. The performance of the model is compared to the lognormal (Black Scholes) benchmark for a sample of option prices for West Texas Intermediate (WTI) crude oil that were traded in the period between January 2016 and December 2017. Results show that the lognormal specification tends to systematically undervalue option prices and that the proposed log-SNP distribution, which explicitly adjusts for negative skewness and excess kurtosis, results in markedly improved accuracy, especially in periods of market instability. As a result, the implied skewness and excess kurtosis are relevant sources of information on market expectations that should be used for hedging and risk management purposes.     

Skewness preference,mean–variance and the demand for put options

This paper compares the mean–variance and the mean–variance–skewness approaches to modelling expected utility. Attention is focused on a problem encountered in risk management: determining the optimal demand for a put option hedging the return on an asset with a negatively skewed return distribution. It is demonstrated theoretically that incorporating positive skewness preference into the decision‐maker's objective function typically produces a reduction in the demand for put options when compared with the mean–variance solution. A state‐dependent example is provided to illustrate how a mean–variance–skewness objective can result in a significant reduction in the optimal amount of crop insurance demanded when compared with the mean–variance solution. Copyright © 1999 John Wiley & Sons, Ltd.     

Asymmetric control limits for small samples

When designing control charts, it is usually assumed that the measurement in the subgroups are normally distributed. The assumption of normality implies that the control limits for a chart for sample averages will be symmetrical about the centerline of the chart. However, the assumption of an underlying normal distribution of the data may not hold in some processes. If the measurements are asymmetrically distributed then the decision maker may choose different actions. One thing that can be done is to consider the degree of skewness. If the nature of the underlying distribution is skewed, then the traditional Shewhart individuals chart may not be valid. This paper presents a technique for constructing appropriate asymmetric control limits when the distribution of data cannot be assumed to be a normal distribution. Meanwhile, it proposes a skewness correction method for the generated Burr, lognormal and exponential distributions. Some numerical calculations are generated for n  =  2, 3, 4 by using MATLAB.     

Forecasting Heavy‐Tailed Densities with Positive Edgeworth and Gram‐Charlier Expansions*

This article presents a new semi‐nonparametric (SNP) density function, named Positive Edgeworth‐Sargan (PES). We show that this distribution belongs to the family of (positive) Gram‐Charlier (GC) densities and thus it preserves all the good properties of this type of SNP distributions but with a much simpler structure. The in‐ and out‐of‐sample performance of the PES is compared with symmetric and skewed GC distributions and other widely used densities in economics and finance. The results confirm the PES as a good alternative to approximate financial returns distribution, specially when skewness is not severe.     

Nonparametric estimation of variance, skewness and kurtosis of the distribution of a statistic by jackknife and bootstrap techniques

While jackknife and bootstrap estimates of the variance of a statistic are well–known, the author extends these nonparametric maximum likelihood techniques to the estimation of skewness and kurtosis. In addition to the usual negative jackknife also a positive jackknife as proposed by BERAN (1984) receives interest in this work. The performance of the methods is investigated by a Monte Carlo study for Kendall's tau in various situations likely to occur in practice. Possible applications of these developments are discussed.     

Properties and estimation of asymmetric exponential power distribution

The new distribution class, Asymmetric Exponential Power Distribution (AEPD), proposed in this paper generalizes the class of Skewed Exponential Power Distributions (SEPD) in a way that in addition to skewness introduces different decay rates of density in the left and right tails. Our parametrization provides an interpretable role for each parameter. We derive moments and moment-based measures: skewness, kurtosis, expected shortfall. It is demonstrated that a maximum entropy property holds for the AEPD distributions. We establish consistency, asymptotic normality and efficiency of the maximum likelihood estimators over a large part of the parameter space by dealing with the problems created by non-smooth likelihood function and derive explicit analytical expressions of the asymptotic covariance matrix; where the results apply to the SEPD class they enlarge on the current literature. Also we give a convenient stochastic representation of the distribution; our Monte Carlo study illustrates the theoretical results. We also provide some empirical evidence for the usefulness of employing AEPD errors in GARCH type models for predicting downside market risk of financial assets.     

基于多标度分形理论的金融资产收益非对称性测度方法研究

基于多标度分形理论,提出了一种新的更适用于实际金融资产收益数据的非对称性测度方法——两阶段非对称性检验法（Two-step asymmetry testing,TAT）,并运用Monte Carlo模拟考察了其与传统的偏度系数检验法的非对称性判定结论差异。实证结果表明：总体来讲,本文提出的两阶段非对称性检验法在常用检验水平下取得了较偏度系数法更为准确的金融资产收益非对称性判定结论,且两阶段非对称性检验法较偏度系数法更适用于具有非独立、非正态特性数据的非对称性检验。     

A reexamination of the equity-premium puzzle: A robust non-parametric approach

Recent tests of stochastic dominance of several orders, proposed by Linton, Maasoumi and Whang [Linton, O., Maasoumi, E., & Whang, Y. (2005). Consistent testing for stochastic dominance under general sampling schemes. Review of Economic Studies, 72(3), 735–765], are applied to reexamine the equity-premium puzzle. An advantage of this non-parametric approach is that it provides a framework to assess whether the existence of a premium is due to particular cardinal choices of either the utility function or the underlying returns distribution, or both. The approach is applied to the original Mehra–Prescott data and more recent data that include daily yields on Treasury bonds and daily returns on the S&P500 and the NASDAQ indexes. The empirical results show little evidence of stochastic dominance among the assets investigated. This suggests that the observed equity premium represents compensation for bearing higher risk, taking into account higher-order moments such as skewness and kurtosis. There is some evidence of a reverse puzzle, whereby Treasury bonds stochastically dominate equities at the third order, a result which potentially reflects insufficient compensation to investors for bearing the negative skewness associated with the S&P500 index.     

Assessing skewness in financial markets

It is a matter of common observation that investors value substantial gains but are averse to heavy losses. Obvious as it may sound, this translates into an interesting preference for right-skewed return distributions, whose right tails are heavier than their left tails. Skewness is thus not only a way to describe the shape of a distribution, but also a tool for risk measurement. We review the statistical literature on skewness and provide a comprehensive framework for its assessment. Then, we present a new measure of skewness, based on the decomposition of variance in its upward and downward components. We argue that this measure fills a gap in the literature and show in a simulation study that it strikes a good balance between robustness and sensitivity.     

Testing equality of shape parameters in several inverse Gaussian populations

Due to the strikingly resemblance to the normal theory and inference methods, the inverse Gaussian (IG) distribution is commonly applied to model positive and right-skewed data. As the shape parameter in the IG distribution is greatly related to other important quantities such as the mean, skewness, kurtosis and the coefficient of variation, it plays an important role in distribution theory. This paper focuses on testing the equality of shape parameters in several inverse Gaussian distributions. Three tests are suggested: the exact generalized inference-based test, the asymptotic test and a test that is based on parametric bootstrap approximation. Simulation studies are undertaken to examine the performances of the these methods, and three real data examples are analyzed for illustration.     

SKEWNESS FOR THE WEIBULL FAMILY

Abstract. The skewness of the Weibull family of distributions is discussed for all values of the shape parameter. This class includes unimodal probability densities for which the coefficient of skewness μ₃/o³ is positive, but the order of the mean, median and mode is μ < m < M. For values of the shape parameter used in practice the distributions are skewed to the right by a well accepted definition of skewness.