Tail dependence analysis of stock markets using extreme value theory

Financial risk modelling frequently uses the assumption of a normal distribution when considering the return series which is inefficient if the data is not normally distributed or if it exhibits extreme tails. Estimation of tail dependence between financial assets plays a vital role in various aspects of financial risk modelling including portfolio theory and hedging amongst applications. Extreme Value Theory (EVT) provides well established methods for considering univariate and multivariate tail distributions which are useful for forecasting financial risk or modelling the tail dependence of risky assets. The empirical analysis in this article uses nonparametric measures based on bivariate EVT to investigate asymptotic dependence and estimate the degree of tail dependence of the ASX-All Ordinaries daily returns with four other international markets, viz., the S&P-500, Nikkei-225, DAX-30 and Heng-Seng for both extreme right and left tails of the return distribution. It is investigated whether the asymptotic dependence between these markets is related to the heteroscedasticity present in the logarithmic return series using GARCH filters. The empirical evidence shows that the asymptotic extreme tail dependence between stock markets does not necessarily exist and rather can be associated with the heteroscedasticity present in the financial time series of the various stock markets.     

股票收益率非正态性的蒙特卡罗模拟检验

现实金融数据的分布通常表现为厚尾性和不对称性,因此用正态分布拟合实际金融数据的分布有很大的局限性.文章利用广义双曲线分布的厚尾性和不对称性对1997年1月2日～2003年9月19日的上证综指日收益率分布分别做了正态分布、广义双曲线分布、正态逆高斯分布和双曲线分布的拟合及蒙特卡罗模拟检验,结果表明广义双曲线分布和正态逆高斯分布可以较好地拟合上证综指日收益率分布.另外,文章还建立了一个带噪声干扰的线性系统,对实际的股票收益率并不服从正态分布,而表现出尖峰厚尾的特征做出了一种可能的解释.     

Power laws and the market structure of tourism industry

In this article, we use both graphical and analytical methods to investigate the market structure of one of the world’s fastest growing industries. For the German and Italian datasets, we show that the size distribution of tourism industry is heavy-tailed and consistent with a power-law behavior in its upper tail. Such a behavior seems quite persistent over the time horizon covered by our study, provided that during the period 2004–2009, the shape parameter is always in the vicinity of 2.5 for Germany and 2.6 for Italy. Size of the tourism industry has been proxied by the lodging capacity of hotel establishments: hotels, boarding houses, inns, lodging houses, motels, apartment hotels, tourist villages, and tourist apartments. Data belonging to the EUROSTAT and ISTAT databases have been used for Germany and Italy, respectively. Our aim is not to provide the best fit to the data but simply to focus our attention on the right tail of the size distribution of tourism industry. Understanding the behavior of the upper tail is indeed fundamental to capture the structure of the market. This study adds a new evidence to the list of empirical phenomena for which power laws hold.     

国际投资组合选择理论研究进展

国际投资组合选择理论研究的是在一定的假设条件下,当经济实现均衡时,投资者所应持有的本国与外国金融资产的比例。它的发展有5个特征:从追求金融市场的局部均衡到追求经济的一般均衡;从不考虑投资者的存在到考虑投资者个人效用的最大化;从单纯的理论模型构建到结合现实数据进行实证检验;从假设金融市场完全到考虑金融市场不完全的情况;从假设金融市场一体化到考虑金融市场存在分割的情况。     

Modelling the spreading process of extreme risks via a simple agent-based model: Evidence from the China stock market

This paper focuses on investigating financial asset returns' extreme risks, which are defined as the negative log-returns over a certain threshold. A simple agent-based model is constructed to explain the behavior of the market traders when extreme risks occur. We consider both the volatility clustering and the heavy tail characteristics when constructing the model. Empirical study uses the China securities index 300 daily level data and applies the method of simulated moments to estimate the model parameters. The stationarity and ergodicity tests provide evidence that the proposed model is good for estimation and prediction. The goodness-of-fit measures show that our proposed model fits the empirical data well. Our estimated model performs well in out-of-sample Value-at-Risk prediction, which contributes to the risk management.     

The distributional effects of progressive capital taxes

Rising inequality since the 1980s has spurred much research examining the underlying causes and potential policy responses. Among the more controversial, One of the more controversial policy proposals is a progressive capital tax in response to rising top wealth shares around the world proposes a progressive capital tax in response to rising top wealth shares around the world. This paper introduces rank-based econometric methods for dynamic power laws as a tool for estimating the effect of progressive capital taxes on the distribution of wealth under different assumptions about the impact of these taxes on household behavior. In most scenarios, we find that a small tax levied on 1% of households would substantially reshape the US wealth distribution and reduce inequality.     

A semi-parametric approach to estimating the operational risk and Expected Shortfall

In this article, we propose improvements to the peak-over-threshold (POT) method and apply this improved method for modelling US business operational losses and estimating operational risks (ORs). In the widely used traditional POT method, the generalized Pareto distribution (GPD) is fitted to severity losses, while an empirical distribution is fitted to small to medium losses. Then, the Expected Loss and the 99.9% operational value-at-risk (OpVaR) are estimated. Additionally, the Expected Shortfall (ES) – a coherent risk measure – is estimated in this article as an alternative to OpVaR. These risk measures constitute the levels of regulatory and economic capitals to cover risks. With the improved POT method, the risks can be estimated more accurately than with the traditional POT method. The results indicate that the OpVaR are much lower than the ES and that the larger the tail losses the greater the difference between these two risk measures. Our findings imply that the ES would provide higher levels of capitals to cover risks than would the OpVaR, particularly during crises, and they have implications for the efficient OR management and regulators.     

Structural Change Tests in Tail Behaviour and the Asian Crisis

This paper explores tests of the hypothesis that the tail thickness of a distribution is constant over time. Using Hill's conditional maximum likelihood estimator for the tail index of a distribution, tests of tail shape constancy are constructed that allow for an unknown breakpoint. The recursive test is shown to be inconsistent in one direction, and only a one-sided test is recommended. Specifically, the test can be used when the alternative hypothesis is that the tail index decreases over time. A rolling and sequential version of the test is consistent in both directions. The methods are illustrated on recent stock price data for Thailand, Malaysia and Indonesia. The period covers the recent Asian financial crisis and enables us to assess whether breakpoints in domestic asset return distributions are related to known changes in institutional arrangements in the foreign currency markets of these countries.     

Joint Allocation of Leisure and Consumption Commodities: A Japanese Extended Consumer Demand System 1979—90

In this study we estimate the parameters of a household expenditure function which includes joint choice of leisure and consumption commodities in scope without a separability assumption. We have used Japanese prices, wage rate, labour supply, and expenditure data on ten commodity groups, collected from 47 cities over 12 years. This data set has the advantage that separate observations are available for each data point for all the variables. We employed the AI demand system, for estimation. Controlling for time-specific effects, the result implied a definite rejection of the weak separability of labour supply and commodity choice, and non-rejection of the homogeneity and symmetry restrictions on the demand system. All the own-price elasticities are significantly negative, and both substitutes and complements are observed across commodity groups. As for the negativity, all but one of the eigenvalues of the substitution matrix are negative. The result as a whole showed consistency with demand theory. The estimated compensated labour supply elasticity is 0.39, which is in reasonable agreement with the previous studies.     

Prediction of volatility based on realized-GARCH-kernel-type models: Evidence from China and the U.S.

We propose three Realized-GARCH-Kernel-type models which do not make the distribution assumptions on the return disturbance terms. We use this type of model to predict the return volatilities of the 50ETF in China and the S&P500 index in the U.S. The semiparametric kernel density estimator of our models, which captures the skewness, asymmetry and fat-tail of financial assets, performs well both statistically and economically. Our models have more predictive power than other eight comparable volatility models that need to pre-specify the distribution of the disturbance terms. Our results are robust to eight measures of realized volatility. Using option straddle strategies, we show that our models generate larger trading profits and greater Sharpe ratios than the other competing models.     

Is constant returns-to-scale a restrictive assumption for sector-level empirical macroeconomics? The case of Europe

Assuming constant returns-to-scale is commonly agreed for empirical macroeconomic studies when countries are of interest. Recently, an increasing number of works have started to look at sectors building on the same assumption. In this letter, we question the reliability of this assumption for 10 European sectors for the period 1995–2014, for different production factor combinations. We make use of a simple sample-based nonparametric test that does not require any assumptions for any aspect of the production process. Our results suggest that, in general, this assumption is rather acceptable and that the specification with only capital and labour is the best in this case.     

Model selection for nonlinear time series

We investigate the finite-sample performance of model selection criteria for local linear regression by simulation. Similarly to linear regression, the penalization term depends on the number of parameters of the model. In the context of nonparametric regression, we use a suitable quantity to account for the Equivalent Number of Parameters as previously suggested in the literature. We consider the following criteria: Rice T, FPE, AIC, Corrected AIC and GCV. To make results comparable with other data-driven selection criteria we consider also Leave-Out CV. We show that the properties of the penalization schemes are very different for some linear and nonlinear models. Finally, we set up a goodness-of-fit test for linearity based on bootstrap methods. The test has correct size and very high power against the alternatives investigated. Application of the methods proposed to macroeconomic and financial time series shows that there is evidence of nonlinearity.First version received: September 2002/Final version received : October 2003I would like to thank Cees Diks, Cars Hommes and an anonymous referee for useful comments that significantly improved the paper.     

Testing for Autocorrelation Using a Modified Box-Pierce Q Test

This article investigates the finite-sample performance of a modified Box-Pierce Q statistic ( Q *) for testing that financial time series are uncorrelated without assuming statistical independence. The finite-sample rejection probabilities of the Q * test under the null and its power are examined in experiments using time series generated by an MA (1) process where the errors are generated by a GARCH (1, 1) model and by a long memory stochastic volatility model. The tests are applied to daily currency returns.     

Theorizing the Financial Statecraft of Emerging Powers

‘Financial statecraft’, or the intentional use of credit, investment and currency levers by the incumbent governments of creditor – and sometimes debtor – states for both international economic and political advantage, has a long history, ranging from money doctors to currency wars. A neorealist, zero-sum framing of international monetary relations is not inevitable, yet casts a persistent shadow especially during periods of prospective interstate power transitions when previously peripheral countries find themselves with unexpected new capabilities. This article seeks to understand and theorise the financial statecraft of emerging economies, moving beyond the traditional understanding that closely identifies the concept with financial sanctions imposed by a strong state on a weaker state. We propose that the aims of financial statecraft may be either ‘defensive' or ‘offensive’. Financial statecraft may be targeted either ‘bilaterally' or ‘systemically’. Finally such statecraft may employ instruments that are either ‘financial' or ‘monetary’. As emerging market economies have moved up in the ranks in the interstate distribution of capabilities, they have also expanded their financial statecraft strategies from narrowly defensive and bilateral to those involving offensive tactics and targeted at the global and systemic level. Historical and contemporary examples illustrate the analysis.     

A discussion on the innovation distribution of the Markov regime-switching GARCH model

The Markov Regime-Switching Generalized autoregressive conditional heteroskedastic (MRS-GARCH) model is a widely used approach to model the financial volatility with potential structural breaks. The original innovation of the MRS-GARCH model is assumed to follow the Normal distribution, which cannot accommodate fat-tailed properties commonly existing in financial time series. Many existing studies point out that this problem can lead to inconsistent estimates. To overcome it, the Student's t-distribution and General Error Distribution (GED) are the two most popular alternatives. However, a recent study points out that the Student's t-distribution lacks stability. Also, it incorporates the α-stable distribution in the GARCH-type model. The issue of the α-stable distribution is that its second moment does not exist. To solve this problem, the tempered stable distribution, which retains most characteristics of the α-stable distribution and has defined moments, is a natural candidate. In this paper, we conduct a series of simulation studies to demonstrate that MRS-GARCH model with tempered stable distribution consistently outperform that with Student's t-distribution and GED. Our empirical study on the S&P 500 daily return volatility also generates robust results. Therefore, we argue that the tempered stable distribution could be a widely useful tool for modeling the financial volatility in general contexts with a MRS-GARCH-type specification.     

Labour participation of Arab women: estimates of the fertility to labour supply link

The standard theoretical framework for analysing households’ intertemporal decisions is the life-cycle/permanent income model. Among its implications, testing the model allows to analyse the response of consumption to fiscal policy. However, the empirical literature with microdata has yielded mixed results. This article examines the sensitivity of the results to the assumption of separability among goods and of homogeneity across households. For that purpose, we test a rational expectations permanent income model with household data drawn from the Spanish Family Expenditure Survey. This survey contains detailed information on total expenditure and the income presents large, exogenous quarterly changes due to an institutional feature. The article shows that assuming separability among commodities biases the test against the model. When separability is not imposed, we show that the rejection of the model depends on heterogeneity across households in terms of their members being unemployed or not. For those households permanently employed, the model cannot be rejected whatever their income status.     

Institutions and the financial development–economic growth nexus in sub-Saharan Africa

Using a sample splitting approach that does not impose an exogenous quadratic term, we examine the effect of financial development on economic growth in sub-Saharan Africa by allowing the link to be mediated by the level of institutions. Our findings reveal a disproportionate growth-enhancing effect of finance, given countries’ distinct level of institutional quality. More specifically, when the International Country Risk Guide-based measure of institutions is used as the threshold variable, below the optimal level of institutional quality, financial development does not significantly promote economic growth. For countries with institutional quality above the threshold, higher finance is associated with growth. However, when institutions are measured by World Governance Indicators proxy, we find a significant effect of financial development, irrespective of whether a country is below or above the threshold. Interestingly, the growth-enhancing effect of finance is greater for low-institution countries relative to high-institution countries. Thus, through its ability to provide some crucial roles, the well-developed financial sector may also perform the function of sound institutions in influencing economic growth.     

A Bayesian approach to model changes in volatility in the Mexican stock exchange index

We model the changes in volatility in the Mexican Stock Exchange Index using a Bayesian approach. We study the time series with a wide set of models characterized by a Markov switching heterogeneity. The advantage of this approach is that it allows for a broader spectrum of possible models since the estimation of the moments of the parameters is done using the finite mixture distribution MCMC method, without relying on assumptions about large sampling and mathematical optimization. This is particularly relevant for emerging markets’ financial data because of its special characteristics, like being more susceptible to jumps and changes in volatility caused by exchange rate swings, financial crises and oil and commodity prices. For model comparison, we use the marginal likelihood approach and the bridge sampling technique. The best representation of the data is given by a switching model with three states rather than any other autoregressive linear or non-linear model. The periods of volatility found by the model coincide with different financial crisis. Whereas other studies of volatility for the same market impose the Markovian model that captures changes in volatility, we let our model to be defined in an endogenous way.     

The calculation of capital requirement using Extreme Value Theory

The Basel Committee has suggested some formulas for calculating capital requirement using the Advanced Internal Ratings-Based Approach. However, these formulas were derived under the assumption of a normal distribution. Thus, the capital requirement estimated by the Basel formula may be incorrect when the asset distributions are not normal. Using an analysis of qualifying revolving retail exposures as an example, this paper introduces a formula based on the Extreme Value Theory to calculate the capital requirement. This formula is more general and accurate than its predecessors, because it can be used with any type of distribution. Numerical examples are provided to demonstrate that the capital requirement estimated by the Basel formula is less than by our formula when the asset distribution has a heavy tail, and more than by our formula when the distribution has a short tail. Our formula is also more sensitive to risk than competing models in the context of the recent financial crisis.     

The effects of mergers and acquisitions on the firm size distribution

This paper provides new empirical evidence on the effects of mergers and acquisitions (M&As) on the shape of the firm size distribution, by using data of the population of manufacturing firms in the Netherlands. Our analysis shows that M&As do not affect the size distribution when we consider the entire population of firms. When we focus on the firms involved in an M&A event, we observe a shift of the firm size distribution towards larger sizes. Firm size distribution becomes more concentrated around the mean, less skewed to the right hand side, and thinner at the tails as a whole. The shift toward higher sizes due to M&A is not uniform but affects firms of different sizes in different ways. While the number of firms in the lower tail decreased, the number of firms in the central size classes increased substantially and outweighed the increase in the number (and mean size) of firms in the upper tail of the distribution (consequently the overall market concentration measured by the Herfindahl index declines). M&As lead to a departure from log-normality of the firm size distribution, suggesting that external growth does not follow Gibrat’s law. Our counterfactual analysis highlights that only internal growth does not affect the shape of the size distribution of firms. On the contrary, it suggests that the change in the size distribution is almost entirely due to the external growth of the firms.