EXTREME VALUE AT RISK: A SCENARIO FOR RISK MANAGEMENT

This paper uses the generalised extreme value (GEV) distribution to model the extreme losses that are likely to occur during market crashes, in the case of an investor who has long positions in stocks and currencies. The null hypothesis – which tests for normality of asset returns – is rejected due to asymmetry of these returns. We assume that the asymmetric behaviour and volatility of the returns are captured by the shape and scale parameters, respectively, of a GEV distribution. The data set includes stock indices for the United States, Japan, the United Kingdom, Germany, France and South Africa, and the South African rand exchange rates against the US dollar observed from 3 January 2005 to 30 December 2009. In addition, we divide this sample period into two periods: the pre‐crisis period, from 3 January 2005 to 31 December 2007 and the crisis period, from 1 January 2008 to 30 December 2009. We compared the estimates of value at risk (VaR) using an extreme value theory (EVT) model, with the estimates derived from the traditional variance–covariance method and found that during the crisis the 99% extreme VaR estimates are more reliable as they lie within the Basel II green zone. These results suggest that, at higher quintiles, the VaR estimates based on EVT are reliable and more accurate than estimates from the traditional method.     

IMPLEMENTING A ROBUST RISK MODEL FOR SOUTH AFRICAN EQUITY MARKETS: A PEAK‐OVER‐THRESHOLD APPROACH

This paper implements a market risk model for the South African equity market using daily returns of the Johannesburg Stock Exchange All Share Index. Firstly, we separate positive returns from negative returns and model them using the peak‐over‐threshold (POT) method in order to compute the downside as well as upside risk measures separately. We thereafter compute the value‐at‐risk (VAR) and the expected shortfall (ES) estimates corresponding to upside and downside risks. We bootstrap these risk measures and compute their standard errors and confidence intervals (CIs) to see whether they fall inside these CIs. Secondly, we compute out‐sample forecasts of VAR estimates using the POT method and the generalised autogressive conditional heteroscedasticity process. Three backtesting methodologies are employed: the unconditional and conditional coverage tests and the counting of number of exceptions according to Basel II green zone. We find that all our VAR and ES estimates are well inside their CIs and that at lower quantiles, parametric ES estimates are equal to POT‐ES estimates, although the difference between the two is more pronounced at higher quantiles (99% or higher). Furthermore, our market risk model falls into the Basel II green zone, as it produces fewer exceptions in out‐sample space.     

An intraday-return-based Value-at-Risk model driven by dynamic conditional score with censored generalized Pareto distribution

Encouraged by the literary fact that high-frequency data such as intraday returns contribute to estimating the tail risk of daily returns, we propose an intraday-return-based Value-at-Risk (VaR) model driven by dynamic conditional score with censored generalized Pareto distribution (hence, Censored GP-DCS-VaR model), which is a novel parametric VaR approach based on dynamic score-driven model and can incorporate intraday information into daily VaR forecast. This model helps present the dynamic evolution of intraday return distribution and well capture its tail feature. Applying bootstrap or a parametric method, we are allowed to form the daily return distribution in light of intraday data and thus can calculate VaR directly. Empirical analysis using the data of the Chinese stock market shows that our model gain an advantage in the risk estimation of extreme returns, proved by the comparison of out-of-sample forecasts between the Censored GP-DCS-VaR and the realized-GARCH-VaR.     

基于BMM模型的金融极端风险研究及实证分析

介绍极值理论,包括广义极值分布、区组最大值模型的拟合方法、检验方法等,重点考虑极值相依机构,引入极值指标,考虑不同频率下收益率的极值分布,并计算相应的VaR。之后对股票的对数收益率进行分析,首先从偏度峰度等基本统计量可知服从左偏尖峰分布,然后拟合边缘分布参数,判断都属于Frechet分布,最后用BMM模型和正态分布进行连接,得出结论正态分布模拟得到的极端损失和极端收益远远低于BMM方法。     

THE PREDICTABILITY OF STOCK MARKET RETURNS IN SOUTH AFRICA: PARAMETRIC VS. NON‐PARAMETRIC METHODS

This paper compares the forecasting performance of a sub‐class of univariate parametric and non‐parametric models in predicting stock market returns in South Africa. To account for conditional heteroskedasticity in stock returns data, the non‐parametric model is generated by the conditional heteroskedastic non‐linear autoregressive (NAR) model, while the parametric model is produced by the generalised autoregressive conditional heteroskedastic in mean (GARCH‐M) model. The results of the paper show that the NAR as a non‐parametric model performs better than the GARCH‐M model in short‐term forecasting horizon, and this indicates the importance of a distribution‐free model in predicting stock returns in South Africa.     

我国证券投资基金风险的实证研究

根据证券投资基金收益率序列的尖峰厚尾特征,建立估计基金风险的VaR-GARCH模型。在正态分布、t分布及GED分布三种不同的分布假设下,对基金的VaR值进行估计,并应用Kupiec失败频率检验方法对VaR模型的准确性进行了返回检验。研究结果表明,相比之下,基于GED分布的GARCH模型计算的VaR值最能真实地反映基金风险。     

基于VaR-GARCH模型对证券投资基金风险的实证研究

根据证券投资基金收益率序列的尖峰厚尾特征,建立估计基金风险的VaR—GARCH模型。在正态分布、t分布及GED分布三种不同的分布假设下,对基金的VaR值进行估计,并应用Kupiec失败频率检验方法对VaR模型的准确性进行了返回检验。研究结果表明,相比之下,基于GED分布的GARCH模型计算的VaR值最能真实地反映基金风险。     

A Tale of Two Tails: Establishment Size and Labour Productivity in United States and German Manufacturing at the Start of the Twentieth Century

This paper studies the importance of establishment size for the German/US labour‐productivity gap in manufacturing at the start of the twentieth century. First, we show that the left tail of the employment distribution by establishment size was larger in Germany than in the USA. Second, using US state data for 1909, we find a positive correlation between establishment size and labour productivity. Third, imposing the coefficients of these estimates on establishment‐size differences between Germany and the USA, we calculate that a redistribution of German employment to larger establishments, as in the USA, reduces the labour‐productivity gap by about 25 per cent.     

Value,Structure and Spatial Distribution of Interprovincial Trade in China

This study uses two different datasets to explore the stylized facts of interprovincial trade in China during the recent two decades. One dataset provides the magnitude of bilateral interprovincial goods trade calculated using firms' value‐added tax invoices. The other supplies estimates of interprovincial trade using provincial input–output tables. We find that China has both a large value and a high growth rate of interprovincial trade, but there still exists a home bias in internal trade for most provinces. In addition, disaggregation by product shows that the manufacturing sector has the largest share of interprovincial trade and this share continues to grow. Finally, the spatial distribution of trade suggests that all provinces can be clustered into a smaller number of trade areas with large intra‐cluster trade. Therefore, China's central government should make more effort to reduce local protection, stimulate domestic demand and coordinate interregional trade among local jurisdictions.     

The size distribution of ‘cities’ delineated with a network theory‐based method and mobile phone GPS data

We delineate “cities” independent of administrative boundaries in Japan by using a network theory‐based method and GPS‐based human mobility data. We divide the country into approximately 1 × 1 km² cells and detect the partition of cells that is optimal from the perspective of information theory. The resulting groups of cells are specified as cities. We find that the combination of two lognormal distributions better fits the city‐size distribution than a distribution with a Pareto upper tail. Moreover, we show that a jump diffusion process is the stochastic process of the city population underlying such a distribution.     

Employee Stock Option Fair‐Value Estimates: Do Managerial Discretion and Incentives Explain Accuracy?*

We examine the determinants of managers' use of discretion over employee stock option (ESO) valuation‐model inputs that determine ESO fair values. We also explore the consequences of such discretion. Firms exercise considerable discretion over all model inputs, and this discretion results in material differences in ESO fair‐value estimates. Contrary to conventional wisdom, we find that a large proportion of firms exercise value‐increasing discretion. Importantly, we find that using discretion improves predictive accuracy for about half of our sample firms. Moreover, we find that both opportunistic and informational managerial incentives together explain the accuracy of firms' ESO fair‐value estimates. Partitioning on the direction of discretion improves our understanding of managerial incentives. Our analysis confirms that financial statement readers can use mandated contextual disclosures to construct powerful ex ante predictions of ex post accuracy.     

Assessing the risk forecasts for Japanese stock market

We evaluate predictive performance of a selection of value-at-risk (VaR) models for Japanese stock market data. We consider traditional VaR models such as Riskmetrics method, historical simulation, variance–covariance method, Monte Carlo method, and their variants which are integrated with various ARCH models. Also considered are more recent models based on non-parametric quantile regression and extreme value theory (EVT). We apply these methods to the Japanese stock market index (1984–2000) and compare their performances in terms of various evaluation criteria using the method of White [Econometrica 68 (5) (2000) 1097–1126] for three out-of-sample periods of 1995–1996, 1997–1998, and 1999–2000.     

RISK–RETURN TRADE‐OFF AND BEHAVIOUR OF VOLATILITY ON THE SOUTH AFRICAN STOCK MARKET: EVIDENCE FROM BOTH AGGREGATE AND DISAGGREGATE DATA

The study analyses the nature and behaviour of volatility, the risk–return relationship and the long‐term trend of volatility on the South African equity markets using aggregate level, industrial level and sectoral level daily data for the period 1995‐2009. By employing dummy variables for the Asian and the sub‐prime financial crises and the 11 September political shock, the study further examines whether the long‐term trend of volatility structurally breaks during financial crises and major political shocks. Three time‐varying generalised autoregressive conditional heteroskedasticity models were employed: one of them symmetric, and the other two asymmetric. Each of these models was estimated based on three error distributional assumptions. The findings of the study are as follows: First, volatility is largely persistent and asymmetric. Second, risk at both aggregate and disaggregate level is generally not a priced factor on the South Africa (SA) stock market. Third, the threshold autoregressive conditional heteroscedasticity (TARCH) model under the generalised error distribution is the most appropriate model for conditional volatility of the SA stock market. Fourth, volatility generally increases over time, and its trend structurally breaks during financial crises and major global shocks. The policy and investment implications of the findings are outlined.     

VaR、CVaR在基金RAROC绩效评价上的应用比较——以科创主题基金为例

选取2020年8支科创主题基金为样本,基于基金收益率的尖峰厚尾特点,运用POT模型度量VaR、CVaR风险,比较基于VaR、CVaR的RAROC指标在基金绩效评价上的效果.实证结果发现:基于极值理论POT模型计算的VaR、CVaR可以很好地体现基金收益率的尾部风险;结合经验法与图示法选择的POT模型最佳门限能够得出有效的VaR、CVaR;基于CVaR的RAROC指标在基金绩效评价方面比基于VaR的RAROC指标表现更稳定,效果更佳,具有正向反映基金收益、规避风险的优点.     

基于GARCH模型的VaR方法在沪深300ETF风险测量的应用

交易所交易基金(ETF)在国际社会上被认为是长线投资、价值投资，规避风险的良好金融工具。中国股市投机炒作风气历来盛行，因此在投资领域有必要增强投资者对ETF的认知度和接受度。选用嘉实沪深300ETF作为研究对象，其所追踪的沪深300指数覆盖面广，基本体现中国沪深两市股市的收益状况。从其风险入手，运用GARCH模型研究分析得出该基金收益率的有效条件方差并结合VaR方法准确测量其风险价值，最终确定在95%的置信水平下GARCH(2,1)-t-分布模型能够最佳度量其风险价值。     

VaR与ES在波罗的海运价指数风险测度中的应用

选取2006年1月3日至2010年12月24日波罗的海运价指数（BDI）数据进行实证分析,将基于GARCH计算的VaR和ES风险测度方法引入到BDI风险测度中,根据所得到的VaR和ES估计值定量的考察BDI的风险状况。     

Systemic Risks Spillovers and Interdependence among Stock Markets: International Evidence with Covar‐Copulas

Empirical studies have provided ample evidence on the potential benefits of international diversification with portfolios that consist of both domestic and foreign assets. This coupled with sudden and periodic crashes in global and developed equity markets have stimulated the interest of investors to diversify across markets that have the potential to provide decorrelation with global markets during turbulent periods. At the same time, international diversification may intensify cross‐border listing of stocks with its antecedent implication of shocks transmission. The above have engendered renewed interest among researchers to explore the dependence levels and spillover effects of shocks among emerging and developed equity markets. This paper examines tail dependence structure and (extreme) systemic risks spillover effects among international equity markets using advanced econometric techniques that underpin the modelling of asset returns. We find evidence of low positive significant dependencies between all African markets and their developed counterparts, except for Egypt. Although no evidence of spillover effects to the markets in Africa was found, both unidirectional and bi‐directional causality between some African and developed equity markets is found, albeit with differences. We are unable to ascribe the dynamics in the causality structure to level of market integration. It is inferred that the degree of individual local markets interdependence with developed counterparts may reflect the relative size, liquidity and degree of foreign investors' participation.     

SOUTH AFRICAN MARKET VOLATILITY,ASYMMETRY AND RETAIL INTEREST RATES PASS‐THROUGH

The purpose of this paper is to examine the interest rate transmission mechanism for South Africa as an emerging economy in a pre‐repo and repo system. It explains how the money market rate is transmitted to the retail interest rates both in the long run and short run, and tests the symmetric and asymmetric interest rate pass‐through using the error‐correction model (ECM) and the adjusted ECM‐exponential generalised autoregressive conditional heteroscedasticity (ECM‐EGARCH) (1,1)‐M methodology. This permitted the examination of the impact of interest rate volatility, along with the leverage effect. An incomplete pass‐through is found in the short run. From the entire sample period, a symmetric adjustment is found in the deposit rate, which had upward rigidity adjustment, while an asymmetric adjustment is found in the lending rate, with a downward rigidity adjustment. All the adjustments supported the collusive pricing arrangements. According to the conditional variance estimation of the ECM‐EGARCH (1,1), negative volatility impact and leverage effect are present and influential only in the symmetric deposit interest rate adjustment process in South Africa.     

Food Price Crisis,Poverty, and Inequality

This paper simulates how a doubling of food prices affects absolute poverty and the food‐price‐adjusted real income distribution. We assume unsubsidized world food prices in order to derive the cost of poverty deepening and poverty expansion. We also estimate the degree to which inequality increases if no measures are put in place to offset rising food prices. Both measures are vulnerability indicators useful for social policy planning. Our results show that low‐income countries experience dramatic increases in absolute poverty as a result of doubling food prices. Middle‐income countries experience the greatest decrease in absolute income, which contributes most to an increase in world income inequality. The paper estimates that the global dollar value of the absolute poverty gap ($1.25/day) has the potential to increase by 400%, with poverty deepening accounting for two thirds of the increase.     

Whence the Beef: The Effect of Repealing Mandatory Country of Origin Labeling (COOL) Using a Vertically Integrated Armington Model with Monte Carlo Simulation

Increasingly, international trade policy analysis explores the economic effects of changes in ad-valorem tariffs or equivalent nontariff measures on vertically integrated markets for which high quality data are unavailable. Standard Constant Elasticity of Substitution (CES) Armington models fail to account for either vertical linkages or parameter uncertainty. Here, we introduce a vertically integrated, nested two-sector Armington model that incorporates uncertainty in the estimates of Armington elasticities through Monte Carlo simulation. As an illustrative case, we model the effects of changes in country of origin labeling (COOL) rules on the market shares of cattle in the U.S. beef market. By accounting for parameter uncertainty in this way, we are able to estimate the distribution of potential effects of repealing mandatory COOL. Ultimately, we predict that, in all but the most extreme cases, Mexico and Canada would not gain as much market share from the repeal of mandatory COOL as they claim in their World Trade Organization (WTO) filings against the regulation.