DISTRIBUTION-INVARIANT RISK MEASURES, INFORMATION, AND DYNAMIC CONSISTENCY

In the first part of the paper, we characterize distribution-invariant risk measures with convex acceptance and rejection sets on the level of distributions. It is shown that these risk measures are closely related to utility-based shortfall risk.
In the second part of the paper, we provide an axiomatic characterization for distribution-invariant dynamic risk measures of terminal payments. We prove a representation theorem and investigate the relation to static risk measures. A key insight of the paper is that dynamic consistency and the notion of "measure convex sets of probability measures" are intimately related. This result implies that under weak conditions dynamically consistent dynamic risk measures can be represented by static utility-based shortfall risk.     

Backtesting expected shortfall: evidence from European securitized real estate

Events such as the European sovereign debt crisis, terrorism and Brexit cause more uncertainty and volatility in capital markets. This encourages us to use both conditional and unconditional forecasts (backtests) for expected shortfall (ES) in 8 indices of listed European real estate securities and Real estate investment trusts (REITs). Using the method proposed by Du and Escanciano, we find that ES is generally superior to Value-at-Risk in describing and capturing risk during extreme events such as the financial crisis. Our results are important to regulators, risk managers and investors.     

基于高阶期望损失的股指期货保证金设置

股指期货交易保证金作为风险控制的手段,应使用满足一致性公理要求的风险测度方法对指数风险进行分析,但现有的方差、Var测度均不满足此要求,高阶期望损失风险测度满足一致性公理要求。在回报率为非正态的情形下运用顺序统计量方法,分别计算了沪深300指数、上证指数、深证成指的高阶期望损失,并进行了回报率绝对风险、波动风险的广义随机占优检验。以检验结果为依据,研究了以这三个指数为标的物的股指期货保证金比例的设置问题,为我国股指期货交易保证金的设定提供了决策参考。     

Portfolio optimization under Expected Shortfall: contour maps of estimation error

The contour maps of the error of historical and parametric estimates of the global minimum risk for large random portfolios optimized under the Expected Shortfall (ES) risk measure are constructed. Similar maps for the VaR of the ES-optimized portfolio are also presented, along with results for the distribution of portfolio weights over the random samples and for the out-of-sample and in-sample estimates for ES. The contour maps allow one to quantitatively determine the sample size (the length of the time series) required by the optimization for a given number of different assets in the portfolio, at a given confidence level and a given level of relative estimation error. The necessary sample sizes invariably turn out to be unrealistically large for any reasonable choice of the number of assets and the confidence level. These results are obtained via analytical calculations based on methods borrowed from the statistical physics of random systems, supported by numerical simulations.     

Coherent Measures of Risk

In this paper we study both market risks and nonmarket risks, without complete markets assumption, and discuss methods of measurement of these risks. We present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties "coherent." We examine the measures of risk provided and the related actions required by SPAN, by the SEC/NASD rules, and by quantile-based methods. We demonstrate the universality of scenario-based methods for providing coherent measures. We offer suggestions concerning the SEC method. We also suggest a method to repair the failure of subadditivity of quantile-based methods.     

我国商业银行系统性风险评估与实证研究——基于预期期望损失方法测度

文章对我国商业银行系统性风险进行评估,采用系统性预期期望损失和边际预期期望损失两个测度变量,以此作为系统重要性指数,通过预期期望损失方法利用我国14家上市商业银行的面板数据评估我国商业银行系统性风险水平。实证结果表明：国有银行系统重要性虽然占据主要地位,但系统性风险贡献排名却远低于其他商业银行,主要原因是国有银行的现金流更稳定,政府隐性担保及政策优惠对弱化系统性风险贡献度有很大帮助。另外我国中小城市商业银行更有可能带来系统性风险,因为股份制商业银行资产总规模虽然相对较小,但资产扩张速度过快、盈利大幅波动、资本充足率低且负债率较高,相比较国有银行更需要得到监管部门的重点监管。     

Forecasting risk with Markov-switching GARCH models:A large-scale performance study

We perform a large-scale empirical study in order to compare the forecasting performances of single-regime and Markov-switching $\text{GARCH}$ ($\text{MSGARCH}$) models from a risk management perspective. We find that $\text{MSGARCH}$ models yield more accurate Value-at-Risk, expected shortfall, and left-tail distribution forecasts than their single-regime counterparts for daily, weekly, and ten-day equity log-returns. Also, our results indicate that accounting for parameter uncertainty improves the left-tail predictions, independently of the inclusion of the Markov-switching mechanism.     

Forecast combinations for value at risk and expected shortfall

Combining provides a pragmatic way of synthesising the information provided by individual forecasting methods. In the context of forecasting the mean, numerous studies have shown that combining often leads to improvements in accuracy. Despite the importance of the value at risk (VaR), though, few papers have considered quantile forecast combinations. One risk measure that is receiving an increasing amount of attention is the expected shortfall (ES), which is the expectation of the exceedances beyond the VaR. There have been no previous studies on combining ES predictions, presumably due to there being no suitable loss function for ES. However, it has been shown recently that a set of scoring functions exist for the joint estimation or backtesting of VaR and ES forecasts. We use such scoring functions to estimate combining weights for VaR and ES prediction. The results from five stock indices show that combining outperforms the individual methods for the 1% and 5% probability levels.