Semiparametric estimation of expected shortfall and its application in finance

Measuring risk effectively is crucial for managing risk in financial markets. The expected shortfall has become an increasingly popular metric for risk in recent years. How to estimate it is important in statistics and financial econometrics. Based on the single index quantile regression, we introduce a new semiparametric approach, namely, weighted single index quantile regression. We assess the performance of the proposed expected shortfall estimator with backtesting. Our simulation results indicate that the estimator has a good finite sample performance and often outperforms existing methods. By applying the new method to both a market index and individual stocks, we show that it not only exhibits the best performance but also reveals an insight about the effect of the COVID pandemic, that is, the pandemic increases the market risk.

Prediction, Risk Assessment and Comparison of Selected Emerging Markets' Stock Indices During COVID-19 Pandemic Using the Coherent Measure: Comparing Selected Emerging Markets' Stock Indices

In this study, we modeled the log-return of three emerging markets' stock indices, namely, Shanghai SSE, Russia MOEX, and Bombay Stock Exchange Sensex using the generalized hyperbolic family of distributions. We found the generalized hyperbolic family of distributions as the best fit for describing the probability density based on AIC and likelihood ratio test. The coherent risk measure, i.e., the expected shortfall, predicted using the best fit probability distribution, was used as a market risk quantification metric. During the COVID-19 period, the Indian stock market showed maximum market risk, followed by the Russian. The Chinese market showed the least market risk. Our experiment demonstrated a significant (p = 0.000) difference in the three markets concerning the coherent risk at different probability levels from 0.001 to 0.05 in the COVID-19 period using the Jonckheere-Terpstra test. The coherent market risk increased substantially in the Indian and Russian markets during the COVID-19 pandemic compared to the pre-COVID-19 period. However, in the Chinese market, we found that the coherent risk decreased during the COVID-19 period compared to the pre-COVID-19 period. We carried out the empirical study using the adjusted daily closing values of SSE, MOEX, and Sensex from July 2018 to July 2021 and dividing the data sets into pre-COVID-19 and COVID-19 periods based on the first emergence of the COVID-19 case.

Tail risk forecasting of realized volatility CAViaR models

This research proposes a new class of RES-CAViaR (conditional autoregressive value-at-risk) models, that incorporate daily realized volatility and expected shortfall (ES) to forecast VaR and ES simultaneously. We further consider weekly and monthly realized volatilities in the proposed model to approximate a long-memory process. We employ the Bayesian adaptive Markov chain Monte Carlo approach to estimate all unknown parameters and to jointly predict daily VaR and ES over a 4-year out-of-sample period including the COVID-19 pandemic. Our results show that the realized CAViaR-type models outperform in terms of three backtests, four loss-function criteria, and ES measurement at the 1% level. © 2022 Elsevier Inc.

The impact of the COVID-19 pandemic on bank systemic risk: some cross-country evidence

Purpose: This study tends to investigate how the outbreak of the coronavirus disease 2019 (COVID-19) pandemic has affected banks' contribution to systemic risk. In addition, the authors examine whether the impact of the pandemic may vary across advanced/emerging economies, and with banks with differed characteristics. Design/methodology/approach: The authors construct the bank-specific conditional value at risk (CoVaR) and marginal expected shortfall (MES) to measure their contribution to systemic risk and define the outbreak of the COVID-19 pandemic by the timing when countries report more than 100 confirmed cases. The authors use the approach of difference-in-differences to assess the impact of the COVID-19 pandemic on banks' contribution to systemic risk. This sample comprises monthly panel data of around 900 listed commercial banks in 39 advanced and emerging economies. Findings: The authors find that, firstly, the COVID-19 pandemic increased banks' contribution to systemic risk significantly around the world. Secondly, the impact of the COVID-19 virus was more pronounced in developed countries than in emerging economies. Finally, banks with a larger size and higher loan-to-deposit ratio are more greatly affected by the COVID-19 pandemic, while a higher capitalization for banks is insufficient to shelter them from the adverse impact of such pandemic. Originality/value: The authors assess the impact of the COVID-19 pandemic on banks' contribution to systemic risk. Using the conditional value at risk (marginal expected shortfall) of banks as the measure, this study's results suggest that banks' contribution to systemic risk increases by around 25% (48%) amid the COVID-19 pandemic. This study's findings may shed some light on the potential policies that financial regulators may employ to ameliorate the adverse outcomes of the ongoing pandemic. © 2022, Emerald Publishing Limited.

A comparison of methods for forecasting value at risk and expected shortfall of cryptocurrencies

Several procedures to forecast daily risk measures in cryptocurrency markets have been recently implemented in the literature. Among them, long-memory processes, procedures taking into account the presence of extreme observations, procedures that include more than a single regime, and quantile regression-based models have performed substantially better than standard methods in terms of forecasting risk measures. Those procedures are revisited in this paper, and their value at risk and expected shortfall forecasting performance are evaluated using recent Bitcoin and Ethereum data that include periods of turbulence due to the COVID-19 pandemic, the third halving of Bitcoin, and the Lexia class action. Additionally, in order to mitigate the influence of model misspecification and enhance the forecasting performance obtained by individual models, we evaluate the use of several forecast combining strategies. Our results, based on a comprehensive backtesting exercise, reveal that, for Bitcoin, there is no single procedure outperforming all other models, but for Ethereum, there is evidence showing that the GAS model is a suitable alternative for forecasting both risk measures. We found that the combining methods were not able to outperform the better of the individual models. © 2022 John Wiley & Sons Ltd.

Semiparametric estimation of expected shortfall and its application in finance

Measuring risk effectively is crucial for managing risk in financial markets. The expected shortfall has become an increasingly popular metric for risk in recent years. How to estimate it is important in statistics and financial econometrics. Based on the single index quantile regression, we introduce a new semiparametric approach, namely, weighted single index quantile regression. We assess the performance of the proposed expected shortfall estimator with backtesting. Our simulation results indicate that the estimator has a good finite sample performance and often outperforms existing methods. By applying the new method to both a market index and individual stocks, we show that it not only exhibits the best performance but also reveals an insight about the effect of the COVID pandemic, that is, the pandemic increases the market risk.

Is Tether a safe haven of safe haven amid COVID-19? An assessment against Bitcoin and oil using improved measures of risk.

Bitcoin is a new speculative investment with extremely volatile movement, thus possibly failing to act as a safe haven for crude oil when the price of this energy commodity plummeted following the global outbreak of COVID-19. Meanwhile, Tether is designed to behave similarly to the US dollar with stable fluctuation. In this study, we assessed their safe-haven properties in terms of risk reduction opportunities by proposing an improved version of Value-at-Risk (VaR) and Expected Shortfall (ES). Using vine copula-based AR-GJR-GARCH models, we demonstrated that Bitcoin exhibited inconsistent risk reduction capability for oil, particularly before COVID-19. When adding Tether into a portfolio containing oil and Bitcoin, the risk reduction was achieved for any portfolio allocation and was more pronounced amid the COVID-19 period. This suggests that Tether consistently served strong support for Bitcoin to protect oil investors against extreme risk and received a significant impact from the COVID-19 outbreak. However, the consistent safe-haven functionality of Tether was not as good as that of the US dollar in most cases, and this implied the vanishing of its stability. These results were robust when considering another asymmetric volatility model and another dependence model. Furthermore, the proposed improved VaR and ES forecasts outperformed their corresponding unimproved version in quantifying portfolio risk and therefore provided a more accurate assessment of safe-haven roles.

Tail risk forecasting of realized volatility CAViaR models

This research proposes a new class of RES-CAViaR (conditional autoregressive value-at-risk) models, that incorporate daily realized volatility and expected shortfall (ES) to forecast VaR and ES simultaneously. We further consider weekly and monthly realized volatilities in the proposed model to approximate a long-memory process. We employ the Bayesian adaptive Markov chain Monte Carlo approach to estimate all unknown parameters and to jointly predict daily VaR and ES over a 4-year out-of-sample period including the COVID-19 pandemic. Our results show that the realized CAViaR-type models outperform in terms of three backtests, four loss-function criteria, and ES measurement at the 1% level.

Oil tail-risk forecasts: from financial crisis to COVID-19

The coronavirus outbreak has caused unprecedented volatility in oil prices. This paper extends previous studies on oil Value-at-Risk (VaR) by providing extra insights into Expected Shortfall (ES) forecasting over the last decade, including several oil crises. We introduce a conditional volatility model combined with the Cornish-Fisher expansion for ES forecasting. In comparison to the widely used volatility models and innovation distributions, this approach is superior for predicting the ES of long positions but overestimates VaR for short positions. Overall, the volatility model addressing leverage effects with skewed t innovation produces the most accurate joint VaR and ES forecasting. Moreover, the magnitude of ES relative to VaR varies across models and time, implying that ES should be used in conjunction with VaR to inform timely risk management decisions. The results would be of interest to the regulatory authorities, energy companies, and financial institutions for oil tail-risk forecasting.

Spillover effects between commodity and stock markets: A SDSES approach

In this paper, we use a state-dependent sensitivity expected shortfall (SDSES) approach using expectiles. This model enables us to quantify the direction, size, and persistence of risk spillovers among the US and emerging market stock indices and different individual commodities as a function of the state of financial markets (tranquil, normal, and volatile). We obtain high and more significant spillovers and financialization process evidence in the volatile state of the post-Draghi speech and COVID-19 period, especially for the copper and wheat market. Market stock indices and commodity US market index appear to play a major role in the transmission of shocks to other markets, mainly to the wheat market.

Bayesian quantile forecasting via the realized hysteretic GARCH model

This research introduces a new model, a realized hysteretic GARCH, that is similar to a three-regime nonlinear framework combined with daily returns and realized volatility. The setup allows the mean and volatility switching in a regime to be delayed when the hysteresis variable lies in a hysteresis zone. This nonlinear model presents explosive persistence and high volatility in Regime 1 in order to capture extreme cases. We employ the Bayesian Markov chain Monte Carlo (MCMC) procedure to estimate model parameters and to forecast volatility, value at risk (VaR), and expected shortfall (ES). A simulation study highlights the properties of the proposed MCMC methods, as well as their accuracy and satisfactory performance as quantile forecasting tools. We also consider two competing models, the realized GARCH and the realized threshold GARCH, for comparison and carry out Bayesian risk forecasting via predictive distributions on four stock markets. The out-of-sample period covers the recent 4 years by a rolling window approach and includes the COVID-19 pandemic period. Among the realized models, the realized hysteretic GARCH model outperforms at the 1% level in terms of violation rates and backtests.

Copulas and Portfolios in the Electric Vehicle Sector

How can investors unlock the returns on the electric vehicle industry? Available investment choices range from individual stocks to exchange traded funds. We select six representative assets and characterize the time-varying joint distribution of their returns by copula-GARCH models. They facilitate portfolio optimization targeted at a chosen combination of risk and reward. With daily data from 2012 to 2020, we illustrate the models’ applicability by building a minimum expected shortfall portfolio and comparing its performance to that of an equally weighted benchmark. Our results should be of interest to investors and risk managers seeking or facing exposure to the electric vehicle sector.

The Role of Risk Forecast and Risk Tolerance in Portfolio Management: A Case Study of the Chinese Financial Sector

Portfolio decisions are affected by the volatility of financial markets and investors’ risk tolerance levels. To better allocate portfolios;we introduce risk tolerance into the portfolio management problem by considering the risk contribution of portfolio components. In this paper, portfolio weights are allocated to two stages. In the first stage, the portfolio risks and the risk contribution of each share are forecasted. In the second stage, we put forward three weighting techniques—“aggressive”, “moderate” and “conservative”, according to three standard levels of risk tolerance. In addition, a new risk measure called “joint extreme risk probability” (JERP), with risk tolerance taken into account, is proposed. A case study of the Chinese financial industry is conducted to verify the performance of our methods. The empirical results demonstrate that weighting techniques constrained by risk tolerance lead to higher gains in a normal market and less loss when a market is risky. Compared with risk-tolerance-adjusted strategies, the relationship between the performance of the traditional conditional value at risk (CVaR) minimization method and the market risk level is less obviously demonstrated. Viewed from the results, JERP functions as an effective signal that helps investors to deal with potential market risks.