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The development of models for variables sampled at different frequencies has attracted substantial interest in the recent literature. In this article, we discuss classical and Bayesian methods of estimating mixed-frequency VARs, and use them for forecasting and structural analysis. We also compare mixed-frequency VARs with other approaches to handling mixed-frequency data.

Value at risk (VaR) and expected shortfall (ES) are popular market risk measurements. The former is not coherent but robust, whereas the latter is coherent but less interpretable, only conditionally backtestable and less robust. In this chapter, we compare an innovative artificial neural network (ANN) model with a time series model in the context of forecasting VaR and ES of the univariate time series of four asset classes: US large capitalization equity index, European large cap equity index, US bond index, and US dollar versus euro exchange rate price index for the period of January 4, 1999, to December 31, 2018. In general, the ANN model has more favorable backtesting results as compared to the autoregressive moving average, generalized autoregressive conditional heteroscedasticity (ARMA-GARCH) time series model. In terms of forecasting accuracy, the ANN model has much fewer in-sample and out-of-sample exceptions than those of the ARMA-GARCH model.

This paper investigates how various strategies for combining forecasts, both simple and optimised approaches, are compared with popular individual risk models in estimating value-at-risk (VaR) and expected shortfall (ES) in emerging market at alternative risk levels.

Using the case study of the Vietnamese stock market, the author produced one-day-ahead VaR and ES forecast from seven individual risk models and ten alternative forecast combinations. Next, the author employed a battery of backtesting procedures and alternative loss functions to evaluate the global predictive accuracy of the different methods. Finally, the author investigated the relative performance over time of VaR and ES forecasts using fluctuation test.

The empirical results indicate that, although combined forecasts have reasonable predictive abilities, they are often outperformed by one individual risk model. Furthermore, the author showed that the complex combining methods with optimised weighting functions do not perform better than simple combining methods. The fluctuation test suggests that the poor performance of combined forecasts is mainly due to their inability to cope with periods of instability.

This study reveals the limitation of combining strategies in the one-day-ahead VaR and ES forecasts in emerging markets. A possible direction for further research is to investigate whether this finding holds for multi-day ahead forecasts. Moreover, the inferior performance of combined forecasts during periods of instability motivates further research on the combining strategies that take into account for potential structure breaks in the performance of individual risk models. A potential approach is to improve the individual risk models with macroeconomic variables using a mixed-data sampling approach.

First, the authors contribute to the literature on the forecasting combinations for VaR and ES measures. Second, the author explored a wide range of alternative risk models to forecast both VaR and ES with recent data including periods of the COVID-19 pandemic. Although forecast combination strategies have been providing several good results in several fields, the literature of forecast combination in the VaR and ES context is surprisingly limited, especially for emerging market returns. To the best of the author’s knowledge, this is the first study investigating predictive power of combining methods for VaR and ES in an emerging market.

The main objective of this paper is to analyze the dynamic volatility spillovers between the investor's behavioral biases, the macroeconomic instability factors and the value at risk of the US Fintech stock market before and during the COVID-19 pandemic.

The authors used the methodologies proposed by Diebold and Yilmaz (2012) and the wavelet approach.

The wavelet coherence results show that during the COVID-19 period, there was a strong co-movement among value at risk and each selected variables in the medium-run and the long-run scales. Diebold and Yilmaz's (2012) method proved that the total connectedness index raised significantly during the COVID-19 period. Moreover, the overconfidence bias and the financial stress index are the net transmitters, while the value at risk and herding behavior variables are the net receivers.

This study offers some important implications for investors and policymakers to explain the impact of the COVID-19 pandemic on the risk of Fintech industry.

The study findings might be useful for investors to better understand the time–frequency connectedness and the volatility spillover effects in the context of COVID-19 pandemic. Future research may deal with investors' ability of constructing portfolios with another alternative index like cryptocurrencies which seems to be a safer investment.

To the best of the authors' knowledge, this is the first study that relies on the continuous wavelet decomposition technique and spillover volatility to examine the connectedness between investor behavioral biases, uncertainty factors, and Value at Risk of US Fintech stock markets, while taking into account the recent COVID-19 pandemic.

Financial asset return series usually exhibit nonnormal characteristics such as high peaks, heavy tails and asymmetry. Traditional risk measures like standard deviation or variance are inadequate for nonnormal distributions. Value at Risk (VaR) is consistent with people's psychological perception of risk. The asymmetric Laplace distribution (ALD) captures the heavy-tailed and biased features of the distribution. VaR is therefore used as a risk measure to explore the problem of VaR-based asset pricing. Assuming returns obey ALD, the study explores the impact of high peaks, heavy tails and asymmetric features of financial asset return data on asset pricing.

A VaR-based capital asset pricing model (CAPM) was constructed under the ALD that follows the logic of the classical CAPM and derive the corresponding VaR-β coefficients under ALD.

ALD-based VaR exhibits a minor tail risk than VaR under normal distribution as the mean increases. The theoretical derivation yields a more complex capital asset pricing formula involving β coefficients compared to the traditional CAPM.The empirical analysis shows that the CAPM under ALD can reflect the β-return relationship, and the results are robust. Finally, comparing the two CAPMs reveals that the β coefficients derived in this paper are smaller than those in the traditional CAPM in 69–80% of cases.

The paper uses VaR as a risk measure for financial time series data following ALD to explore asset pricing problems. The findings complement existing literature on the effects of high peaks, heavy tails and asymmetry on asset pricing, providing valuable insights for investors, policymakers and regulators.

This study explores the effect of video assistant referee (VAR) sponsorship on spectator response and compares it with advertising and conventional sponsorship.

An experiment with 809 subjects is conducted by analyzing 20 one-minute video clip stimuli from a Premier League soccer game divided into four formats: two formats of VAR sponsorship, advertising, and conventional sponsorship.

The results show that the indicators of recall, credibility, and perceived congruence improve when the VAR sponsorship format is used.

This is the first manuscript to examine the effectiveness of a new type of sponsorship: VAR sponsorship. This manuscript provides metrics that will guide practitioners on whether to use this type of sponsorship.

This paper aims to better jointly estimate Value at Risk (VaR) and expected shortfall (ES) by using the joint regression combined forecasting (JRCF) model.

Combining different forecasting models in financial risk measurement can improve their prediction accuracy by integrating the individual models’ information. This paper applies the JRCF model to measure VaR and ES at 5%, 2.5% and 1% probability levels in the Chinese stock market. While ES is not elicitable on its own, the joint elicitability property of VaR and ES is established by the joint consistent scoring functions, which further refines the ES’s backtest. In addition, a variety of backtesting and evaluation methods are used to analyze and compare the alternative risk measurement models.

The empirical results show that the JRCF model outperforms the competing models. Based on the evaluation results of the joint scoring functions, the proposed model obtains the minimum scoring function value compared to the individual forecasting models and the average combined forecasting model overall. Moreover, Murphy diagrams’ results further reveal that this model has consistent comparative advantages among all considered models.

The JRCF model of risk measures is proposed, and the application of the joint scoring functions of VaR and ES is expanded. Additionally, this paper comprehensively backtests and evaluates the competing risk models and examines the characteristics of Chinese financial market risks.

The purpose of this article is to estimate value at risk (VaR) using quantile regression and provide a risk analysis for defaultable bond portfolios.

The method proposed is based on quantile regression pioneered by Koenker and Bassett. The quantile regression approach allows for a general treatment on the error distribution and is robust to distributions with heavy tails.

This article provides a risk analysis for defaultable bond portfolios using quantile regression method. In the proposed model we use information variables such as short‐term interest rates and term spreads as covariates to improve the estimation accuracy. The study also finds that confidence intervals constructed around the estimated VaRs can be very wide under volatile market conditions, making the estimated VaRs less reliable when their accurate measurement is most needed.

Provides a risk analysis for defaultable bond using quantile regression approach.

This paper aims to perform an analytical analysis on portfolio allocation when a tracking error volatility (TEV) constraint holds, drawing specific attention to the portfolio efficiency issue. Indeed, it is well known that investors can assign part of their funds to asset managers who are given the task of beating a benchmark portfolio. However, the risk management office often imposes a TEV constraint to the asset managers’ activity to maintain the portfolio risk near to the risk of the benchmark. This situation could lead asset managers to select non efficient portfolios in the total return and absolute risk perspective. However, the risk management office can impose further constraints, such as on maximum variance or maximum value at risk (VaR) to maintain the overall portfolio risk under control.

First the authors define the TEV constrained-efficient frontier (ECTF), a set of TEV constrained portfolios that are mean–variance efficient. Second, they define two new portfolio frontiers analyzing how the imposition of a maximum variance or maximum VaR restriction can reduce the ECTF. Third, they investigate the feasibility of such portfolio frontiers and their relationships.

The authors find that variance or VaR constraint can force asset managers to pursue portfolio efficiency.

This is a practically important issue given that asset managers often receive a constraint on TEV from the risk management office, but the risk management office does not ask them to minimize the TEV as often assumed in the optimizations performed in the literature on this topic.