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The paper aims to analyse the drivers of changes in European equity tail risk.

For this purpose, the paper uses a panel data model with fixed effects based on five explanatory variables including the VIX, the variance risk premium (VRP), the one-year lagged slope of the riskless term-structure, the default spread and market-specific illiquidity via the measure of Bao et al. (2011). The study analyses a comprehensive database of representative European equity indices from February 2003 to December 2013. The database just contains markets of euro member states to avoid biases due to different currencies. To measure equity tail risk, the ex post realized value-at-risk was used.

There is empirical evidence that the VIX, the VRP and the default spread are key determinants of equity tail risk changes across all markets. Moreover, the results reveal that market-specific illiquidity is an important determinant in PIIGS markets and the one-year lagged term-structure slope in core markets. The analysis also documents that market-specific risk premia are a relevant determinant of equity tail risk changes. Another finding is that risk premia in PIIGS markets are basically higher as in core markets, which reflect the higher risk involved in investing in PIIGS markets.

The paper offers a unique perspective on equity tail risk in aggregate equity markets and helps both investors and risk managers to get a comprehensive understanding of relevant drivers.

The use of risk proxies in internal models remains a popular modelling solution. However, there is some risk that a proxy may not constitute an adequate representation of the underlying asset in terms of capturing tail risk. Therefore, using empirical examples for the financial collateral haircut model, this paper aims to critically review available statistical tools for measuring the adequacy of capturing tail risk by proxies used in the internal risk models of banks. In doing so, this paper advises on the most appropriate solutions for validating risk proxies.

This paper reviews statistical tools used to validate if the equity index/fund benchmark are proxies that adequately represent tail risk in the returns on an individual asset (equity/fund). The following statistical tools for comparing return distributions of the proxies and the portfolio items are discussed: the two-sample Kolmogorov–Smirnov test, the spillover test and the Harrell’s C test.

Upon the empirical review of the available statistical tools, this paper suggests using the two-sample Kolmogorov–Smirnov test to validate the adequacy of capturing tail risk by the assigned proxy and the Harrell’s C test to capture the discriminatory power of the proxy-based collateral haircuts models. This paper also suggests a tool that compares the reactions of risk proxies to tail events to verify possible underestimation of risk in times of significant stress.

The current regulations require banks to prove that the modelled proxies are representative of the real price observations without underestimation of tail risk and asset price volatility. This paper shows how to validate proxy-based financial collateral haircuts models.

Considering the frequency of extreme events, enhancing the global financial system's stability has become crucial. This study aims to investigate the contagion effects of extreme risk events in the international commodity market on China's financial industry. It highlights the significance of comprehending the origins, severity and potential impacts of extreme risks within China's financial market.

This study uses the tail-event driven network risk (TENET) model to construct a tail risk spillover network between China's financial market and the international commodity market. Combining with the characteristics of the network, this study employs an autoregressive distributed lag (ARDL) model to examine the factors influencing systemic risks in China's financial market and to explore the early identification of indicators for systemic risks in China's financial market.

The research reveals a strong tail risk contagion effect between China's financial market and the international commodity market, with a more pronounced impact from the latter to the former. Industrial raw materials, food, metals, oils, livestock and textiles notably influence China's currency market. The systemic risk in China's financial market is driven by systemic risks in the international commodity market and network centrality and can be accurately predicted with the ARDL-error correction model (ECM) model. Based on these, Chinese regulatory authorities can establish a monitoring and early warning mechanism to promptly identify contagion signs, issue timely warnings and adjust regulatory measures.

This study provides new insights into predicting systemic risk in China's financial market by revealing the tail risk spillover network structure between China's financial and international commodity markets.

The authors examined whether stocks with higher left-tail risk measures earn higher or lower futures returns. Specifically, the authors estimate the cross-sectional principal component of a battery of left-tail risk measures and analyze future returns on stocks with high principal component values. In contrast to finance theories on the risk–return trade-off relationship, the study results show that high left-tail risk stocks have lower future returns. This finding is robust to various left-tail risk measures and controls for other risk factors. Moreover, the negative relationship between the left-tail risk and returns is more pronounced for stocks that are actively traded by retail investors. This empirical result is consistent with behavioral theory that when investors make decisions based on experience, they tend to underweight the likelihood of rare events.

The purpose of this paper is to present theoretical and empirical support that the fear component associated with rare events has an impact on risk premium and market returns.

Extension of jump-diffusion model to extract the fear component from representative agent risk aversion, Standard VAR and impulse response function analysis, Event study analysis.

The model implicates that investor fear of tail jumps in the financial market impacts equity risk premium. The empirical findings show both positive stock and monetary policy shocks decrease investor’s fear. It can be attributed to that a bullish stock market and an increase in interest rate reflects expanding economy, and it leads to a decrease in fear. Moreover, a surprise decline in the expected short-term rate has a mixed impact on tail risk aversion. A plausible explanation is that investors believe a surprise drop in an expected short-term rate reflects a fast deteriorating economic outlook during unconventional monetary policy period.

This paper provides theoretical framework to decompose risk aversion into two separate components: one component associated with daily volatility, and the fear component associated with rare events. The study uses risk premiums decomposed from Chicago Board Options Exchange volatility index as proxies for the two components of risk aversion, and then utilizes standard value at risk and event study analysis to show the fear component plays a role in risk premium and market return.

This paper aims to provide new perspectives on the integration of East Asian stock markets and the dynamic volatility transmission to the Bitcoin market utilising daily data from 2014 to 2020.

The authors undertake comprehensive analyses of the dependency dynamics, systemic risk and volatility spillover between major East Asian stock and Bitcoin markets. The authors employ a vine-copula-CoVaR framework and a VAR-BEKK-GARCH method with a Wald test.

(a) With exception of KS11 and N225; HSI and SSE; HSI and KS11, which have moderate dependence, dependencies among other markets are low. In terms of tail risk, the upper tail risk is more significant in capturing strong common variation. (b) Two-way and asymmetric risk spillover effects exist in all markets. The Hong Kong and Japanese stock markets have significant risk spillovers to other markets, and quite notably, the Chinese stock market is the largest recipient of systemic risk. However, the authors observe a more significant risk spillover from the Chinese stock market to the Bitcoin market. (c) The VAR-BEKK-GARCH results confirm that the Korean market is a significant emitter of volatility spillovers. The Bitcoin market does provide diversification benefits. Interestingly, the Chinese stock market has an intriguing relationship with Bitcoin. (d) An increase in spillovers in East Asia boosts spillovers to Bitcoin, but there is no intuitive effect of Bitcoin spillovers on East Asian spillovers.

For the first time, the authors examine the dynamic linkage between Bitcoin and the major East Asian stock markets.

Application of financial risk models in the emerging markets poses special challenges. A fundamental challenge is to accurately model the return distributions which are particularly fat tailed and skewed. Value-at-Risk (VaR) measures based on the Extreme Value Theory (EVT) have been suggested, but typically data histories are limited, making it hard to test and apply EVT. The chapter addresses issues in (i) modeling the VaR measure in the presence of structural breaks in an economy, (ii) the choice of stable innovation distribution with volatility clustering effects, (iii) modeling the tails of the empirical distribution, and (iv) fixing the cut-off point for isolating extreme observations. Pakistan offers an instructive case since its equity market exhibits high volatility and incidence of extreme returns. The recent Global Financial Crisis has been another source of extreme returns. The confluence of the two sources of volatility provides us with a rich data set to test the VaR/EVT model rigorously and examine practical challenges in its application in an emerging market.

This study examines problems that may occur when conventional Value‐at‐Risk (VaR) estimators are used to quantify market risks in an agricultural context. For example, standard VaR methods, such as the variance‐covariance method or historical simulation, can fail when the return distribution is fat tailed. This problem is aggravated when long‐term VaR forecasts are desired. Extreme Value Theory (EVT) is proposed to overcome these problems. The application of EVT is illustrated by an example from the German hog market. Multi‐period VaR forecasts derived by EVT are found to deviate considerably from standard forecasts. We conclude that EVT is a useful complement to traditional VaR methods.

This study aims to investigate the risk-return trade-off in the Indian equity market at both the aggregate equity market level and in the cross-sections of stock return using alternative risk measures.

The study uses weekly and monthly data of 3,085 Bombay Stock Exchange-listed stocks spanning over 20 years from January 2000 to December 2019. The study evaluates the risk-return trade-off at the aggregate equity market level using the value-weighted and the equal-weighted broader portfolios. Eight different risk proxies belonging to the conventional, downside and extreme risk categories are considered to analyse the cross-sectional risk-return relationship.

The results show a positive equity premium on the value-weighted portfolio; however, the equal-weighted portfolio of these stocks shows an average return lower than the return on the 91-day Treasury Bills. The inverted size premium mainly causes this anomaly in the Indian equity market as the small stocks have lower returns than big stocks. The study presents a strong negative risk-return relationship across different risk proxies. However, under the subsample of more liquid stocks, the low-risk anomaly regarding other risk proxies becomes moderate except the beta-anomaly. This anomalous relationship seems to be caused by small and less liquid stocks having low institutional ownership and higher short-selling constraints.

The findings have important implications for investors, managers and practitioners. Investors can incorporate the effects of different highlighted anomalies in their investment strategies to fetch higher returns. Managers can also use these findings in their capital budgeting decisions, resource allocations and other diverse range of direct and indirect decisions, particularly in emerging markets such as India. The findings provide insights to practitioners while valuing the firms.

The study is among the earlier attempts to examine the risk-return trade-off in an emerging equity market at both the aggregate equity market level and in the cross-sections of stock returns using alternative measures of risk and expected returns.

The purpose of this paper (the first of two) is to consider measures of risk commonly used in the analysis of both investment and insurance portfolios, and argue that there is a need for more appropriate measures to capture the uncertainty inherent in non‐normal (i.e. asymmetric and/or long tailed) probability distributions.

In Part 1, the risk measures used most frequently in finance and insurance – i.e. the standard deviation (variance), value at risk, tail value at risk, default value, etc. – are reviewed and then the paper explores whether such measures are sufficient for all contexts, including those in which the subject random variable is characterized by asymmetry and/or long tails. As an alternative to conventional measures, the paper assesses the potential of a general p‐norm‐based definition of “risk”.

Virtually, all commonly used risk measures, even those designed specifically to capture the behavior of asymmetric randomness, require that the underlying random variable possess a finite variance, or at least a finite mean. To overcome such difficulties, the paper considers a general definition of “risk” based upon a quantity closely related to the p‐norm – the p‐mean of absolute‐centered deviations (of which the standard deviation is a special case) – and show that this approach yields a single, but degenerate, result for all distributions.

The paper explores the use of p‐norm‐based measures in constructing a general definition of “risk” that is equally applicable to asymmetric and long‐tailed random variables as to normal random variables.