Tail Risk Research Articles

A Bayesian realized threshold measurement GARCH framework for financial tail risk forecasting

AbstractThis paper proposes an innovative threshold measurement equation to be employed in a Realized‐Generalized Autoregressive Conditional Heteroskedastic (GARCH) framework. The proposed framework incorporates a nonlinear threshold regression specification to consider the leverage effect and model the contemporaneous dependence between the observed realized measure and hidden volatility. A Bayesian Markov chain Monte Carlo method is adapted and employed for model estimation, with its validity assessed via a simulation study. The validity of incorporating the proposed measurement equation in Realized‐GARCH type models is evaluated via an empirical study, forecasting the 1% and 2.5% Value‐at‐Risk and expected shortfall on six market indices with two different out‐of‐sample sizes. The proposed framework is shown to be capable of producing competitive tail risk forecasting results in comparison with the GARCH and Realized‐GARCH type models.

Macroeconomic tail risk, currency crises and the inter‐war gold standard

AbstractWe introduce macroeconomic tail risk into the canonical global game model of currency crises. The exchange rate peg is attacked if fundamentals reach a critical threshold, or if there is a sufficiently large public shock. Large shocks generate doubt amongst investors about both the state of the world and about what others know, giving rise to multiple equilibria. We find a non‐monotonic relationship between tail risk and the probability of (a fundamentals‐based) crisis and show how this effect depends on the magnitude and direction of public shocks. We consider the implications of policy intervention and identify conditions under which active intervention produces doubt about the level of fundamentals and, hence, how others will respond. Our analysis clarifies how financial contagion in Europe precipitated the sterling crisis of 1931.

Reduced Nodal Admittance Matrix Method for Probabilistic GIC Analysis in Power Grids

Efficient probabilistic geomagnetically induced current (GIC) analysis in power grids provides tools for assessing and mitigating small-probability tail risks of geomagnetic disturbances, especially in early warning and real-time scenarios. This letter employs the reduced nodal admittance matrix (RNAM) to speed up GIC calculation based on Kron reduction. Moreover, the proposed RNAM method is used to achieve a more efficient analysis of probabilistic GICs, which considers the uncertainty of the substation grounding resistances. The novel method is compared with the classical algorithms including the nodal admittance matrix method, the Lehtinen-Pirjola method, and the bus admittance matrix method, and its efficiency improvement is illustrated with several power grid test cases.

A capital asset pricing model based on the value at risk under asymmetric Laplace distribution

PurposeFinancial 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.Design/methodology/approachA 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.FindingsALD-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.Originality/valueThe 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.

Tail risk of international equity market and oil volatility

This paper employs the approach prompted by Kelly and Jiang (2014) to calculate a tail risk index for the global stock market. Our empirical results demonstrate that tail risk of the international stock market is statistically and economically informative about oil volatility. After controlling for EMV and VIX variables, tail risk of international stock market is still useful for predicting oil volatility. Our results prove that tail risk could provide incremental information for the connection between stock market and oil volatility.

Multi-period portfolio optimization based on credibilistic lower and upper VaR ratios

Emerging markets, such as the Chinese financial market, are occasionally subject to extreme risk events that result in investor losses during the investment process. To address the challenge of investment selection amidst market fluctuations, considering the fuzzy uncertainty and tail risk compensation based on the asymmetric perspective, we propose to use the lower VaR ratio and the upper VaR ratio as investment objectives to construct a multi-period credibilistic portfolio selection model. The study reveals that the cumulative returns and terminal wealth of the constructed model surpassed those of the benchmark models, delivering greater social and economic welfare to investors. During extreme events, investors could promptly adjust their portfolio structure to achieve higher investment returns. Investors who prefer the lower VaR ratio tend to make conservative investment decisions and allocate a higher proportion to defensive assets, such as bonds and risk-free assets. Conversely, investors who favor the upper VaR ratio are inclined to adopt aggressive investment strategies and allocate a larger proportion to high-risk stocks. The findings demonstrate that the proposed model offers differentiated investment decisions, and the research conclusions serve as valuable references for investors engaged in multi-period asset allocation and risk management.

Policy uncertainty and bank systemic risk: A perspective of risk decomposition

This paper examines the driving effect of economic policy uncertainty on bank systemic risk with a distinction between systemic linkage and bank tail risk. Using bank-level data of 25 economies during the period 2010–2020, we find consistent and robust evidence that policy uncertainty is negatively associated with bank tail risk but positively related to systemic linkage. When policy uncertainty emerges, banks tend to perform less risk-taking activities but with more homogeneous business patterns, which reflect in market performance. We also investigate the role of national culture that a more individualistic and short-term orientated culture environment will aggravate bank systemic risk.

Housing Boom‐Bust Cycles and Asymmetric Macroprudential Policy

AbstractIn this paper, I argue that occasionally binding borrowing constraints are a source of nonlinearity that warrant an appropriate nonlinear macroprudential policy response. Nonlinear policy responses likely better capture the spirit of macroprudential policy. I show that an asymmetric macroprudential policy rule, which lowers the borrowing limit more aggressively during credit booms, obtains better economic outcomes compared to an optimized symmetric rule that is typically studied in the literature. An asymmetric policy response reduces output and inflation tail risks, generating not only better economic stabilization but also positive externalities to monetary policy.

Value‐at‐Risk with quantile regression neural network: New evidence from internet finance firms

AbstractTraditional risk measurements have proven inadequate in capturing tail risk and nonlinear correlation. This study proposes a novel approach to measure financial risk in the Internet finance industry: a new Value‐at‐Risk (VaR) measurement based on quantile regression neural network (QRNN). Sparrow Search Algorithm (SSA) is utilized to optimize the QRNN model, which improves the model's performance in predicting internet finance risk. By comparing the TGARCH‐VaR and QR‐VaR approaches, our study demonstrates the effectiveness of the QRNN‐VaR approach and its potential to improve the accuracy of risk prediction in the Internet finance industry. This study further examines and compares the risks between the traditional and internet finance industries. It also considers the unique impact of COVID‐19 on industry risk based on statistical testing for differences and machine learning models. Our results indicate that the level of risk in the Internet finance industry is higher than in the traditional finance industry. Moreover, COVID‐19 has contributed to increased risk within the Internet finance industry. These findings have significant implications for investors and policymakers seeking to better understand and manage risks within the Internet finance industry, particularly in the ongoing COVID‐19 pandemic.

Is tail risk priced in the cross-section of international stock index returns?

This study examines the predictive power of tail risk measures in stock indices returns using a comprehensive dataset covering 50 countries from 1926 to 2021. Our findings reveal that tail risk measures exhibit predictive power when considered independently. However, their forecasting abilities disappear when other risk and return factors are incorporated. This suggests that tail risk measures do not contain incremental information about the cross-section of stock returns beyond the commonly used global factors. Our findings are robust across various considerations, holding for alternative tail risk measure types, estimation periods, and different control variables subsets.

Links between US and Turkish agricultural commodity Markets: Nonlinear dependence and tail risk

In these unprecedented times, marred by the effects of the Covid-19 pandemic, global warming, and the war in Ukraine that began in February 2022, new approaches such as tail dependence have attracted more interest than conventional market dependence methodologies in analyzing time series in order to evaluate market linkage. In this study, we use the tail-restricted integrated regression function (IRF), introduced as a new methodology for nonlinear tail-mean dependence analysis. The IRF approach has several advantages over the existing tail-dependence measures focused solely on the occurrence of single tail events. To examine market dependence and tail risk, we analyze the nexus between the US and Turkish agricultural commodity markets over the period January 5, 2016–May 31, 2022. In addition to the daily prices of barley, corn, and wheat on agricultural commodity markets, we use Brent oil as a representative for the energy market, interest, and foreign exchange rates for financial markets as variables in our study. The results of upside and downside asymmetric risk spillovers show the direction of impact from the US agricultural market to the Turkish agricultural market. The findings suggest that, following the launch of a spot market in Türkiye, the launch of an agricultural commodity futures market will enhance the completeness and the link between the spot and derivatives markets there.

On the Diversification Effect in Solvency II for Extremely Dependent Risks

In this article, we investigate the validity of diversification effect under extreme-value copulas, when the marginal risks of the portfolio are identically distributed, which can be any one having a finite endpoint or belonging to one of the three maximum domains of attraction. We show that Value-at-Risk (V@R) under extreme-value copulas is asymptotically subadditive for marginal risks with finite mean, while it is asymptotically superadditive for risks with infinite mean. Our major findings enrich and supplement the context of the second fundamental theorem of quantitative risk management in existing literature, which states that V@R of a portfolio is typically non-subadditive for non-elliptically distributed risk vectors. In particular, we now pin down when the V@R is super or subadditive depending on the heaviness of the marginal tail risk. According to our results, one can take advantages from the diversification effect for marginal risks with finite mean. This justifies the standard formula for calculating the capital requirement under Solvency II in which imperfect correlations are used for various risk exposures.

Tail risk in the Chinese stock market: An AEV model on the maximal drawdowns

This paper proposes a novel autoregressive extreme value (AEV) framework with covariates to capture the time-dependent dynamics of financial tail risk. Using the intra-day maxima of 5-minute potential drawdowns for CSI300 in the Chinese stock market, the study estimates an AEV(1,1) model with the effects of the foreign exchange market, interest rate market, and commodity futures market. The empirical results suggest that the commodity futures market plays a role in driving the maximal drawdown. Moreover, the tail index of AEV sensitively captures the clustering of tail behaviors in the Chinese stock market. Finally, the backtesting evidence further demonstrates that AEV exhibits satisfactory forecasting performance for Value-at-Risk in the Chinese stock market.

Delays in Climate Transition Can Increase Financial Tail Risks: A Global Lesson from a Study in Mexico

Delays in Climate Transition Can Increase Financial Tail Risks: A Global Lesson from a Study in Mexico

A continuous heterogeneous agent model for multi-asset pricing and portfolio construction under market matching friction

We propose a novel continuous Heterogeneous Agent Model (HAM) that applies to the general n>1 risky assets. In this model, every heterogeneous investor is identified with the continuous variables reflecting their personal characteristics. The heterogeneity of the market is captured by the distribution of these variables. By introducing market friction via a matching-based pricing mechanism, we derive a pricing equation from market clearing. The equation extends the classical CAPM and specifies how the bounded rationality and heterogeneity of investors can drive the actual price of risky assets away from their CAPM price. A system of ordinary (stochastic) differential equations are derived to govern the evolution of the total wealth and market value of risky assets held by the entire market (individual investors). From the equation system, a rolling-window-based maximum likelihood algorithm is developed to calibrate the model, which turn our HAM to a forecast tool for stock returns and an adaptive adjustment strategy for portfolio construction. This bridges the theoretical study on HAMs with the empirical studies of asset pricing and portfolio theory. We apply this tool to the Chinese A-share market and make a comparative analysis on its performance. The results demonstrate that compared to the classical forecast approaches in literature, our HAM has the advantage in identifying the tail risk in real market, which results in a more profitable portfolio in a variety of different investment horizons.

Does sharia-compliant debt financing reduce stock price crash risk?

PurposeThis paper examines the impact of sharia-compliant debt financing on stock price crash risk. Unlike those previous studies that took Sukuk or sharia-compliant firms, this study tests the impact of the proportion reported sharia-compliant debt financing in the balance sheet on the risk of price crash of a firm.Design/methodology/approachUsing the data from 2,752 firm-year observations of 344 Malaysian non-financial listed companies from 2012 to 2019, this article used a robust panel data estimation technique for statistical inferences. This study also employs panel GMM and quantile least squares as the robustness check.FindingsThis study established a negative relationship between sharia-compliant debt financing and stock price crash risk. The robustness checks with different estimation techniques confirm the results. It implies that firms with a more significant proportion of Sharia-compliant financing tend to have lower future stock price crash risk.Practical implicationsConsistent with the Islamic finance literature, the present study contributes to the existing literature on Islamic capital markets from the perspective of stock price crash risk because it is vital for risk management and investment decision-making as a measure of tail risk for stocks. The findings of this research will assist investors in developing portfolio strategies that incorporate firms with higher levels of sharia-compliant debt financing in their balance sheets. Additionally, the results of this study suggest that policymakers and regulatory bodies should consider revising their monitoring approaches for publicly listed firms.Originality/valueThis study is interesting and unique, as it is a pioneer in testing the impact of sharia-compliant debt financing on reducing stock price crash risk.

Extreme downside risk transmission between green cryptocurrencies and energy markets: The diversification benefits

This study investigates the connectedness between renewable energy cryptocurrencies and various energy categories, focusing on extreme downside risk or tail risk. The research employs a novel framework that combines the CAViaR model with the TVP-VAR based connectedness approach to analyze the systematic tail risk transmission mechanisms. The study covers a period from January 2, 2018, to January 25, 2023, and reveals that Solar and WILDERHILL clean energy markets had the highest risk levels. Conversely, clean energy cryptocurrencies like GARID, POWR, and SNC demonstrated stable tail risk over time, offering diversification benefits, particularly in relation to energy metals and fossil fuels. The study identified strong intra-class connectedness clusters and highlighted extreme risk spillovers during crisis periods through time-varying trends. Several implications for policymakers, investors, and financial market participants are suggested.

The fatter the tail, the shorter the sail

AbstractGuided by the extreme value theory, this study empirically investigates the impact of tail risk measures on financial distress of publicly traded bank holding companies (BHCs) in the United States. Our results show that tail risk measures namely, value‐at‐risk and expected shortfall, are significantly and positively related to banks distress risk. Implying that BHCs with more frequent extreme negative daily equity returns induce higher tail risks, thereby increasing their likelihood of experiencing financial distress. Our results also show that tail risk measures enhance the explanatory power of traditional models explaining banks distress risk based on accounting information. These results indicate that market discipline is generally beneficial in managing and regulating banks, bolstering claims of the importance of macro‐prudential supervision of financial institutions.

Can firms with higher ESG ratings bear higher bank systemic tail risk spillover?—Evidence from Chinese A-share market

How can non-financial enterprises mitigate the tail risk shock from the banking system? This paper considers this problem by constructing six indices to measure the tail risk spillover from the banking system to firms (TRiskSB2F), and studies how ESG ratings of firms affect TRiskSB2F. Empirical results find that firms with high ESG ratings can bear the higher bank systemic tail risk spillover, and one standard deviation increases in the logarithm of ESG scores is associated with 0.169 percentage points lower per quarter in TRiskSB2F. Further results show that ESG ratings of firms with the small size, low liquidity stocks, listed on the main board or more long-term loans have higher sensitivity to reduce the impact of TRiskSB2F, but the sensitivity is significantly lowered in the pre-2015 bull market period. The mechanism analysis shows that firms with high ESG ratings have generally the relatively low financial constraints, good reputations and more resource superiority, which are important reasons to reduce the tail risk shock from the banking system. Our results can provide valuable evidence supporting companies to increase ESG investing.

Risk modellingof ESG (environmental, social, and governance), healthcare, and financial sectors.

Climate change poses enormous ecological, socio-economic, health, and financial challenges. A novel extreme value theory is employed in this study to model the risk to environmental, social, and governance (ESG), healthcare, and financial sectors and assess their downside risk, extreme systemic risk, and extreme spillover risk. We use a rich set of global daily data of exchange-traded funds (ETFs) from 1 July 1999 to 30 June 2022 in the case of healthcare and financial sectors and from 1 July 2007 to 30 June 2022 in the case of ESG sector. We find that the financial sector is the riskiest when we consider the tail index, tail quantile, and tail expected shortfall. However, the ESG sector exhibits the highest tail risk in the extreme environment when we consider a shock in the form of an ETF drop of 25% or 50%. The ESG sector poses the highest extreme systemic risk when a shock comes from China. Finally, we find that ESG and healthcare sectors have lower extreme spillover risk (contagion risk) compared to the financial sector. Our study seeks to provide valuable insights for developing sustainable economic, business, and financial strategies. To achieve this, we conduct a comprehensive risk assessment of the ESG, healthcare, and financial sectors, employing an innovative approach to risk modelling in response to ecological challenges.