Tail Risk Research Articles

Downside Risk in Australian and Japanese Stock Markets: Evidence Based on the Expectile Regression

The expectile-based Value at Risk (EVaR) has gained popularity as it is more sensitive to the magnitude of extreme losses than the conventional quantile-based VaR (QVaR). This paper applies the expectile regression approach to evaluate the EVaR of stock market indices of Australia and Japan. We use an expectile regression model that considers lagged returns and common risk factors to calculate the EVaR for each stock market and to evaluate the interdependence of downside risk between the two markets. Our findings suggest that both Australian and Japanese stock markets are affected by their past development and the international stock markets. Additionally, ASX 200 index has significant impact on Nikkei 225 in terms of downside tail risk, while the impact of Nikkei 225 on ASX is not significant.

Does Unconditional Accounting Conservatism Imply Upside or Downside Risk? Evidence from the Options Market

SYNOPSIS Conservatism captures an asymmetric reporting practice in response to uncertainty in business operations (earnings). Such uncertainty in business operations implies that investors are exposed to tail risk such that there is a probability of large earnings growth, offset by the probability of a large earnings decline. Existing literature has shown that accounting conservatism relates positively to stock returns. However, the literature is silent on whether this pricing is driven by positive earnings expectation or by the potential negative earnings growth. Using option-implied assets, we find that conservatism is priced by investors’ risk aversion (downside risk) rather than the potential upside. Several robustness tests confirm the findings. We also provide evidence that the returns are not driven by mispricing but as compensation for the risk implied by conservative reporting. We further decompose an alternate conservatism measure and find that our results are driven by the uncertainty in expenses rather than revenues.

Green Assets and Global Portfolio Tail Risk? A Stress-Testing exercise under multiple asset classes under distinct market phases

Despite a burgeoning literature in the sphere of cryptocurrencies and green assets, yet, as of date, the literature fares poorly in terms of a holistic assessment of all asset classes, let alone stress testing such global portfolio risk under various market conditions. Our paper fulfills such a gap in the literature. Findings reveal that, irrespective of bearish or bullish market phases, green assets should be incorporated to mute down portfolio tail risk. Robustness tests performed either via different distribution type or CVaR analysis do not materially alter the main findings of our paper. The confluence of two forces substantially boosts tail risk, namely, passive investment strategy coupled with a crypto-augmented base model. Overall, our paper advocates the inclusion of green assets not as a choice but as an obligation to portfolio managers in view of curtailing both VaR and CVaR risk levels, all geared towards hitting two birds with one stone-simultaneously buttressing a greener world while effectively mitigating global portfolio tail risk.

Risk dynamics in energy transition: Evaluating downside risks and interconnectedness in fossil fuel and renewable energy markets

Amidst rising concerns over climate change, the global shift from oil-powered vehicles to lithium-powered electric vehicles marks a critical pivot in the energy sector. This transition holds profound implications for the traditional dominance of oil in the energy market. This study aims to investigate the risk dynamics between the fossil fuel sector, represented by the crude oil, and the renewable energy sector, symbolized by lithium, focusing on the risk spillover and interconnectedness. The study employs a two-step approach that combines the conditional autoregressive value-at-risk (CAViaR) and time-varying parameters vector-autoregression (TVP-VAR). The study spans from January 2011 to August 2023, focusing on extreme market events like the COVID-19 pandemic and the Russia-Ukraine conflict. Findings reveal a strong tail-risk connectedness between the lithium stocks of the same country, and during extreme market events such as the COVID-19 pandemic and the Russia-Ukraine conflict, there is a strong transmission of tail risk across the lithium stocks of different countries. Moreover, a strong bidirectional tail-risk connectedness is observed between crude oil and lithium stocks. The study has important implications for portfolio managers, fund managers and investors with respect to portfolio optimization and asset allocation. Also, the findings have important implications for financial risk management with respect to energy transition from fossil fuels to renewable energy.

The Tail Mean–Variance optimal capital allocation under the extended skew-elliptical distribution

In this paper we introduce a novel Tail Mean-Variance (TMV) model intended to optimize capital allocation in financial decision-making. The TMV model has many intriguing properties, such as considering the variability and tail risk of the loss function simultaneously. We specifically consider the multivariate extended skew-elliptical (ESE) distributions, which are widely applicable in financial and insurance data modeling. Additionally, we explore the probabilistic properties of the multivariate extended skew-elliptical (ESE) distributions and present explicit formulas for the TMV model within this distribution. Finally, a numerical example is provided to illustrate the results.

Extreme co-movements between decomposed oil price shocks and sustainable investments

This paper investigates the extreme co-movements between three types of decomposed oil price shocks, e.g., supply shock, demand shock, and risk shock, and sustainable investments, using the generalized extreme value - autoregressive conditional Fréchet - tail quotient correlation coefficient (GEV-AcF-TQCC) analytical framework. The empirical results have identified that there are regular extreme co-movements between the three types of oil shocks and sustainable investments under extreme market conditions, especially, during the 2014–2016 oil crisis, the COVID-19 pandemic and the event of negative oil prices in 2020, according to the dynamic tail quotient correlation coefficient (TQCC) method. Specifically, the upside and downside trends of supply shocks, the downside trend of demand shocks, and the upside trend of risk shocks act as transmitters of the tail risks between oil prices and sustainable investments. The results also have demonstrated that the tail risk indexes for both the upside and downside trends of decomposed oil price shocks and sustainable investments have time-varying and asymmetric characteristics. Additionally, the static TQCC results have validated that among the three types of oil shocks, demand shocks exhibit the most pronounced tail risk spillover effects on sustainable investments, followed by supply and risk shocks, whose tail risk spillovers are close to each other. A series of alternative analyses ensure the robustness of the findings presented in this paper, which can offer valuable guidance and insights to policymakers and financial investors.

Coordinated risk-averse distributionally robust optimization for maintenance and generation schedules of offshore wind farm cluster

The coordinated optimization of maintenance and generation schedules of multiple offshore wind farms (OWFs) bring great benefits in reducing the maintenance and operation cost of OWF cluster. Firstly, a two-stage coordinated risk-averse distributionally robust optimization (CRDRO) model for maintenance and generation schedules of wind turbines (WTs) in OWF cluster is proposed. This model takes into account uncertainties related to the prediction errors in WTs’ maximum available active power outputs, the travel time of maintenance vessels, and the high operational cost risks associated with these uncertainties. A feasible route generating algorithm is designed to obtain all feasible maintenance combinations for WTs and the corresponding routes of maintenance vessels for the CRDRO model. The risk-averse term, which is a weighted sum of expected operation costs and GlueVaR value, is used to measure the tail risk of the worst probability distribution. To solve the two-stage CRDRO model, the risk-averse term is simplified into the form of expected value calculation, which can be further transformed into the tractable form by using the strong duality theorem. Finally, the two-stage CRDRO model is solved by the column-and-constraint generation algorithm, with the nonconvex sub-problem being addressed by the outer approximation algorithm. Case studies on an real-world cluster comprising three OWFs verify the correctness and efficiency of the proposed method, and demonstrate that the CRDRO model enhances the overall economic efficiency and reduces the high operational cost risk under extreme scenarios.

COAALA: A Novel Approach to Understanding Extreme Stock–Bond Comovement

Abstract This article proposes a novel copula model to understand the dependence between extreme variations in stock and government bond returns. This model is used to introduce a tail-based extension of the safe haven concept, which we refer to as a tail risk dampener. Our findings reveal significant cross-country differences in stock–bond local tail dependence and tail risk dampening abilities. Some countries’ bond market can lessen the impact on portfolio returns of extreme negative stock returns, while for others no such negative tail comovement is found. This tail comovement is also not always aligned with global comovement between stocks and bonds. The article concludes that a comprehensive understanding of the comovement and the resulting diversification potential between stock and bond returns necessitates complementing global measures of dependence with local tail measures.

The tail risk of crude oil Price_Based on EPU and geopolitical risk perspective

This study investigates the conditional prediction of crude oil price growth rates as a function of geopolitical risk (GPR) and economic policy uncertainty (EPU), characterizing the extreme tail risk characteristics. Utilizing monthly data on crude oil futures price growth rates from 1997 Jan to 2022 Dec, we employ Quantile Regression and Growth at Risk models to capture the heterogeneous and asymmetric effects of GPR and EPU across different quantiles of the oil price distribution. The sample period covers major geopolitical events, economic recessions, and the emergence of new energy sources, providing a comprehensive view of the factors influencing crude oil market dynamics.The empirical findings reveal significant asymmetries in the forecast density function of crude oil price growth rates, with periodic right-skewed deviations during financial crises and epidemic situations, and prevalent left-skewed deviations during the remaining sample periods. The impact of EPU on crude oil prices is found to be more pronounced in the short to medium term, while the influence of GPR persists over a longer duration, exacerbating the upside risk of price growth. The study highlights the effectiveness of EPU and GPR in capturing the tail characteristics of crude oil price growth, offering valuable risk identification indicators for policymakers and market participants.Furthermore, the analysis uncovers the heterogeneous effects of EPU and GPR across different quantiles of the oil price distribution. The results indicate that the relationship between these uncertainty measures and crude oil prices varies depending on the market conditions and the specific quantile examined. This finding underscores the importance of considering the entire distribution of crude oil prices rather than focusing solely on the conditional mean.The study contributes to the existing literature by providing a comprehensive examination of the role of geopolitical risk and economic policy uncertainty in driving crude oil price dynamics, with a particular focus on tail risks. The findings have important implications for risk management strategies in the energy sector.By employing advanced econometric techniques and considering a wide range of geopolitical and economic factors, this study offers new insights into the complex and evolving nature of crude oil price dynamics. The results highlight the need for policymakers and market participants to consider the asymmetric and heterogeneous effects of uncertainty measures when assessing the risks and opportunities in the crude oil market.

Economic policy uncertainty and capital flows' tail risk in China

Since the financial crisis, uncertainty has been a focus of attention in the financial sector. As the two-way opening-up of China's financial market continues to accelerate, special attention must be paid to the risks and challenges arising from cross-border capital flows to maintain financial market stability in China. This study uses predictive quantile regression and skewed t-distribution fitting method to examine the impact of Economic Policy Uncertainty (EPU) on the full probability distribution and tail risks of capital flows. Additionally, we apply the “Capital Flows at Risk (CFaR)” analysis framework from the new paradigm of macroeconomic research to the situation in China, to study the impact of EPU on CFaR. We find that EPU significantly affects the predictive distribution of capital flows. When EPU is rising, the downside risk of capital flows, that is, the left-tail risk of capital flows, will increase; however, when EPU is declining, the upside risk of capital flows, that is, the right-tail risk of capital flows, will increase. In recent years, the scale of China's CFaR has shown a fluctuating upward trend, and EPU has increased the scale of CFaR in the country. This study is significant for stabilizing international capital flows and preventing and defusing the external financial shocks of cross-border capital inflows and outflows.

The spillover effects of U.S. uncertainties on the systemic tail risk of Chinese enterprises

This study examines the impact of U.S. uncertainties, as indicated by the Macroeconomic Uncertainty Index (MU), Financial Uncertainty Index (FU), and Economic Policy Uncertainty Index (EPU), on the systemic tail risk within Chinese enterprises. Our findings reveal a significant positive relationship between U.S. uncertainties and systemic tail risk of Chinese enterprises. Additionally, this relationship is mediated through two main transmission channels—investor sentiment and financing constraints.

Tail risk transmission from the United States to emerging stock Markets: Empirical evidence from multivariate quantile analysis

This paper explores the transmission of risk from the United States equity market to the equity markets of the BRICS countries using a multivariate quantile process. The focus is on the contagion effect at the extreme quantiles, both upside and downside. In addition, a pseudo-impulse-response function (PIRF) analysis is conducted to investigate the responses of the five emerging stock markets to a shock in the US market. We conduct an empirical study against the backdrop of the COVID-19 event and the Russia-Ukraine conflict, finding that risk spillovers between the US stock market and the five emerging stock markets are significantly enhanced during the COVID-19 period. Moreover, a shock in the US market produces a stronger and more persistent negative effect at the downside quantiles compared to upside quantiles. However, we find little evidence of cross-market risk spillovers among the investigated variables during the Russia-Ukraine conflict period. We also discuss the implications of these findings for investors and policymakers in terms of portfolio holdings and policy coordination.

Distortion risk measures for tail-risk multicriteria decision-making based on a probabilistic linguistic environment

Probabilistic linguistic term sets (PLTSs) provide a flexible tool to express linguistic preferences, and several multi-criteria decision models based on PLTSs have been recently developed. In this framework, distortion risk measures are extensively used in finance and insurance applications, but are rarely applied in fuzzy systems. In this paper, distortion risk measures are applied to fuzzy tail decisions. In particular, three tail risk measurement methods are put forward, referred to as probabilistic linguistic VaR (PLVaR), expected probability linguistic VaR (EPLVaR), and Wang tail risk measure and extensively study their properties. Our novel methods help to clarify the connections between distortion risk measure and fuzzy tail decision-making. In particular, the Wang tail risk measure is characterized by consistency and stability of decision results. The criteria and expert weights are unknown or only partially known during the decision making process, and the maximising PLTSs deviations are showed how to determine them. The theoretical results are showcased on an optimal stock fund selection problem, where the three tail risk measures are compared and analyzed.

Constructing density forecasts from quantile regressions: Multimodality in macrofinancial dynamics

SummaryQuantile regression methods are increasingly used to forecast tail risks and uncertainties in macroeconomic outcomes. This paper reconsiders how to construct predictive densities from quantile regressions. We compare a popular two‐step approach that fits a specific parametric density to the quantile forecasts with a nonparametric alternative that lets the “data speak.” Simulation evidence and an application revisiting GDP growth uncertainties in the United States demonstrate the flexibility of the nonparametric approach when constructing density forecasts from both frequentist and Bayesian quantile regressions. They identify its ability to unmask deviations from symmetrical and unimodal densities. The dominant macroeconomic narrative becomes one of the evolution, over the business cycle, of multimodalities rather than asymmetries in the predictive distribution of GDP growth when conditioned on financial conditions.

Climate damage projections beyond annual temperature

Estimates of global economic damage from climate change assess the effect of annual temperature changes. However, the roles of precipitation, temperature variability and extreme events are not yet known. Here, by combining projections of climate models with empirical dose–response functions translating shifts in temperature means and variability, rainfall patterns and extreme precipitation into economic damage, we show that at +3 °C global average losses reach 10% of gross domestic product, with worst effects (up to 17%) in poorer, low-latitude countries. Relative to annual temperature damage, the additional impacts of projecting variability and extremes are smaller and dominated by interannual variability, especially at lower latitudes. However, accounting for variability and extremes when estimating the temperature dose–response function raises global economic losses by nearly two percentage points and exacerbates economic tail risks. These results call for region-specific risk assessments and the integration of other climate variables for a better understanding of climate change impacts.

To hedge or not to hedge? Cryptocurrencies, gold and oil against stock market risk

The article aims to determine whether any hedging strategy against stock market risk, performed using instruments popular in the literature (gold, cryptocurrencies and oil), can beat index futures. As a hedging strategy, we understand a pair-wise portfolio consisting of a long position in stocks and a short position in a hedging instrument put together to minimise the portfolio variance. As a benchmark, we analyse optimal and naive hedging strategies with futures contracts. We demonstrate that, regardless of the stock market, the best hedging strategy focused on variance minimisation requires using index futures. Both strategies: the optimisation-based one and the naive one, beat the dynamic strategies utilising the remaining hedging assets. Therefore, from a risk-minimisation point of view, investors have no motivation to implement cryptocurrencies, gold or oil in hedging strategy against stock market risk. The results are robust with respect to hedging against tail risk.

Extreme downside risk connectedness and portfolio hedging among the G10 currencies

This study investigates the frequency connectedness among foreign exchange markets of G10 countries, focusing on tail risk and its implications for portfolio management. To do so, we use a novel framework that combines the Conditional Autoregressive Value-at-Risk (CAViaR) model with the novel time-varying frequency and quantile connectedness method developed by Chatziantoniou et al. (2022) based on Baruník and Křehlík (2018) and Ando et al. (2018) approach. A key value of this paper to the literature is the provision of fresh empirical evidence on the extreme downside linkages among the markets examined. From the average connectedness measures, the top shock transmitters within the network were EUR, NOK, AUD, SEK, and NZD, while the main shock receivers emerged to be JPY and CHF, followed by CAD and GBP. We note that events in the major funding markets (the Eurozone, Japan) have a higher impact on the participants in these same markets than in relatively small markets (New Zealand, Norway). From the dynamic connectedness results, the magnitude of connectedness for the entire sample period increased during the COVID-19 era, compared to the magnitude before the COVID-19 outbreak. The cumulative spillover also reveals that USDNOK is the vastest net transmitter of spillovers to other markets, including SEK, CHF, and AUD. However, the EUR is the largest net beneficiary followed by JPY and CAD. Findings from the time-varying extreme downside analysis suggest that throughout the period, SEK and NOK are the other currencies' strongest and most frequent net spillover shock emitters for the short-, medium-, and long-term dynamics. Currency portfolio implications are discussed.

Measuring macroeconomic tail risk

This paper estimates consumption and GDP tail risk dynamics over the long run (1900–2020). Our predictive approach circumvents the scarcity of large macroeconomic crises by exploiting a rich information set covering 42 countries. This flexible approach does not require asset price information and can thus serve as a benchmark to evaluate the empirical validity of rare disaster models. Our estimates covary with asset prices and forecast future stock returns, in line with theory. A calibration disciplined by our estimates supports the prediction that macroeconomic tail risk drives the equity premium.

Tail risk aversion and backwardation of index futures

We show that tail risk aversion, proxied by the skewness risk premium implied from the SSE 50 ETF options market, explains a significant proportion of the unusually deep backwardation of index futures during the 2015 Chinese stock market crash, while traditional factors such as non-synchronous trading, spot return, volatility and liquidity, all fail to explain the backwardation. These empirical results imply that investors' concern over the crash risk causes speculators to charge a high ‘insurance premium’ on hedgers. On the other hand, short-sale constraints, namely high security borrowing costs and other barriers, prevent reverse arbitrage such that the deep backwardation of index futures persists.

Risk assessment for synthetic GICs: a quantitative framework for asset–liability management

AbstractThis study addresses a research gap in quantitative modeling framework and scenario analysis for the risk management of stable value fund wraps, a crucial segment of the U.S. financial market with over USD $400 billion in assets. In this paper, we present an asset–liability model that encompasses an innovative approach to modeling the assets of fixed-income funds coupled with a liability model backed by empirical analysis on a unique data set covering 80% of the stand-alone plan sponsor market, contrasting with models based solely on regular deterministic cash flows and interest rate differences. Our model identifies and analyzes two critical risk scenarios from the insurer’s perspective: inflationary and yield spike. Our approach demonstrates that the tail risk of wraps, used as an economic capital measure, is sensitive to characteristic parameters of the fund, such as the duration, portfolio composition and credit quality of assets. This finding significantly differs from U.S. regulatory approaches like the NAIC’s, which often result in a zero capital requirement. These findings reveal limitations in current actuarial risk and profitability metrics for U.S. insurers and argue that a more sophisticated risk model reproducing the two critical scenarios is necessary.