Stochastic dominance statistics for risk averters and risk seekers: an analysis of stock preferences for USA and China

Recent research has found a number of scaling law relationships in foreign exchange data. These relationships, estimated using simple ordinary least squares, can be used to forecast losses in foreign exchange time series from as little as one month’s tick data. We compare the loss forecasts from a new scaling law against six parametric Value at Risk models. Compared to these models, the new scaling law is easier to fit, provides more stable forecasts and is very accurate.     

Portfolio selection: An extreme value approach

We show theoretically that lower tail dependence (χ), a measure of the probability that a portfolio will suffer large losses given that the market does, contains important information for risk-averse investors. We then estimate χ for a sample of DJIA stocks and show that it differs systematically from other risk measures including variance, semi-variance, skewness, kurtosis, beta, and coskewness. In out-of-sample tests, portfolios constructed to have low values of χ outperform the market index, the mean return of the stocks in our sample, and portfolios with high values of χ. Our results indicate that χ is conceptually important for risk-averse investors, differs substantially from other risk measures, and provides useful information for portfolio selection.     

Co-dependence of extreme events in high frequency FX returns

In this paper, we investigate extreme events in high frequency, multivariate FX returns within a purposely built framework. We generalize univariate tests and concepts to multidimensional settings and employ these novel techniques for parametric and nonparametric analysis. In particular, we investigate and quantify the co-dependence of cross-sectional and intertemporal extreme events. We find evidence of the cubic law of extreme returns, their increasing and asymmetric dependence and of the scaling property of extreme risk in joint symmetric tails.     

Varying the VaR for unconditional and conditional environments

Accurate forecasting of risk is the key to successful risk management techniques. Using the largest stock index futures from 12 European bourses, this paper presents VaR measures based on their unconditional and conditional distributions for single and multi-period settings. These measures underpinned by extreme value theory are statistically robust explicitly allowing for fat-tailed densities. Conditional tail estimates accounting for volatility clustering are obtained by adjusting the unconditional extreme value procedure with GARCH filtered returns. The conditional modelling results in iid returns allowing for the use of a simple and efficient multi-period extreme value scaling law. The paper examines the properties of these distinct conditional and unconditional trading models. The paper finds that the biases inherent in unconditional single and multi-period estimates assuming normality extend to the conditional setting.     

Alternative modeling for long term risk

In this paper, we propose an alternative approach to estimate long-term risk. Instead of using the static square root of time method, we use a dynamic approach based on volatility forecasting by non-linear models. We explore the possibility of improving the estimations using different models and distributions. By comparing the estimations of two risk measures, value at risk and expected shortfall, with different models and innovations at short-, median- and long-term horizon, we find that the best model varies with the forecasting horizon and that the generalized Pareto distribution gives the most conservative estimations with all the models at all the horizons. The empirical results show that the square root method underestimates risk at long horizons and our approach is more competitive for risk estimation over a long term.     

Extreme spectral risk measures: An application to futures clearinghouse margin requirements

This paper applies the extreme-value (EV) generalised pareto distribution to the extreme tails of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses tail estimators from these contracts to estimate spectral risk measures, which are coherent risk measures that reflect a user’s risk-aversion function. It compares these to VaR and expected shortfall (ES) risk measures, and compares the precision of their estimators. It also discusses the usefulness of these risk measures in the context of clearinghouses setting initial margin requirements, and compares these to the SPAN measures typically used.     

中国股票市场风险度量的模型选择与比较研究

分别采用等权移动平均方法、指教加权移动平均方法、GARCH(1,1)方法、GARCH(1,1)-t方法和Pareto型极值分布方法计算上海和深圳股票日收益率的VaR.向后检验表明,Pareto型极值分布方法比其他方法更能准确地反映我国股市的风险.     

Estimation of tail‐related risk measures in the Indian stock market: An extreme value approach

The purpose of the study is to estimate tail-related risk measures using extreme value theory (EVT) in the Indian stock market. The study employs a two stage approach of conditional EVT originally proposed by McNeil and Frey (2000) to estimate dynamic Value at Risk (VaR) and expected shortfall (ES). The dynamic risk measures have been estimated for different percentiles for negative and positive returns. The estimates of risk measures computed under different quantile levels exhibit strong stability across a range of the selected thresholds, implying the accuracy and reliability of the estimated quantile based risk measures.     

Measuring systemic importance of financial institutions: An extreme value theory approach

This paper proposes a set of market-based measures on the systemic importance of a financial institution or a group of financial institutions, each designed to capture different aspects of systemic importance of financial institutions. Multivariate extreme value theory approach is used to estimate these measures. Using six big Canadian banks as the proxy for Canadian banking sector, we apply these measures to identify systemically important banks in Canadian banking sector and major risk contributors from international financial institutions to Canadian banking sector. The empirical evidence reveals that (i) the top three banks, RBC Financial Group, TD Bank Financial Group, and Scotiabank, are more systemically important than other banks, while we also find that the size of a financial institution should not be considered as a proxy of systemic importance; (ii) compared to the European and Asian banks, the crashes of the U.S. banks, on average, are the most damaging to Canadian banking sector, while the risk contribution to the Canadian banking sector from Asian banks is quite lower than that from banks in the U.S. and euro area; (iii) the risk contribution to Canadian banking sector exhibits “home bias”, that is, cross-country risk contribution tends to be smaller than domestic risk contribution.     

基于风险价值法和压力测试法的企业风险管理方法研究

本文提出风险价值法和压力测试法的企业风险管理方法,克服了传统方法只给出风险相对严重程度的不足。建立风险量化评估、预警和控制体系,采用优化组合方法,实施一体化风险管理,规避重大风险事件的发生。     

Conditional extreme risk,black swan hedging,and asset prices

Motivated by the asset pricing theory with safety-first preference, we introduce and operationalize a conditional extreme risk (CER) measure to describe expected stock performance conditional on a small-probability market downturn (black swan). We document a significant CER premium in the cross-section of expected returns. We also demonstrate that CER explains the premia to downside beta, coskewness, and cokurtosis. CER provides distinct information regarding black swan hedging that cannot be captured by co-crash-based tail dependence measures. As we find that the pricing effect is stronger among black swan hedging stocks, this distinction helps explain the absence of premium to tail dependence.     

Learning about Risk: Some Lessons from Insurance

This paper argues that in the fundamental subject of financialrisk analysis, some valuable lessons may be drawn from insurance.The probability of ruin, defined as a first passage time, carriesa dynamic element whose absence in Value at Risk is one liability,among others. Extreme value theory, which has been successfullyapplied to insurance shortly after it was introduced in probability,may offer a coherent framework for analyzing the extreme movessuch as the ones observed in recent foreign exchange and financialcrises. Lastly, we show that the genuine hazards generated byglobal capital markets and illustrated by the events of summer1998, generate a market incompleteness that existing modelsof defaultable bonds do not fully address. In contrast, thelong experience of risk premium analysis in the insurance andreinsurance industry, as well as the existence of historicaldata on natural disasters, render the valuation of catastrophebonds less perilous than that of defaultable bonds.     

Estimating the basis risk of index-linked hedging strategies using multivariate extreme value theory

This paper studies the empirical quantification of basis risk in the context of index-linked hedging strategies. Basis risk refers to the risk of non-payment of the index-linked instrument, given that the hedger’s loss exceeds some critical level. The quantification of such risk measures from empirical data can be done in various ways and requires special consideration of the dependence structure between the index and the company’s losses as well as the estimation of the tails of a distribution. In this context, previous literature shows that extreme value theory can be superior to traditional methods with respect to estimating quantile risk measures such as the value at risk. Thus, the aim of this paper is to conduct an empirical analysis of basis risk using multivariate extreme value theory and extreme value copulas to estimate the underlying risk processes and their dependence structure in order to obtain a more adequate picture of basis risk associated with index-linked hedging strategies. Our results emphasize that the application of extreme value theory leads to better fits of the tails of the marginal distributions in the considered stock price sample and that traditional methods in regard to estimating marginal distributions tend to overestimate basis risk, while basis risk can in contrast be higher when taking into account extreme value copulas.     

Systemic risk and asymmetric responses in the financial industry

To date, an operational measure of systemic risk capturing nonlinear tail-comovements between system-wide and individual bank returns has not yet been developed. This paper proposes an extension of the CoVaR methodology in Adrian and Brunnermeier (2011) to capture the asymmetric response of the banking system to positive and negative shocks to the market-valued balance sheets of individual banks. Building on a comprehensive sample of U.S. banks in the period 1990–2010, the evidence in this paper shows that ignoring asymmetries that feature tail-interdependences may lead to a severe underestimation of systemic risk. On average, the relative impact on the system of a fall in individual market value is sevenfold that of an increase. Moreover, the downward bias in systemic-risk measuring from ignoring this asymmetric pattern increases with bank size. In particular, the conditional tail-comovement between the banking system and a bank that is losing market value belonging to the top size-sorted decile is nearly 5.5 times larger than the unconditional tail-comovement versus 3.3 times for banks in the bottom decile. The asymmetric model also produces much better fitting, with the restriction that gives rise to the standard symmetric model being rejected for most firms in the sample, particularly, in the segment of large-scale banks. This result is important from a regulatory and supervisory perspective, since the asymmetric generalization enhances the capacity to monitor systemic interdependences.     

A Value at Risk Approach to Background Risk

This paper studies the effects of an uninsurable background risk (BR) on the demand for insurance (proportional and with deductible). We study both the case of BR uncorrelated with the insurable one and the perfectly correlated one, in a Gaussian world. In order to perform our study, we exploit the new risk measure known as Value at Risk (VaR) and consider insurance contracts which are Mean-VaR efficient. We obtain results which depend on the parameters (moments) of both risks and on the magnitude of loadings charged by the insurance company, instead of depending on the risk attitudes of the insured, such as risk aversion and prudence.We demonstrate that, if loadings are not too high, the demand for insurance increases with positively correlated BR; it decreases with BR negatively correlated if the latter is less risky than the insurable one (in this case it can even go to zero, if loadings are too high); it goes to zero with BR which is negatively correlated and more risky than the insurable one.     

Tail dependence and indicators of systemic risk for large US depositories

In this study, we investigate the extreme loss tail dependence between stock returns of large US depository institutions. We find that stock returns exhibit strong loss dependence even in their limiting joint extremes. Motivated by this result, we derive extremal dependence-based systemic risk indicators. The proposed systemic risk indicators reflect downturns in the US financial industry very well. We also develop a set of firm-level average extremal dependence measures. We show that these firm-level measures could have been used to identify the firms that were more vulnerable to the 2007–2008 financial crisis. Additionally, we explore the performance of selected systemic risk indicators in predicting the crisis performance of large US depository institutions and find that the average stock return correlations are also good predictors of crisis period returns. Finally, we identify factors predictive of extremal dependence for the US depository institutions in a panel regression setting. Strength of extremal dependence increases with asset size and similarity of financial fundamentals. On the other hand, strength of extremal dependence decreases with capitalization, liquidity, funding stability and asset quality. We believe the proposed indicators have the potential to inform the prudential supervision of systemic risk.     

Electricity spot price modelling with a view towards extreme spike risk

Sums of Lévy-driven Ornstein–Uhlenbeck processes are appropriate for modelling electricity spot price data. In this paper we present a new estimation method with particular emphasis on capturing the high peaks, which is one of the stylized features of such data. After introducing our method we show it at work for the EEX Phelix Base electricity price index. We also present a small simulation study to demonstrate the performance of our estimation procedure.     

Pension plan solvency and extreme market movements: a regime switching approach

We develop and test a new approach to assess defined benefit (DB) pension plan solvency risk in the presence of extreme market movements. Our method captures both the ‘fat-tailed’ nature of asset returns and their correlation with discount rate changes. We show that the standard assumption of constant discount rates leads to dramatic underestimation of future projections of pension plan solvency risk. Failing to incorporate leptokurtosis into asset returns also leads to downward biased estimates of risk, but this is less pronounced than the time-varying discount rate effect. Further modifying the model to capture the correlation between asset returns and the discount rate provides additional improvements in the projection of future pension plan solvency. This reduces the perceived future risk of underfunding because of the negative correlation between interest rate changes and asset returns. These results have important implications for those with responsibility for balancing risk against expected return when seeking to improve the current poor funding positions of DB pension schemes.