Alternative Value At Risk Research Articles

Value at risk, mispricing and expected returns

This study investigates how the relation between value-at-risk (VaR) and expected returns differs under different mispricing statuses. We find that a significantly negative VaR-return relation, defined as the VaR effect, is observed only for overpriced stocks, but not for underpriced stocks. Moreover, VaR has an amplification effect on mispricing, indicating that VaR captures risk that deters arbitrage and thus leads to an increase in mispricing. Our results are robust to alternative VaR definitions, subperiod analysis, different market states, and after controlling for other firm characteristics, well-known risk factors, and those variables that have been shown to have amplifying effects on mispricing. Finally, this study also examines the pricing effect of short sale constraints on the VaR effect under different mispricing statuses. Our findings suggest that the VaR effect observed in overpriced stocks becomes more severe as short sales are more constrained.

Volatility specifications versus probability distributions in VaR forecasting

AbstractWe provide evidence suggesting that the assumption on the probability distribution for return innovations is more influential for value‐at‐risk (VaR) performance than the conditional volatility specification. We also show that some recently proposed asymmetric probability distributions and the APARCH and FGARCH volatility specifications beat more standard alternatives for VaR forecasting, and they should be preferred when estimating tail risk. The flexibility of the free power parameter in conditional volatility in the APARCH and FGARCH models explains their better performance. Indeed, our estimates suggest that for a number of financial assets the dynamics of volatility should be specified in terms of the conditional standard deviation. We draw our results on VaR forecasting performance from (i) a variety of backtesting approaches, (ii) the model confidence set approach, as well as (iii) establishing a ranking among alternative VaR models using a precedence criterion that we introduce in this paper.

A novel multi period mean-VaR portfolio optimization model considering practical constraints and transaction cost

The portfolio optimization literature has spent a little effort to consider the fat tail characteristic of asset returns as well as their extreme events. To remove such shortcomings, in this paper, a novel portfolio optimization model is developed in which Value at Risk (VaR) is utilized as a risk measure to account extreme risk so that VaR is estimated use of Extreme Value Theory (EVT). To enrich the practicality of our proposed model, set of real trading constraints are considered such as cardinality, budget, floor and ceiling constraints. Since these modifications lead to a non-convex NP-hard problem which is computationally difficult, a new design of Non-dominated Sorting Genetic Algorithm (NSGA-II) is proposed to solve it. To evaluate the performance of EVT approach in our proposed mean-VaR model, three well-known alternative VaR estimation methods are also considered such as historical simulation, GARCH and t-student GARCH. Experimental results using historical daily financial market data from S & P 100 indices demonstrates that our proposed NSGA-II has great capability of treating the mean-VaR portfolio optimization problem. In addition, the validation study confirmed that our enhanced NSGA-II not only offers superior result compared with that of delivered by benchmark problem in a much lower solving time, but its performance is better than the original NSGA-II. Also, the results indicate that our proposed model outperforms other mean-VaR models especially in low risk area of Pareto front. Finally, the proposed algorithm is compared with set of Non-dominated-based algorithms including SPEA-II, NSPSO and NSACO which results illustrated that our enhanced NSGA-II suggests superior solutions rather than other algorithms. • A novel Multiperiod portfolio optimization model with real constraints is proposed. • Four different VaR models are deployed to account portfolio risk measure. • An enhanced NSGA-II algorithm is developed by utilizing a new repairing mechanism. • The Proposed model offers more appropriate results relative to other Mean-VaR models. • The proposed NSGA-II outperforms other metaheuristics SPEA-II, NSACO and NSPSO.

How does the choice of Value-at-Risk estimator influence asset allocation decisions?

Considering the growing need for managing financial risk, Value-at-Risk (VaR) prediction and portfolio optimisation with a focus on VaR have taken up an important role in banking and finance. Motivated by recent results showing that the choice of VaR estimator does not crucially influence decision-making in certain practical applications (e.g. in investment rankings), this study analyses the important question of how asset allocation decisions are affected when alternative VaR estimation methodologies are used. Focusing on the most popular, successful and conceptually different conditional VaR estimation techniques (i.e. historical simulation, peak over threshold method and quantile regression) and the flexible portfolio model of Campbell et al. [J. Banking Finance. 2001, 25(9), 1789–1804], we show in an empirical example and in a simulation study that these methods tend to deliver similar asset weights. In other words, optimal portfolio allocations appear to be not very sensitive to the choice of VaR estimator. This finding, which is robust in a variety of distributional environments and pre-whitening settings, supports the notion that, depending on the specific application, simple standard methods (i.e. historical simulation) used by many commercial banks do not necessarily have to be replaced by more complex approaches (based on, e.g. extreme value theory).

The Burr X Pareto Distribution: Properties, Applications and VaR Estimation

In this paper, a new three-parameter Pareto distribution is introduced and studied. We discuss various mathematical and statistical properties of the new model. Some estimation methods of the model parameters are performed. Moreover, the peaks-over-threshold method is used to estimate Value-at-Risk (VaR) by means of the proposed distribution. We compare the distribution with a few other models to show its versatility in modelling data with heavy tails. VaR estimation with the Burr X Pareto distribution is presented using time series data, and the new model could be considered as an alternative VaR model against the generalized Pareto model for financial institutions.

Volatility Speciications Versus Probability Distributions in VAR Forecasting

We provide evidence suggesting that the assumption on the probability distribution for return innovations is more influential for Value at Risk (VaR) performance than the conditional volatility specification. We also show that some recently proposed asymmetric probability distributions and the APARCH and FGARCH volatility specifications beat more standard alternatives for VaR forecasting, and they should be preferred when estimating tail risk. The flexibility of the free power parameter in conditional volatility in the APARCH and FGARCH models explains their better performance. Indeed, our estimates suggest that for a number of financial assets, the dynamics of volatility should not be specified in terms of the conditional variance. We draw our results on the basis of: i) performance in a variety of backtesting approaches, ii) the Model Confidence Set approach, as well as, iii) applying a dominance criterion among alternative VaR models that we introduce in this paper.

가중 포트폴리오에서의 CTE

다변량 분포에서의 VaR (Value at Risk)와 CTE (Conditional Tail Expectation)에 관한 많은 연구문헌에서는 특정한 포트폴리오 구성비를 이용하여 일변량 분포로 변환하여 추정하였다. 다변량 분포에서 분위수에 관한 많은 연구가 존재한다. 그러나 분위수가 유일하게 존재하지 않으므로, VaR와 CTE의 추정에 어려움이 있다. 본 연구에서는 다변량 분위 벡터를 이용한 대안적인 VaR와 통합적인 다변량 CTE의 연구를 확장하여, 여러 종류의 포트폴리오로 구성된 다양한 비율 조합에 따른 가중 CTE 벡터들을 제안한다. 일변량에 대한 CTE 관계식을 다차원의 관계식으로 확장하고, 일변량의 관계식과의 특징과 차이점에 대하여 토론한다. 정규분포로부터 추출한 자료와 실증 예제를 통하여 본 연구에서 제안한 가중 CTE를 탐색하면서 가중 CTE의 활용성과 장점을 유도한다. In many literatures on VaR and CTE for multivariate distribution, these are estimated by using transformed univariate distribution with a specific ratio of many kinds of portfolios. Even though there are lots of works to define quantiles for multivariate distributions, there does not exist a quantile uniquely. Hence, it is not easy to define the VaR and CTE. In this paper, we propose the weighted CTE vectors corresponding to various ratio combinations of many kinds of portfolios by extending the researches on the alternative VaR and integrated multivariate CTE based on multivariate quantiles. We extend relation equations about univariate CTEs to multivariate CTE vectors and discuss their characteristics. The proposed weighted CTEs are explored with some data from multivariate normal distribution and illustrative examples.

Vector at Risk와 대안적인 VaR

The most useful method for financial market risk management may be Value at Risk (VaR) which estimates the maximum loss amount statistically. The VaR is used as a risk measure for one industry. Many real cases estimate VaRs for many industries or nationwide industries; consequently, it is necessary to estimate the VaR for multivariate distributions when a specific portfolio is established. In this paper, the multivariate quantile vector is proposed to estimate VaR for multivariate distribution, and the Vector at Risk for multivariate space is defined based on the quantile vector. When a weight vector for a specific portfolio is given, one point among Vector at Risk could be found as the best VaR which is called as an alternative VaR. The alternative VaR proposed in this work is compared with the VaR of Morgan with bivariate and trivariate examples; in addition, some properties of the alternative VaR are also explored.

A directional multivariate value at risk

In economics, insurance and finance, value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, time horizon, and probability α, the 100α% VaR is defined as a threshold loss value, such that the probability that the loss on the portfolio over the given time horizon exceeds this value is α. That is to say, it is a quantile of the distribution of the losses, which has both good analytic properties and easy interpretation as a risk measure. However, its extension to the multivariate framework is not unique because a unique definition of multivariate quantile does not exist. In the current literature, the multivariate quantiles are related to a specific partial order considered in Rn, or to a property of the univariate quantile that is desirable to be extended to Rn. In this work, we introduce a multivariate value at risk as a vector-valued directional risk measure, based on a directional multivariate quantile, which has recently been introduced in the literature. The directional approach allows the manager to consider external information or risk preferences in her/his analysis. We derive some properties of the risk measure and we compare the univariate VaR over the marginals with the components of the directional multivariate VaR. We also analyze the relationship between some families of copulas, for which it is possible to obtain closed forms of the multivariate VaR that we propose. Finally, comparisons with other alternative multivariate VaR given in the literature, are provided in terms of robustness.

Option Pricing Under Time-Varying Risk-Aversion with Applications to Risk Forecasting

We present a new option-pricing model, which explicitly captures the difference in the persistence of volatility under historical and risk-neutral probabilities. The model also allows to capture the empirical properties of pricing kernels, such as time-variation and the typical S-shape. We apply our model for two purposes. First, we analyze the risk preferences of market participants invested in S&P 500 index options during 2001-2009. We find that risk-aversion strongly increases during stressed market conditions and relaxes during normal market conditions. Second, we extract forward-looking information from S&P 500 index options and perform out-of-sample Value-at-Risk (VaR) forecasts during the period of the subprime mortgage crises. We compare the VaR forecasting performance of our model with four alternative VaR models and find that 2-Factor Stochastic Volatility models have the best forecasting performance.

The interrelation of stock markets in China, Taiwan and Hong Kong and their constructional portfolio’s value-at-risk estimate

This study employs a bivariate asymmetric generalized autoregressive conditional heteroscedasticity (GARCH) model to estimate the return, variance and covariance for three stock-based portfolios composed of two alternative indexes of the stock markets in China, Hong Kong and Taiwan, explores the return and volatility spillover effects between two indexes of the portfolio constructed and estimates the out-of-sample value-at-risk (VaR). Using the effective validation framework proposed by the Board of Governors of the US Federal Reserve System, this study finds that, as shown in the price levels and spillover effects on return and volatility, the stock markets in these three regions are closely related and are significantly positively correlated. Moreover, there is a volatility feedback effect in China's stock market and a significant leverage effect in the Hong Kong and Taiwan stock markets. Furthermore, via the construction of portfolios, market risk can be reduced and the stock-based portfolio, which is composed of stock indexes in China and Taiwan, has the optimal risk dispersion. Finally, from the performance competition of alternative VaR models, two semiparametric approaches, weighted historical simulation (WHS) and, in particular, filtered historical simulation (FHS), can reduce the underestimation of the true risk caused by an inappropriate return distribution setting of the parametric approach. Moreover, the effects of this approach are more influential than the leverage effect on the VaR estimates. Hence, the FHS approach with the asymmetric volatility specification model, FHS-B-JR, is optimal, enabling precise forecasting of theVaR. In addition, regarding the backtesting, the loss functions are more sensitive than the accuracy measure tests.

An Evaluation of Bank VaR Measures for Market Risk During and Before the Financial Crisis

We study the performance and behavior of Value at Risk (VaR) measures used by a number of large banks during and before the financial crisis. Alternative benchmark VaR measures, including GARCH-based measures, are also estimated directly from the banks' trading revenues and help to explain the bank VaR performance results. While highly conservative in the pre-crisis period, bank VaR exceedances were excessive and clustered in the crisis period. All benchmark VaRs were more accurate in the pre-crisis period with GARCH VaR measures the most accurate in the crisis period having lower exceedance rates with no exceedance clustering. Variance decompositions indicate a limited ability of the banks' VaR methodologies to adjust to the crisis-period market conditions. Despite their weaker performance, the bank VaRs exhibited greater predictive power for a measure of realized PnL volatility than benchmark VaR measures. Benchmark Expected Shortfall measures are also considered.

An Evaluation of Bank VaR Measures for Market Risk During and Before the Financial Crisis

We study the performance and behavior of Value at Risk (VaR) measures used by a number of large banks during and before the financial crisis. Alternative benchmark VaR measures, including GARCH-based measures, are also estimated directly from the banks' trading revenues and help to explain the bank VaR performance results. While highly conservative in the pre-crisis period, bank VaR exceedances were excessive and clustered in the crisis period. All benchmark VaRs were more accurate in the pre-crisis period with GARCH VaR measures the most accurate in the crisis period having lower exceedance rates with no exceedance clustering. Variance decompositions indicate a limited ability of the banks' VaR methodologies to adjust to the crisis-period market conditions. Despite their weaker performance, the bank VaRs exhibited greater predictive power for a measure of realized PnL volatility than benchmark VaR measures. Benchmark Expected Shortfall measures are also considered.

The Sign RCA Models: Comparing Predictive Accuracy of VaR Measures

Evaluating Value at Risk (VaR) methods of predictive accuracy in an objective and effective framework is important for both efficient capital allocation and loss prediction. From this reasons, finding an adequate method of estimating and backtesting is crucial for both the regulators and the risk managers’. The Sign RCA models may be useful to obtain the accurate forecasts of VaR. In this research one briefly describes the Sign RCA models, the Value at Risk and backtesting. We compare the predictive accuracy of alternative VaR forecasts obtained from different models. Empirical example is mainly related to the PBG Capital Group shares on the Warsaw Stock Exchange.

First-passage probability, jump models, and intra-horizon risk

This paper proposes a risk measure, based on first-passage probability, which reflects intra-horizon risk in jump models with finite or infinite jump activity. Our empirical investigation shows, first, that the proposed risk measure consistently exceeds the benchmark value-at-risk (VaR). Second, jump risk tends to amplify intra-horizon risk. Third, we find large variation in our risk measure across jump models, indicative of model risk. Fourth, among the jump models we consider, the finite-moment log-stable model provides the most conservative risk estimates. Fifth, imposing more stringent VaR levels accentuates the impact of intra-horizon risk in jump models. Finally, using an alternative benchmark VaR does not dilute the role of intra-horizon risk. Overall, we contribute by showing that ignoring intra-horizon risk can lead to underestimation of risk exposures.

The structure of dynamic correlations in multivariate stochastic volatility models

This paper proposes two types of stochastic correlation structures for Multivariate Stochastic Volatility (MSV) models, namely the constant correlation (CC) MSV and dynamic correlation (DC) MSV models, from which the stochastic covariance structures can easily be obtained. Both structures can be used for purposes of determining optimal portfolio and risk management strategies through the use of correlation matrices, and for calculating Value-at-Risk (VaR) forecasts and optimal capital charges under the Basel Accord through the use of covariance matrices. A technique is developed to estimate the DC MSV model using the Markov Chain Monte Carlo (MCMC) procedure, and simulated data show that the estimation method works well. Various multivariate conditional volatility and MSV models are compared via simulation, including an evaluation of alternative VaR estimators. The DC MSV model is also estimated using three sets of empirical data, namely Nikkei 225 Index, Hang Seng Index and Straits Times Index returns, and significant dynamic correlations are found. The Dynamic Conditional Correlation (DCC) model is also estimated, and is found to be far less sensitive to the covariation in the shocks to the indexes. The correlation process for the DCC model also appears to have a unit root, and hence constant conditional correlations in the long run. In contrast, the estimates arising from the DC MSV model indicate that the dynamic correlation process is stationary.

Heavy-tailed value-at-risk analysis for Malaysian stock exchange

This article investigates the comparison of power-law value-at-risk (VaR) evaluation with quantile and non-linear time-varying volatility approaches. A simple Pareto distribution is proposed to account the heavy-tailed property in the empirical distribution of returns. Alternative VaR measurement such as non-parametric quantile estimate is implemented using interpolation method. In addition, we also used the well-known two components ARCH modelling technique under the assumptions of normality and heavy-tailed (student- t distribution) for the innovations. Our results evidenced that the predicted VaR under the Pareto distribution exhibited similar results with the symmetric heavy-tailed long-memory ARCH model. However, it is found that only the Pareto distribution is able to provide a convenient framework for asymmetric properties in both the lower and upper tails.

Can the student‐t distribution provide accurate value at risk?

PurposeThis paper aims to investigate how effectively the value at risk (VaR) estimated using the student‐t distribution captures the market risk.Design/methodology/approachTwo alternative VaR models, VaR‐t and VaR‐x models, are presented and compared with the benchmark model (VaR‐n model). In this study, we consider the Student‐t distribution as a fit to the empirical distribution for estimating the VaR measure, namely, VaR‐t method. Since the Student‐t distribution is criticized for its inability to capture the asymmetry of distribution of asset returns, we use the extreme value theory (EVT)‐based model, VaR‐x model, to take into account the asymmetry of distribution of asset returns. In addition, two different approaches, excess‐kurtosis and tail‐index techniques, for determining the degrees of freedom of the Student‐t distribution in VaR estimation are introduced.FindingsThe main finding of the study is that using the student‐t distribution for estimating VaR can improve the VaR estimation and offer accurate VaR estimates, particularly when tail index technique is used to determine the degrees of freedom and the confidence level exceeds 98.5 percent.Originality/valueThe main value is to demonstrate in detail how well the student‐t distribution behaves in estimating VaR measure for stock market index. Moreover, this study illustrates the easy process for determining the degrees of freedom of the student‐t, which is required in VaR estimation.

Evaluating predictive performance of value-at-risk models in emerging markets: a reality check

We investigate the predictive performance of various classes of value-at-risk (VaR) models in several dimensions—unfiltered versus filtered VaR models, parametric versus nonparametric distributions, conventional versus extreme value distributions, and quantile regression versus inverting the conditional distribution function. By using the reality check test of White (2000), we compare the predictive power of alternative VaR models in terms of the empirical coverage probability and the predictive quantile loss for the stock markets of five Asian economies that suffered from the 1997–1998 financial crisis. The results based on these two criteria are largely compatible and indicate some empirical regularities of risk forecasts. The Riskmetrics model behaves reasonably well in tranquil periods, while some extreme value theory (EVT)-based models do better in the crisis period. Filtering often appears to be useful for some models, particularly for the EVT models, though it could be harmful for some other models. The CaViaR quantile regression models of Engle and Manganelli (2004) have shown some success in predicting the VaR risk measure for various periods, generally more stable than those that invert a distribution function. Overall, the forecasting performance of the VaR models considered varies over the three periods before, during and after the crisis. Copyright © 2006 John Wiley & Sons, Ltd.

Evaluating the style-based risk model for equity mutual funds investing in Europe

American equity mutual funds of varying investment styles investing in Europe is examined, using Value at Risk (VaR) and expected tail loss (ETL) models developed through three techniques (parametric, nonparametric and style-based approach). Alternative VaR and ETL implementations might impact the market risk forecast. It is necessary to avoid biasing fund risk estimates. Particular attention is given to the style-based risk approach by comparing it to the other methods. A performance evaluation of the models is approached from two directions: statisical model selection and model selection based on a loss function. The empirical results show that the particular investment style of a mutual fund must guide and determine which VaR and ETL model may be applied in order to extract accurate risk estimates. For the least diversified funds that overweight growth and underweight value stocks, the style-based risk model produce significantly lower VaR and ETL estimates than do the other models. The results for the...