On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles

Chen, James Ming

doi:10.3390/risks6020061

Cited by 44 publications

(22 citation statements)

References 137 publications

(90 reference statements)

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“…VaR function is stretched on all figures twice to the left of point 1  to compare it with other functions as in [7,14,16].…”

Section: Fx  mentioning

confidence: 99%

A New Family of Expectiles and its Properties

Kuzmenko

2020

Cybernetics and Computer Technologies

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Introduction. This paper considers a risk measure called expectile. Expectile is a characteristic of a random variable calculated using the asymmetric least square method. The level of asymmetry is defined by a parameter in the interval (0, 1). Expectile is used in financial applications, portfolio optimization problems, and other applications as well as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). But expectile has a set of advantageous properties. Expectile is both a coherent and elicitable risk measure that takes into account the whole distribution and assigns greater weight to the right tail. The purpose of the paper. As a rule, expectile is compared with quantile (VaR). Our goal is to compare expectile with CVaR by introducing the same parameter – confidence level. To do this we first give a new representation of expectile using the weighted sum of mean and CVaR. Then we consider a new family of expectiles defined by two parameters. Such expectiles are compared with quantile and CVaR for different continuous and finite discrete distributions. Our next goal is to build a regular risk quadrangle where expectile is a risk function. Results. We propose and substantiate two new expressions that define expectile. The first expression uses maximization by varying confidence level of CVaR and varying coefficient before CVaR. It is specified for continuous and finite discrete distributions. The second expression uses minimization of the new error function of the new expectile-based risk quadrangle. The use of two parameters in expectile definition changes the dependence of expectile on its confidence level and generates a new family of expectiles. Comparison of new expectiles with quantile and CVaR for a set of distributions shows that the proposed expectiles can be closer to the quantile than the standard expectile. We propose two variants for expectile linearization and show how to use them with a linear loss function. Keywords: Expectile, EVaR, Quantile, Conditional Value-at-Risk, CVaR, Kusuoka representation, Fundamental Risk Quadrangle, Portfolio Safeguard package.

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“…VaR function is stretched on all figures twice to the left of point 1  to compare it with other functions as in [7,14,16].…”

Section: Fx  mentioning

confidence: 99%

A New Family of Expectiles and its Properties

Kuzmenko

2020

Cybernetics and Computer Technologies

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“…A look at past studies in finance literature shows that, as opposed to other models, Value at Risk can be calculated much more accurately, using the EVT (Gencay and Selcuk 2004;Omari et al 2017). However, VaR is not only incoherent but also fails to precisely estimate the risk of loss when the loss distributions show "fat tails" (Rockafellar and Uryasev 2002), and this significantly hurts the accuracy of this risk measure (Chen 2018). Kourouma et al (2010) investigated the VaR and the Expected Shortfall during the 2008 financial crisis, and showed that VaR, as opposed to CVaR, underestimated the risk of loss, while the conditional EVT model performed more accurately.…”

Section: Research Backgroundmentioning

confidence: 99%

Estimating Conditional Value at Risk in the Tehran Stock Exchange Based on the Extreme Value Theory Using GARCH Models

Tabasi

Yousefi

Tamošaitienė

et al. 2019

Administrative Sciences

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This paper attempted to calculate the market risk in the Tehran Stock Exchange by estimating the Conditional Value at Risk. Since the Conditional Value at Risk is a tail-related measure, Extreme Value Theory has been utilized to estimate the risk more accurately. Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models were used to model the volatility-clustering feature, and to estimate the parameters of the model, the Maximum Likelihood method was applied. The results of the study showed that in the estimation of model parameters, assuming T-student distribution function gave better results than the Normal distribution function. The Monte Carlo simulation method was used for backtesting the Conditional Value at Risk model, and in the end, the performance of different models, in the estimation of this measure, was compared.

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“…It is therefore important to model these price fluctuations and implement an effective tool for managing energy price risk. VaR has become a popular risk measure in the financial industry among many other alternative risk measures (e.g., [3,4]). The internal model approach under the Basel II framework proposes VaR as a risk measure to gauge the amount of assets needed to cover possible losses, that is, the minimum regulatory capital requirements.…”

Section: Literature Reviewmentioning

confidence: 99%

Quantifying Risk in Traditional Energy and Sustainable Investments

2019

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These days we are witnessing a deep change in the characteristics of the type of energy that our economies are supplied with. A clear trend is that sustainable and green energies are decisively replacing traditional fossil fuel-based sources of energy. For various reasons, this fundamental change implies an increasing risk in investments on portfolios heavily based on traditional energy industries. What is less known, is that these industries have returns that show a very low correlation with sustainable fossil fuel-free stock portfolios making them an appealing tool for portfolio managers to design properly diversified investments. In this study we examine this and related phenomena proposing statistical methods to implement the expected shortfall (ES), the challenging risk measure recently adopted by the financial regulator. We obtain evidence that a newly proposed backtesting procedure for the ES based on multinomial tests is an adequate and simple method to validate these risk measures when applied to a highly volatile stock index. Backtesting results of the ES show that flexible heavy-tailed distribution α–stable performs well for modelling the loss distribution. These results are even improved when the variances of fossil fuel price returns are included as external regressors in the GARCH model variance equation. In this case, the ES computed from the four considered loss distributions perform properly.

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On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles

Cited by 44 publications

References 137 publications

A New Family of Expectiles and its Properties

A New Family of Expectiles and its Properties

Estimating Conditional Value at Risk in the Tehran Stock Exchange Based on the Extreme Value Theory Using GARCH Models

Quantifying Risk in Traditional Energy and Sustainable Investments

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