Remark on the Paper “Entropic Value-at-Risk: A New Coherent Risk Measure” by Amir Ahmadi-Javid, J. Optim. Theory Appl., 155(3) (2001) 1105–1123

2019 ◽  
pp. 151-158
Author(s):  
Freddy Delbaen
Author(s):  
RENATO PELESSONI ◽  
PAOLO VICIG

In this paper the theory of coherent imprecise previsions is applied to risk measurement. We introduce the notion of coherent risk measure defined on an arbitrary set of risks, showing that it can be considered a special case of coherent upper prevision. We also prove that our definition generalizes the notion of coherence for risk measures defined on a linear space of random numbers, given in literature. Consistency properties of Value-at-Risk (VaR), currently one of the most used risk measures, are investigated too, showing that it does not necessarily satisfy a weaker notion of consistency called 'avoiding sure loss'. We introduce sufficient conditions for VaR to avoid sure loss and to be coherent. Finally we discuss ways of modifying incoherent risk measures into coherent ones.


2016 ◽  
Vol 31 (1) ◽  
pp. 73-75 ◽  
Author(s):  
Georg Ch. Pflug

The conditional-value-at-risk (C V@R) has been widely used as a risk measure. It is well known, that C V@R is coherent in the sense of Artzner, Delbaen, Eber, Heath (1999). The class of coherent risk measures is convex. It was conjectured, that all coherent risk measures can be represented as convex combinations of C V@R’s. In this note we show that this conjecture is wrong.


2021 ◽  
Vol 14 (11) ◽  
pp. 540
Author(s):  
Eyden Samunderu ◽  
Yvonne T. Murahwa

Developments in the world of finance have led the authors to assess the adequacy of using the normal distribution assumptions alone in measuring risk. Cushioning against risk has always created a plethora of complexities and challenges; hence, this paper attempts to analyse statistical properties of various risk measures in a not normal distribution and provide a financial blueprint on how to manage risk. It is assumed that using old assumptions of normality alone in a distribution is not as accurate, which has led to the use of models that do not give accurate risk measures. Our empirical design of study firstly examined an overview of the use of returns in measuring risk and an assessment of the current financial environment. As an alternative to conventional measures, our paper employs a mosaic of risk techniques in order to ascertain the fact that there is no one universal risk measure. The next step involved looking at the current risk proxy measures adopted, such as the Gaussian-based, value at risk (VaR) measure. Furthermore, the authors analysed multiple alternative approaches that do not take into account the normality assumption, such as other variations of VaR, as well as econometric models that can be used in risk measurement and forecasting. Value at risk (VaR) is a widely used measure of financial risk, which provides a way of quantifying and managing the risk of a portfolio. Arguably, VaR represents the most important tool for evaluating market risk as one of the several threats to the global financial system. Upon carrying out an extensive literature review, a data set was applied which was composed of three main asset classes: bonds, equities and hedge funds. The first part was to determine to what extent returns are not normally distributed. After testing the hypothesis, it was found that the majority of returns are not normally distributed but instead exhibit skewness and kurtosis greater or less than three. The study then applied various VaR methods to measure risk in order to determine the most efficient ones. Different timelines were used to carry out stressed value at risks, and it was seen that during periods of crisis, the volatility of asset returns was higher. The other steps that followed examined the relationship of the variables, correlation tests and time series analysis conducted and led to the forecasting of the returns. It was noted that these methods could not be used in isolation. We adopted the use of a mosaic of all the methods from the VaR measures, which included studying the behaviour and relation of assets with each other. Furthermore, we also examined the environment as a whole, then applied forecasting models to accurately value returns; this gave a much more accurate and relevant risk measure as compared to the initial assumption of normality.


Risks ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 76
Author(s):  
Saswat Patra ◽  
Malay Bhattacharyya

This paper investigates the risk exposure for options and proposes MaxVaR as an alternative risk measure which captures the risk better than Value-at-Risk especially. While VaR is a measure of end-of-horizon risk, MaxVaR captures the interim risk exposure of a position or a portfolio. MaxVaR is a more stringent risk measure as it assesses the risk during the risk horizon. For a 30-day maturity option, we find that MaxVaR can be 40% higher than VaR at a 5% significance level. It highlights the importance of MaxVaR as a risk measure and shows that the risk is vastly underestimated when VaR is used as the measure for risk. The sensitivity of MaxVaR with respect to option characteristics like moneyness, time to maturity and risk horizons at different significance levels are observed. Further, interestingly enough we find that the MaxVar to VaR ratio is higher for stocks than the options and we can surmise that stock returns are more volatile than options. For robustness, the study is carried out under different distributional assumptions on residuals and for different stock index options.


2015 ◽  
Vol 4 (4) ◽  
pp. 188
Author(s):  
HERLINA HIDAYATI ◽  
KOMANG DHARMAWAN ◽  
I WAYAN SUMARJAYA

Copula is already widely used in financial assets, especially in risk management. It is due to the ability of copula, to capture the nonlinear dependence structure on multivariate assets. In addition, using copula function doesn’t require the assumption of normal distribution. There fore it is suitable to be applied to financial data. To manage a risk the necessary measurement tools can help mitigate the risks. One measure that can be used to measure risk is Value at Risk (VaR). Although VaR is very popular, it has several weaknesses. To overcome the weakness in VaR, an alternative risk measure called CVaR can be used. The porpose of this study is to estimate CVaR using Gaussian copula. The data we used are the closing price of Facebook and Twitter stocks. The results from the calculation using 90%  confidence level showed that the risk that may be experienced is at 4,7%, for 95% confidence level it is at 6,1%, and for 99% confidence level it is at 10,6%.


2019 ◽  
Vol 8 (1) ◽  
pp. 15
Author(s):  
NI WAYAN UCHI YUSHI ARI SUDINA ◽  
KOMANG DHARMAWAN ◽  
I WAYAN SUMARJAYA

Conditional value at risk (CVaR) is widely used in risk measure that takes into account losses exceeding the value at risk level. The aim of this research is to compare the performance of the EVT-GJR-vine copula method and EVT-GARCH-vine copula method in estimating CVaR of the portfolio using backtesting. Based on the backtesting results, it was found that the EVT-GJR-vine copula method have better performance when compared to the EVT-GARCH-vine copula method in estimating the CVaR value of the portfolio. This can be seen from the statistical values ??, and  of EVT-GJR-vine copula method which is generally smaller than the statistical values , and of the EVT-GARCH-vine copula method.


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