scholarly journals Return Based Risk Measures for Non-Normally Distributed Returns: An Alternative Modelling Approach

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.

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2080
Author(s):  
Maria-Teresa Bosch-Badia ◽  
Joan Montllor-Serrats ◽  
Maria-Antonia Tarrazon-Rodon

We study the applicability of the half-normal distribution to the probability–severity risk analysis traditionally performed through risk matrices and continuous probability–consequence diagrams (CPCDs). To this end, we develop a model that adapts the financial risk measures Value-at-Risk (VaR) and Conditional Value at Risk (CVaR) to risky scenarios that face only negative impacts. This model leads to three risk indicators: The Hazards Index-at-Risk (HIaR), the Expected Hazards Damage (EHD), and the Conditional HIaR (CHIaR). HIaR measures the expected highest hazards impact under a certain probability, while EHD consists of the expected impact that stems from truncating the half-normal distribution at the HIaR point. CHIaR, in turn, measures the expected damage in the case it exceeds the HIaR. Therefore, the Truncated Risk Model that we develop generates a measure for hazards expectations (EHD) and another measure for hazards surprises (CHIaR). Our analysis includes deduction of the mathematical functions that relate HIaR, EHD, and CHIaR to one another as well as the expected loss estimated by risk matrices. By extending the model to the generalised half-normal distribution, we incorporate a shape parameter into the model that can be interpreted as a hazard aversion coefficient.


2015 ◽  
Vol 4 (1and2) ◽  
pp. 28
Author(s):  
Marcelo Brutti Righi ◽  
Paulo Sergio Ceretta

We investigate whether there can exist an optimal estimation window for financial risk measures. Accordingly, we propose a procedure that achieves optimal estimation window by minimizing estimation bias. Using results from a Monte Carlo simulation for Value at Risk and Expected Shortfall in distinct scenarios, we conclude that the optimal length for the estimation window is not random but has very clear patterns. Our findings can contribute to the literature, as studies have typically neglected the estimation window choice or relied on arbitrary choices.


Author(s):  
Evangelos Vasileiou ◽  
Themistoclis Pantos

In this paper, we examine how value at risk (VaR) contributes to the financial market's stability. We apply the Guidelines on Risk Measurement and the Calculation of Global Exposure and Counterparty Risk for UCITS of the Committee of European Securities Regulators (CESR 2010) to the main indices of the 12 stock markets of the countries that have used the euro as their official currency since its initial circulation. We show that gaps in the legislative framework give incentives to investment funds to adopt conventional models for the VaR estimation in order to avoid the increased costs that the advanced models involve. For this reason, we apply the commonly used historical simulation VaR (HVaR) model, which is: (i) taught at most finance classes; (ii) widely applied in the financial industry; and (iii) accepted by CESR (2010). The empirical evidence shows the HVaR does not really contribute to financial stability, and the legislative framework does not offer the appropriate guidance. The HVaR model is not representative of the real financial risk, and does not give any signal for trends in the near future. The HVaR is absolutely backward-looking and this increases the stock market's overreaction. The fact that the suggested confidence level in CESR (2010) is set at 99 percent leads to hidden pro-cyclicality. Scholars and researchers should focus on issues such as the abovementioned, otherwise the VaR estimations will become, sooner or later, just a formality, and such conventional statistical measures rarely contribute to financial stability.


2011 ◽  
Vol 3 (2) ◽  
pp. 93-108
Author(s):  
Rangga Handika

This paper offers a new measurement of risk, Value-at-Risk (VaR) for LQ-45 index in Indonesian Stock Exchange (ISX). Basic finance uses standard deviation in measuring and quantifying the risks. This paper uses VaR as a risk measure by using historical and analytical methods. This study uses the data containing all LQ-45 weekly data from January 1st, 2005 to December, 31st 2010. Moreover, this paper also calculates VaR of three indices (IHSG, Dow Jones, and S&P 500) for benchmarking purpose. This study finds that LQ-45 companies have VaR ranging from -5.30 to -41.05 percent with 95 percent level of confidence. It means that we can expect to suffer a minimum weekly loss between 5.30 to 41.05 percent in 5 percent probability when we invest in the LQ-45 companies stocks individually. Furthermore, this study finds that individual LQ-45 stock is riskier than indices based on VaR measure. This paper also concludes that individual LQ-45 stock tends not to follow normal distribution while index tends to follow by comparing their historical and analytical VaR calculation.


2018 ◽  
Vol 21 (03) ◽  
pp. 1850010 ◽  
Author(s):  
LAKSHITHE WAGALATH ◽  
JORGE P. ZUBELLI

This paper proposes an intuitive and flexible framework to quantify liquidation risk for financial institutions. We develop a model where the “fundamental” dynamics of assets is modified by price impacts from fund liquidations. We characterize mathematically the liquidation schedule of financial institutions and study in detail the fire sales resulting endogenously from margin constraints when a financial institution trades through an exchange. Our study enables to obtain tractable formulas for the value at risk and expected shortfall of a financial institution in the presence of fund liquidation. In particular, we find an additive decomposition for liquidation-adjusted risk measures. We show that such a measure can be expressed as a “fundamental” risk measure plus a liquidation risk adjustment that is proportional to the size of fund positions as a fraction of asset market depths. Our results can be used by risk managers in financial institutions to tackle liquidity events arising from fund liquidations better and adjust their portfolio allocations to liquidation risk more accurately.


2021 ◽  
Vol 17 (3) ◽  
pp. 370-380
Author(s):  
Ervin Indarwati ◽  
Rosita Kusumawati

Portfolio risk shows the large deviations in portfolio returns from expected portfolio returns. Value at Risk (VaR) is one method for determining the maximum risk of loss of a portfolio or an asset based on a certain probability and time. There are three methods to estimate VaR, namely variance-covariance, historical, and Monte Carlo simulations. One disadvantage of VaR is that it is incoherent because it does not have sub-additive properties. Conditional Value at Risk (CVaR) is a coherent or related risk measure and has a sub-additive nature which indicates that the loss on the portfolio is smaller or equal to the amount of loss of each asset. CVaR can provide loss information above the maximum loss. Estimating portfolio risk from the CVaR value using Monte Carlo simulation and its application to PT. Bank Negara Indonesia (Persero) Tbk (BBNI.JK) and PT. Bank Tabungan Negara (Persero) Tbk (BBTN.JK) will be discussed in this study.  The  daily  closing  price  of  each  BBNI  and BBTN share from 6 January 2019 to 30 December 2019 is used to measure the CVaR of the two banks' stock portfolios with this Monte Carlo simulation. The steps taken are determining the return value of assets, testing the normality of return of assets, looking for risk measures of returning assets that form a normally distributed portfolio, simulate the return of assets with monte carlo, calculate portfolio weights, looking for returns portfolio, calculate the quartile of portfolio return as a VaR value, and calculate the average loss above the VaR value as a CVaR value. The results of portfolio risk estimation of the value of CVaR using Monte Carlo simulation on PT. Bank Negara Indonesia (Persero) Tbk and PT. Bank Tabungan Negara (Persero) Tbk at a confidence level of 90%, 95%, and 99% is 5.82%, 6.39%, and 7.1% with a standard error of 0.58%, 0.59%, and 0.59%. If the initial funds that will be invested in this portfolio are illustrated at Rp 100,000,000, it can be interpreted that the maximum possible risk that investors will receive in the future will not exceed Rp 5,820,000, Rp 6,390,000 and Rp 7,100,000 at the significant level 90%, 95%, and 99%


Author(s):  
Khreshna Syuhada

In financial and insurance industries, risks may come from several sources. It is therefore important to predict future risk by using the concept of aggregate risk. Risk measure prediction plays important role in allocating capital as well as in controlling (and avoiding) worse risk. In this paper, we consider several risk measures such as Value-at-Risk (VaR), Tail VaR (TVaR) and its extension namely Adjusted TVaR (Adj-TVaR). Specifically, we perform an upper bound for such risk measure applied for aggregate risk models. The concept and property of comonotonicity and convex order are utilized to obtain such upper bound.Keywords:        Coherent property, comonotonic rv, convex order, tail property, Value-at-Risk (VaR).


Author(s):  
Omer Hadzic ◽  
Smajo Bisanovic

The power trading and ancillary services provision comprise technical and financial risks and therefore require a structured risk management. Focus in this paper is on financial risk management that is important for the system operator faces when providing and using ancillary services for balancing of power system. Risk on ancillary services portfolio is modeled through value at risk and conditional value at risk measures. The application of these risk measures in power system is given in detail to show how to using the risk concept in practice. Conditional value at risk optimization is analysed in the context of portfolio selection and how to apply this optimization for hedging a portfolio consisting of different types of ancillary services.


2018 ◽  
Vol 15 (4) ◽  
pp. 17-34 ◽  
Author(s):  
Tom Burdorf ◽  
Gary van Vuuren

As a risk measure, Value at Risk (VaR) is neither sub-additive nor coherent. These drawbacks have coerced regulatory authorities to introduce and mandate Expected Shortfall (ES) as a mainstream regulatory risk management metric. VaR is, however, still needed to estimate the tail conditional expectation (the ES): the average of losses that are greater than the VaR at a significance level These two risk measures behave quite differently during growth and recession periods in developed and emerging economies. Using equity portfolios assembled from securities of the banking and retail sectors in the UK and South Africa, historical, variance-covariance and Monte Carlo approaches are used to determine VaR (and hence ES). The results are back-tested and compared, and normality assumptions are tested. Key findings are that the results of the variance covariance and the Monte Carlo approach are more consistent in all environments in comparison to the historical outcomes regardless of the equity portfolio regarded. The industries and periods analysed influenced the accuracy of the risk measures; the different economies did not.


2011 ◽  
Vol 204-210 ◽  
pp. 537-540
Author(s):  
Yu Ling Wang ◽  
Jun Hai Ma ◽  
Yu Hua Xu

Mean-variance model, value at risk and Conditional Value at Risk are three chief methods to measure financial risk recently. The demonstrative research shows that three optional questions are equivalence when the security rates have a multivariate normal distribution and the given confidence level is more than a special value. Applications to real data provide empirical support to this methodology. This result has provided new methods for us about further research of risk portfolios.


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