Value-at-Risk Estimates Research Articles

A Computationally more Efficient Distance based VaR Methodology for Real Time Market Risk Measurement

Measurement of market risk requires lots of computational resources when the Value-at-Risk (VaR) is computed using the historical simulation approach as it involves full revaluation of the portfolio for the considered data points. Although approximations can be done using the delta-normal, delta-gamma and delta-gamma-theta approaches, historical simulation approach alone is straight forward method that uses past data to generate future values without assuming any distribution for the underlying returns. The requirement of intensive computational effort in case of historical simulation hinders it’s usage for applying to real time VaR calculation. In this work we propose a methodology that doesn’t forego the benefits of historical simulation approach but can be applied to calculate market risk VaR in real time. The VaR calculated using the proposed methodology converges as the range of the portfolio returns is increased. The proposed methodology is also superior to the historical simulation approach in terms of usage of the computational resources and applicability to real time without sacrificing accuracy obtained using historical simulation approach.

Intraday risk management in International stock markets: A conditional EVT approach

The study compares the predictive ability of various models in estimating intraday Value-at-Risk (VaR) and Expected Shortfall (ES) using high frequency share price index data from sixteen different countries across the world for a period of seven and half months from September 20, 2013 to May 07, 2014. The main emphasis of the study has been given to Extreme Value Theory (EVT) and to evaluate how well Conditional EVT model performs in modeling tails of distributions and in estimating and forecasting intraday VaR and ES measures. We have followed McNeil and Frey's (2000) two stage approach called Conditional EVT to estimate dynamic intraday VaR and ES. We have compared the accuracy of Conditional EVT approach to intraday VaR and ES estimation with other competing models. The best performing model is found to be the Conditional EVT in estimating both the quantiles for the entire sample. The study is useful for market participants (such as intraday traders and market makers) involved in frequent intraday trading in such equity markets.

Value-at-risk for the USD/ZAR exchange rate: The Variance-Gamma model

A country’s level of exchange risk is closely linked to its financial stability, on a macro-economic scale. South African exchange rates, in particular, have a significant impact on imports, inflation, consumer prices and monetary policies. Consequently, it is imperative for economists and investors to assess accurately the associated exchange risks. Exchange rates, like most financial time series, are leptokurtic and contradict the classical Gaussian assumption. We therefore introduce subclasses of the generalised hyperbolic distribution as alternative models and contrast these with the normal distribution. We conclude that the variance-gamma model is the most robust for describing the log-returns of daily USD/ZAR exchange rates and their related Value-at-Risk (VaR) estimates. The model selection methodologies utilised in our analyses include the robust Kolmogorov-Smirnov test and the Akaike information criterion. Backtesting on the adequacy of VaR estimates is also performed using the Kupiec likelihood ratio test.

Ex-ante real estate Value at Risk calculation method

The computation of Value at Risk (VaR) has long been a problematic issue in commercial real estate. Difficulties mainly arise from the lack of appropriate data, the lack of transactions, the non-normality of returns, and the inapplicability of many of the traditional methodologies. In addition, specific risks remain latent in investors’ portfolios and thus risk measurements based on market index do not represent the risks of a specific portfolio. Following a spate of new regulations such as Basel II, Basel III, NAIC and Solvency II, financial institutions have increasingly been required to estimate and control their exposure to market risk. Hence, financial institutions now commonly use “internal” VaR (or Expected Shortfall) models in order to assess their market risk exposure. This paper proposes the first model designed especially for static real estate VaR computation. The proposal accounts for specific real estate characteristics such that the lease structures or the vacancies. The paper contributes to the real estate risk management literature by proposing for the first time a model that incorporates characteristics of real estate investments. It allows more precise real estate risk measurements and is derived from a regulators’ approach.

High level quantile approximations of sums of risks

Abstract The approximation of a high level quantile or of the expectation over a high quantile (Value at Risk (VaR) or Tail Value at Risk (TVaR) in risk management) is crucial for the insurance industry.We propose a new method to estimate high level quantiles of sums of risks. It is based on the estimation of the ratio between the VaR (or TVaR) of the sum and the VaR (or TVaR) of the maximum of the risks. We show that using the distribution of the maximum to approximate the VaR is much better than using the marginal. Our method seems to work well in high dimension (100 and higher) and gives good results when approximating the VaR or TVaR in high levels on strongly dependent risks where at least one of the risks is heavy tailed.

Extreme value theory, asset ranking and threshold choice: a practical note on VaR estimation

We analyze asset rankings derived from state-of-the-art peak-over-threshold (POT) approaches to estimate value-at-risk (VaR). Supported by a variety of robustness checks, we gain three important insights for portfolio managers investing in equity and commodity markets. First, even though POT methods are known to yield more precise VaR estimates than classic techniques based on the normal distribution assumption or historical simulation, all techniques yield almost identical rankings. Second, even though the choice of threshold crucially influences VaR estimates, it does not significantly change asset rankings. These two results are most pronounced when the portfolio manager's focus is on identifying the best or worst assets in terms of VaR. Third, unconditional and conditional POT approaches differ considerably in the rankings they generate. Thus, neglecting the non-independent-and-identically-distributed property of returns can lead to distinctly different decisions in a risk-based asset selection process.

Backtesting of Value at Risk Methodology: Analysis of Banking Shares in India

Value at risk (VaR) is used by financial experts to calculate and predict the risk of financial exposure. In the presence of volatility and long memory, it is a model useful for the prediction of loss in the equity index return series. Checking the accuracy of this model is necessary from the practitioners’ point of view. This article initially checks the presence of autoregressive conditional heteroscedastic (ARCH) and long-memory effects in the daily closing price of the Bombay Stock Exchange (BSE)-BANKEX return series. After confirming the ARCH and long-memory presence, it analyses the different methods of VaR calculation such as asymmetric power ARCH (APARCH), fractionally integrated exponential generalised ARCH (FIEGARCH), hyperbolic generalised GARCH (HYGARCH) and risk metrics. Then, it empirically tests the forecasting capacity of these VaR methods through techniques such as the Kupiec likelihood ratio (LR test) and dynamic quantile test. Furthermore, it checks the root-mean-squared error (RMSE) and mean absolute error (MAE) to determine the model with the least error. From the set of VaR models used here, by and large it concludes that the BANKEX return series has both long-memory and asymmetry effects. By comparing these models, it is implied that the HYGARCH model gives a better result, although the other models have their significance in the estimation and forecasting of the BANKEX return series. JEL: C12, D81, C530

The Promise and the Peril of Parametric Value-at-Risk (VaR) Analysis

Leptokurtosis, or the risk lurking in “fat tails,” poses the deepest epistemic threat to economic forecasting. Parametric value-at-risk (VaR) models are extremely vulnerable to kurtosis in excess of the levels associated with a normal, Gaussian distribution. This article provides step-by-step guidance on the use of Student’s t-distribution to enhance the statistical robustness of VaR forecasts. For degrees of freedom greater than 4, Student’s t-distribution can emulate any level of kurtosis exceeding that of a Gaussian distribution. Because VaR is elicitable from historical data, observed levels of excess kurtosis can inform the proper use of Student’s t-distribution to measure value-at-risk. In addition, the calculation of parametric VaR according to the number of degrees of freedom implied by historical levels of excess kurtosis leads directly to the corresponding value of expected shortfall. Conducted in this fashion, parametric VaR not only exploits the elicitability of that quantile-based measure, but also informs the computation of expected shortfall as a theoretically coherent risk measure.

Value at risk estimation by threshold stochastic volatility model

This article proposes a threshold stochastic volatility model that generates volatility forecasts specifically designed for value at risk (VaR) estimation. The method incorporates extreme downside shocks by modelling left-tail returns separately from other returns. Left-tail returns are generated with a t-distributional process based on the historically observed conditional excess kurtosis. This specification allows VaR estimates to be generated with extreme downside impacts, yet remains empirically widely applicable. This article applies the model to daily returns of seven major stock indices over a 22-year period and compares its forecasts to those of several other forecasting methods. Based on back-testing outcomes and likelihood ratio tests, the new model provides reliable estimates and outperforms others.

THE PERSISTENCY AND THE SUSTAINABILITY OF THE INDONESIA'S CURRENT ACCOUNT DEFICIT

Asian and European crises were witnesses of banks’ vulnerable due to market risks. The Basel Committee requires an internal risk assessment applying Value at Risk (VaR). However, a replacement of VaR with Expected Shortfall (ES) has been suggested recently due to an excessive losses produced by banks which are beyond VaR estimations. This paper studied the risk of Indonesian banks applying a historical expected shortfall. We used JIBOR (overnight) from 2009 – 2012 as a proxy of market risk. The assessment of a historical expected shortfall of the net position of 27 banks accounts for October 2012 showed that state owned banks placed among the five highest value of each component (net position) in the balance sheet, namely placement to Bank Indonesia, interbank placement, spot and derivatives claims, securities, and loans. It means that the state owned banks had the highest risk and were the most aggressive among Indonesian banks. It might be due to carrying some of the government’s program, such as small enterprise loans. Keywords: expected shortfall, value at risk, banks, risk. JEL Classification: D81, G210

RISK OF INDONESIAN BANKS: AN APPLICATION OF HISTORICAL EXPECTED SHORTFALL METHOD

Asian and European crises were witnesses of banks’ vulnerable due to market risks. The Basel Committee requires an internal risk assessment applying Value at Risk (VaR). However, a replacement of VaR with Expected Shortfall (ES) has been suggested recently due to an excessive losses produced by banks which are beyond VaR estimations. This paper studied the risk of Indonesian banks applying a historical expected shortfall. We used JIBOR (overnight) from 2009 – 2012 as a proxy of market risk. The assessment of a historical expected shortfall of the net position of 27 banks accounts for October 2012 showed that state owned banks placed among the five highest value of each component (net position) in the balance sheet, namely placement to Bank Indonesia, interbank placement, spot and derivatives claims, securities, and loans. It means that the state owned banks had the highest risk and were the most aggressive among Indonesian banks. It might be due to carrying some of the government’s program, such as small enterprise loans. Keywords: expected shortfall, value at risk, banks, risk. JEL Classification: D81, G210

Computing value-at-risk using genetic algorithm

Purpose – Value-at-risk (VaR) is a risk measure of potential loss on a specific portfolio. The main uses of VaR are in risk management and financial reporting. Researchers are continuously looking for new and efficient ways to evaluate VaR, and the 2008 financial crisis has given further impetus to finding new and reliable ways of evaluating and using VaR. In this study, the authors use genetic algorithm (GA) to evaluate VaR and compare the results with conventional VaR techniques. Design/methodology/approach – In essence, the authors propose two modifications to the standard GA: normalized population selection and strict population selection. For a typical set of simulation, eight chromosomes were used each with eight stored values, and the authors get eight values for VaR. Findings – The experiments using data from four different market indices show that by adjusting the volatility, the VaR computed using GA is more conservative as compared to those computed using Monte Carlo simulation. Research limitations/implications – The proposed methodology is designed for VaR computation only. This could be generalized for other applications. Practical implications – This is achieved with much less cost of computation, and hence, the proposed methodology could be a viable practical approach for computing VaR. Originality/value – The proposed methodology is simple and, at the same time, novel that could have far-reaching impact on practitioners.

English

The present study aimed at evaluating the predictive ability of the models of market risk estimation in times of financial crises. To this end, models were tested to estimate the financial indicator Value-at-Risk (VaR) applied to the daily returns of the BM&FBovespa, the Ibovespa index. Traditional models and those based on the Extreme Value Theory (EVT), considered as two types of distribution, the Generalized Extreme Value (GEV) and generalized Pareto distribution (GPD) were tested. The data relating to two periods of international financial crises termed the 1997 Asian Financial Crisis and the U.S. Subprime Meltdown in 2008 were explored in the study. The results indicated the inefficiency of most statistical models for VaR estimation in moments of high volatility for both periods of crisis. In contrast, the exception refers to the model based on EVT, GPD distribution that proved satisfactory in the estimates in both periods of crisis. The results are in agreement with other studies in the field. Key words: Value-at-risk, IBovespa, Extreme Value Theory (EVT).

Índice y evaluación de riesgo de los Certificados de Vivienda (CEDEVIS).

As a consequence of the amendments to the Housing Act in 2001, there have emerged several ways to obtain funding for the construction of housing developments. One form of funding is going to the stock market,specifically the Mexican Stock Exchange, where ad hoc instruments have been designed for this purpose. On the one hand, private emit Borhis (Bonds backed by mortgages) and, secondly, Infonavit CEDEVIS issues, or Certificates of Housing, which as its name suggests but are stock certificates that are backed by mortgages originated by Infonavit through a trust. This paper shows the construction of an index that groups all outstanding CEDEVIS emissions and calculation of VaR (Value at Risk) to determine the maximum loss an investor would have to invest in these financial instruments.

Performance of Value at Risk models in the midst of the global financial crisis in selected CEE emerging capital markets

The aim of this paper is to investigate the performance of Value at Risk (VaR) models in selected Central and Eastern European (CEE) emerging capital markets. Daily returns of Croatian (CROBEX), Czech (PX50), Hungarian (BUX) and Romanian (BET) stock exchange indices are analysed for the period January, 2000 – February, 2012, while daily returns of the Serbian (BELEX15) index is examined for the period September, 2005 – February, 2012. In recent years there has been much research conducted into VaR in developed markets, while papers dealing with VaR calculation in CEE are rare. Furthermore, VaR models created and suited for liquid and well-developed markets that assume normal distribution are less reliable for capital markets in emerging economies, such as Central and Eastern European Union member and candidate states. Since capital markets in European emerging economies are highly volatile, less liquid and strongly dependent on the unexpected external shocks, market risk estimation based on normality assumption in CEE countries is more problematic. This motivates us to implement GARCH-type methods that involve time varying volatility and heavy tails of the empirical distribution of returns. We test the hypothesis that using the assumption of heavy tailed distribution it is possible to forecast market risk more precisely, especially in times of crisis, than under the assumption of normal distribution or using historical simulations method. Our backtesting results for the last 500 observations are based on the Kupiec POF and Christoffersen independence test. They show that GARCH-type models with t error distribution in most analysed cases give better VaR estimation than GARCH type models with normal errors in the case of a 99% confidence level, while in the case of a 95% confidence level it is the opposite. The results of backtesting analysis for the crisis period (after the collapse of Lehman Brothers) show that GARCH-type models with t-distribution of residuals provide better VaR estimates compared with GARCH-type models with normal distribution, historical simulations and RiskMetrics methods. The RiskMetrics method in the most cases underestimates market risk.

Daily VaR forecasts with realized volatility and GARCH models

In this paper we evaluate alternative volatility forecasting methods under Value at Risk (VaR) modelling. We calculate one-step-ahead forecasts of daily VaR for the WIG20 index quoted on the Warsaw Stock Exchange within the period from 2007 to 2011. Our analysis extends the existing research by broadening the class of the models, including both the GARCH class models based on daily data and models for realized volatility based on intraday returns (HAR-RV, HAR-RV-J and ARFIMA). We find that the VaR estimates obtained from the models for daily returns and realized volatility give comparable results. Both long memory features and asymmetry are found to improve the VaR forecasts. However, when loss functions are considered, the models based on daily data allow minimizing regulatory loss function, whereas the models based on realized volatility allow minimizing the opportunity cost of capital.

Efficient Density Estimation and Value at Risk Using Fejér-Type Kernel Functions

This paper presents a nonparametric method for computing the Value at Risk (VaR) based on efficient density estimators with Fejer-type kernel functions and empirical bandwidths obtained from Fourier analysis techniques. The kernel-type estimator with a Fejer-type kernel was recently found to dominate all other known density estimators under the -risk, . This theoretical finding is supported via simulations by comparing the quality of the density estimator in question with other fixed kernel estimators using the common -risk. Two data-driven bandwidth selection methods, cross-validation and the one based on the Fourier analysis of a kernel density estimator, are used and compared to the theoretical bandwidth. The proposed nonparametric method for computing the VaR is applied to two fictitious portfolios. The performance of the new VaR computation method is compared to the commonly used Gaussian and historical simulation methods using a standard back-test procedure. The obtained results show that the proposed VaR model provides more reliable estimates than the standard VaR models.

Value-at-risk for the USD/ZAR exchange rate : the variance-gamma model

A country’s level of exchange risk is closely linked to its financial stability, on a macro-economic scale. South African exchange rates, in particular, have a significant impact on imports, inflation, consumer prices and monetary policies. Consequently, it is imperative for economists and investors to assess accurately the associated exchange risks. Exchange rates, like most financial time series, are leptokurtic and contradict the classical Gaussian assumption. We therefore introduce subclasses of the generalised hyperbolic distribution as alternative models and contrast these with the normal distribution. We conclude that the variance-gamma model is the most robust for describing the log-returns of daily USD/ZAR exchange rates and their related Value-at-Risk (VaR) estimates. The model selection methodologies utilised in our analyses include the robust Kolmogorov-Smirnov test and the Akaike information criterion. Backtesting on the adequacy of VaR estimates is also performed using the Kupiec likelihood ratio test.

Value At Risk, Minimum Capital Requirement And The Use Of Extreme Value Distributions: An Application To BRICS Markets

This paper uses closing prices of the BRICS (Brazil, Russia, India, China, and South Africa) financial markets to implement a risk model that generates point estimates of both Value at Risk (VaR); and Expected Shortfall (ES). The risk model is thereafter backtested using three techniques namely the Basel II green zone, the unconditional test, and the conditional test. We first filter the log-return data using an Autoregressive Regression model (AR) of order one for the conditional mean and an Exponential Generalised Autoregressive Conditional Heteroscedasticity of order one (EGARCH 1,1) for the conditional variance. We thereafter fit the filtered returns by using the Generalised Pareto Distribution (GPD) model before we compute both VaR and ES estimates. We find that the use of the GPD is well suited to financial markets that are highly exposed to global financial risks. Our results show that both VaR and ES estimates for South Africa are very low when compared with those of other BRICS financial markets. We argue that South Africas credit and loan regulations, pioneered by the National Credit Regulator (NCR), might have decreased its exposure to global financial risks. The resulting minimum capital requirement values are found to be significantly different depending on whether the Variance-Covariance or the GPD methodology is used. The backtesting methodologies show that the VaR model used in the paper is more robust and practically reliable.

Extreme Risk, Value-At-Risk And Expected Shortfall In The Gold Market

Extreme value theory (EVT) has been widely applied in fields such as hydrology and insurance. It is a tool used to reflect on probabilities associated with extreme, and thus rare, events. EVT is useful in modeling the impact of crashes or situations of extreme stress on investor portfolios. It describes the behavior of maxima or minima in a time series, i.e., tails of a distribution. In this paper, we propose the use of generalised Pareto distribution (GPD) to model extreme returns in the gold market. This method provides effective means of estimating tail risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES). This is confirmed by various backtesting procedures. In particular, we utilize the Kupiec unconditional coverage test and the Christoffersen conditional coverage test for VaR backtesting, while the Bootstrap test is used for ES backtesting. The results indicate that GPD is superior to the traditional Gaussian and Students t models for VaR and ES estimations.