Value-at-Risk Estimates Research Articles

PENENTUAN VALUE AT RISK (VAR) PADA PORTOFOLIO BIVARIAT DENGAN PENDEKATAN COPULA GUMBEL

One way to minimize risk in stock investment is stock portfolio. Value at Risk (VaR) is a calculation method that can be used to estimate the risk of a stock portfolio. VaR can be measured by parametric and non-parametric approaches. Calculation of VaR with Monte Carlo simulation assumes the data is normally distributed. Stock return data generally has high volatility so that the residual variance of the model is not constant (heteroscedasticity) and not normally distributed. The ARIMA-GARCH model can be used to solve heteroscedasticity problems. Copula is a tool used to model the combined distribution of residuals from the ARIMA-GARCH model which does not require normality assumptions. Gumbel's copula is copula that has the best sensitivity to high risk. This study uses stock data of PT Bukit Asam Tbk (PTBA) and PT Chandra Asri Petrochemical Tbk (TPIA) for the period April 1 2020 – December 1 2022. The initial step of this research is model stock returns using the ARIMA-GARCH method and then calculate portfolio VaR using the Gumbel’s copula. The results showed that the best model for PTBA is ARIMA(2,0,2) GARCH(1,1) and for TPIA is ARIMA(1,0,0) GARCH (1,1). At the 95% confidence level, the portfolio risk is 2,41%.

VALUE AT RISK ESTIMATION FOR STOCK PORTFOLIO USING THE ARCHIMEDEAN COPULA APPROACH

Investment is one of the many ways to achieve future profits. One form of investment that is widely made is stocks. The return obtained in investing in stocks is potentially higher than other investment alternatives, but the risks borne are amplified, so it is necessary to analyze these risks that may occur. In this study, the Archimedean copula method is used to estimate the Value at Risk on shares of PT Bank Rakyat Indonesia Tbk (BBRI) and PT Telekomunikasi Indonesia Tbk (TLKM) for the period September 1, 2021, to August 31, 2023. The stock data is used to determine the Archimedean copula model and calculate the estimated value of Value at Risk (VaR) on the stock return portfolio using the Archimedean copula approach. The Archimedean copula models used are the Clayton copula model, Gumbel copula, and Frank copula. Of the three Archimedean copula models, the best model was selected by looking at the largest Maximum Likelihood Estimation (MLE) value. In this study, the log-likelihood value of Clayton copula is 7.958, Gumbel copula is 6.663, and Frank copula is 8.398. Therefore, Frank copula is the best Archimedean copula model with the largest log-likelihood value of 8.398 for the said data. Then the VaR estimation is done with the Frank copula model. The Value at Risk estimation results based on the Frank copula model show maximum loss rates of -0.0277 at the 90% confidence level, -0.0363 at the 95% confidence level, and -0.0516 at the 99% confidence level.

Joint value-at-risk and expected shortfall regression for location-scale time series models

. This article studies the joint value-at-risk (VaR) and expected shortfall (ES) regression for a wide class of location-scale time series models including autoregressive and moving average models with generalized autoregressive conditional heteroscedasticity errors. In contrast to the quasi-maximum likelihood estimation, we estimate the model parameters with the aim of more accurate VaR and ES estimation. Then, we show consistency and asymptotic normality for parameter estimators under weak regularity conditions. Finally, a simulation study and a real data analysis are shown to illustrate our results.

Hybrid Fourier asymmetric-garch estimation of value at risk and expected shortfall: Empirical evidence from crude oil prices

We propose a hybrid Fourier approximation in an autoregressive fractional integrated moving average (ARFIMA) model, to account for periodic unoberved components in financial time series. We apply this hybrid model on parametric estimation of value at risk (VaR) and expected shortfall (ES). Using crude oil returns, we show that Fourier approximation inclusion significantly accounts for unobserved periodic components in a VaR estimation using exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model under generalized error distribution (GED). Similarly, in VaR estimation, Fourier approximation inclusion significantly accounts for unobserved periodic components using asymmetric power generalized autoregressive conditional heteroscedasticity (APARCH) model under skewed normal distribution (SNORM). For ES estimation, Fourier approximation inclusion only significantly accounts for unobserved periodic components of APARCH under SNORM.

Analyzing downside risk of BRICS stock indices: insights from value at risk and time series econometrics

Purpose This paper aims to analyze the downside risk for the stock indices of BRICS countries. The study also aimed to study the interrelationship, directional influence and interdependence among the stock exchanges of BRICS economies to provide insights for policymakers, fund managers, investors and other stakeholders. Design/methodology/approach The authors used Value at Risk (VaR) as an indicator of downside risk and time series econometrics for measuring the long run relationship, directional influence and interdependence. Findings The calculated VaR estimates, long-run linkages and strong interdependence among these indices especially with the returns of Brazil exerting a notable impact on the returns of other BRICS nations. These results emphasize the significance of taking into account cross-country spillover effects and domestic market dynamics in the context of portfolio management and risk assessment strategies. Further, from the extended results of variance decomposition analysis, the authors find that Brazil’s, China’s and South African stock market returns have a significantly lagged impact on their own stock market, while Russia’s and India stock market returns do not have a significantly lagged impact on their own stock markets. Originality/value To the best of the authors’ knowledge, this is the first study comprehensively analyzing the BRICS indices downside risk through the historical simulation method of VaR estimation, which is an unexplored area of risk management.

Adaptive Conformal Inference for Computing Market Risk Measures: An Analysis with Four Thousand Crypto-Assets

This paper investigates the estimation of the value at risk (VaR) across various probability levels for the log-returns of a comprehensive dataset comprising four thousand crypto-assets. Employing four recently introduced adaptive conformal inference (ACI) algorithms, we aim to provide robust uncertainty estimates crucial for effective risk management in financial markets. We contrast the performance of these ACI algorithms with that of traditional benchmark models, including GARCH models and daily range models. Despite the substantial volatility observed in the majority of crypto-assets, our findings indicate that ACI algorithms exhibit notable efficacy. In contrast, daily range models, and to a lesser extent, GARCH models, encounter challenges related to numerical convergence issues and structural breaks. Among the ACI algorithms, Fully Adaptive Conformal Inference (FACI) and Scale-Free Online Gradient Descent (SF-OGD) stand out for their ability to provide precise VaR estimates across all quantiles examined. Conversely, Aggregated Adaptive Conformal Inference (AgACI) and Strongly Adaptive Online Conformal Prediction (SAOCP) demonstrate proficiency in estimating VaR for extreme quantiles but tend to be overly conservative for higher probability levels. These conclusions withstand robustness checks encompassing the market capitalization of crypto-assets, time-series size, and different forecasting methods for asset log-returns. This study underscores the promise of ACI algorithms in enhancing risk assessment practices in the context of volatile and dynamic crypto-asset markets.

Risk Modeling and Connectedness Across Global and Industrial US Fintech Stock Market: Evidence from the COVID‑19 Crisis

The main purpose of this paper is to test the performance of GARCH models in estimating and forecasting VaR (value at risk) of the US Fintech stock market from July 20, 2016, to December 31, 2021. In addition, this study examines the impact of COVID‑19 on the risk spillover between the adequate VaR series of the US global KFTX index and the five Fintech industries. Specifically, we compare different VaR estimates (862 in‑sample daily returns) and predictions (550 out‑of‑sample daily returns) of several GARCH model specifications under a normal and Student‑t distribution with 1% and 5% significance. The Backtesting results indicate that I‑GARCH with Student‑t distribution is a good model for estimating and forecasting VaR of the US Fintech stock market before and during COVID-19. Moreover, the total connectedness results suggest that global and each Fintech industry increases significantly under turbulent market conditions. Given these considerations, this paper provides policymakers and regulators with a better understanding of risk in the Fintech industry without inhibiting innovation.

Financial Decisions and Value-at-Risk: Empirical Evidence from BIST 100 Companies

This study examines the relationship between financial decisions and the value-at-risk (VaR) of companies operating in the Turkish stock market. The study contains semi-annual data of non-financial BIST 100 Index companies spanning from January 2010 to June 2023. Companies’ VaR are calculated using Monte-Carlo simulation, bootstrap, delta-normal, and historical simulation methods and included in separate econometric models as dependent variables. Financial decisions are represented through financial ratios in line with the basic principles of corporate finance and included as explanatory variables in econometric models. The study employs a five-stage panel data methodology. 
 Findings reveal that the impact of financial decisions regarding working capital management, capital structure, dividend pay-out, and growth policies on companies’ VaR differ according to the VaR calculation method. Notably, findings show that financial decisions explain the changes in VaR calculated by Bootstrap method with the highest success rate, aligning with existing finance literature. Prudent financing policies and flexible investment strategies in working capital management, enhanced profitability and financial performance, and sales growth exhibit dampening effects on VaR. Conversely, heightened leverage and long-term borrowings, decisions to pay-out dividends, and growth in foreign investments have increasing effects on VaR. Furthermore, the study identifies the Covid-19 pandemic as exerting a negative influence on VaR.

Evaluating Financial Risk in the Transition from EONIA to ESTER: A TimeGAN Approach with Enhanced VaR Estimations

This study investigates the evaluation of multivariate time series data using a Generative Adversarial Network (GAN). Calculating the Value at Risk (VaR) for the Euro Overnight Index Average (EONIA) over different time periods and evaluating the financial risk consequences of the EONIA to Euro Short-Term Rate (ESTER) transition are the main objectives. Through the use of a particular GAN called TimeGAN, which focuses on macro-finance temporal and latent representation, the study aims to predict short-rate risk for EONIA. When estimating lower VaR and the 1-day higher VaR for EONIA, the TimeGAN model performs poorly. However, it performs well when estimating upper VaR for 10-day and 20-day periods. The variation of TimeGAN with PLS+FM, which uses Positive Label Smoothing and Feature Matching shows the upper and lower VaR for EONIA over 10 and 20-day periods are excellently estimated by this enhanced model. Simulations for the 20-day EONIA show less variation between TimeGAN variations than a one-factor Vasicek model, even with the proper VaR estimations. This study evaluates the proposed transition mapping from ESTER to EONIA by the European Central Bank (ECB), calculating an ESTER+8.5bps shift with the TimeGAN with PLS+FM. The results do not refute the validity of the ECB's proposed EONIA-ESTER mapping. Additionally, the TimeGAN with PLS+FM accurately predicts VaR for 10 and 20-day periods for ESTER using the EONIA-ESTER mapping. Whereas the one-factor Vasicek model finds it difficult to estimate higher VaR for ESTER over the same time frames.

Is the hybrid method more adequate for measuring operational risk?

Research aims: Risk management in financial institutions struggles with setting suitable capital charges for operational losses, resulting in large, disproportionate reserves that impact profits. This study, therefore, aims to develop a tailored operational risk measurement model for general takaful companies, addressing this challenge and optimizing capital allocation.Design/Methodology/Approach: This study employed a hybrid approach, merging the loss distribution approach (LDA) with historical data and scenario analysis for insurance company loss events. Compiling data into distributions, it utilized Monte Carlo simulations to determine value at risk (VaR). The resulting VaR guided the calculation of operational risk capital charges for future periods.Research findings: Measurement using the hybrid method could produce more adequate operational risk capital charges. These results confirm the acceptability of the VaR calculation and have been validated by the Kupic test.Theoretical contribution/Originality: This research offers a more comprehensive alternative method of measuring operational risk by combining historical company data with expert opinions, making it more likely to be practiced in the industry.Practitioner/Policy implication: The results of this study put forward an alternative, more suitable model for industry and regulators to measure operational risk management in general takaful companies.

Forecasting VaR and ES by using deep quantile regression, GANs-based scenario generation, and heterogeneous market hypothesis

Value at risk (VaR) and expected shortfall (ES) have emerged as standard measures for detecting the market risk of financial assets and play essential roles in investment decisions, external regulations, and risk capital allocation. However, existing VaR estimation approaches fail to accurately reflect downside risks, and the ES estimation technique is quite limited owing to its challenging implementation. This causes financial institutions to overestimate or underestimate investment risk and finally leads to the inefficient allocation of financial resources. The main purpose of this study is to use machine learning to improve the accuracy of VaR estimation and provide an effective tool for ES estimation. Specifically, this study proposes a VaR estimator by combining quantile regression with “Mogrifier” recurrent neural networks to capture the “long memory” and “clustering” properties of financial assets; while for estimating ES, this study directly models the quantile of assets and employs generative adversarial networks to generate future tail risk scenarios. In addition to the typical properties of financial assets, the model design is also consistent with heterogeneous market theory. An empirical application to four major global stock indices shows that our model is superior to other existing models.

VaR calculation by binary response models

<p>The original Risk-Metrics method is underpinned by the assumption that daily asset returns are conditional Gaussian independently identically distributed (iid) random variables with a mean of zero. In this paper, a new method to calculate Value at Risk (VaR) was suggested to overcome the shortcoming of Risk-Metrics by employing binary response models to compute probability forecasts of the portfolio return by exceeding a grid of candidate quantile values. From those values, the VaR quantile value was selected. The proposed model was called BRV (Binary Response VaR method). Consistent application of BRV to the Dow Jones Industrial Average (INDEXDJX: DJI) and Dow Jones U.S. Marine Transportation Index (DJUSMT) time series proved that it was more accurate than the Risk-Metric system. This method not only worked similar to quantile regression but had the advantage that conventional maximum likelihood methods could be used for parameter estimation and inference. The BRV method was the best performing method for computing the daily VaR at both the 95% and 99% confidence levels over the period 02/01/06–31/12/08. The BRV and the QR (quantile regression) methods performed similarly, but the BRV method had the practical advantage that conventional maximum likelihood (ML) technique could be used for parameter estimation and robust inference.</p>

High-frequency enhanced VaR: A robust univariate realized volatility model for diverse portfolios and market conditions.

In the field of financial risk management, the accuracy of portfolio Value-at-Risk (VaR) forecasts is of critical importance to both practitioners and academics. This study pioneers a comprehensive evaluation of a univariate model that leverages high-frequency intraday data to improve portfolio VaR forecasts, providing a novel contrast to both univariate and multivariate models based on daily data. Existing research has used such high-frequency-based univariate models for index portfolios, it has not adequately studied their robustness for portfolios with diverse risk profiles, particularly under changing market conditions, such as during crises. Our research fills this gap by proposing a refined univariate long-memory realized volatility model that incorporates realized variance and covariance metrics, eliminating the necessity for a parametric covariance matrix. This model captures the long-run dependencies inherent in the volatility process and provides a flexible alternative that can be paired with appropriate return innovation distributions for VaR estimation. Empirical analyses show that our methodology significantly outperforms traditional univariate and multivariate Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) models in terms of forecasting accuracy while maintaining computational simplicity and ease of implementation. In particular, the inclusion of high-frequency data in univariate volatility models not only improves forecasting accuracy but also streamlines the complexity of portfolio risk assessment. This research extends the discourse between academic research and financial practice, highlighting the transformative impact of high-frequency data on risk management strategies within the financial sector.

Optimal Portfolio Risk Analysis Using the Monte Carlo Method

Investment is an activity carried out with the expectation of gaining profits in the future through the management of investment assets. Investment assets can include buildings, gold, and stocks. Investment activities are inseparable from the concepts of return and risk. The relationship between the expected rate of return and the level of risk is linear. However, risk can be avoided or reduced through portfolio diversification. Evaluating investment risk is crucial for investors to determine which risky assets to choose. One popular method for assessing the risk of a portfolio is using Value at Risk (VaR). In VaR calculations, Monte Carlo is considered the most effective method. In this paper, a risk analysis of the optimal portfolio is conducted using the Monte Carlo method. The analyzed optimal portfolio consists of shares in BBCA, TLKM, BBRI, BBNI, BMRI, ADRO, GGRM, and UNTR. The results indicate that the potential loss for the investor is no more than IDR 705.634,- with an initial fund of 1 billion.

Efficiency gains in value-at-risk and expected shortfall estimation by using copulas and full maximum likelihood

We provide Monte Carlo evidence on the efficiency gains obtained in GARCH-based estimations of value-at-risk (VaR) and expected shortfall (ES) by incorporating dependence information through copulas and subsequently using full maximum likelihood (FML) estimates. First, we consider an individual returns series; in this case, the efficiency gain stems from exploiting the relationship with another returns series using a copula model. Second, we consider a portfolio returns series obtained as a linear combination of returns series related through a copula model; in this case, the efficiency gain stems from using FML estimates instead of two-stage ML estimates. We consider three copulas models in order to analyze the effect of the type and degree of tail dependence on the results. Our results show that, in these situations, using copula models and FML leads to a substantial reduction in the mean squared error of the VaR and ES estimates when there is a relatively high degree of dependence between returns (up to 70% in the presence of lower-tail dependence) and a notable improvement in the performance of backtesting procedures.

Value at Risk Calculation of Digital Bank Stocks Portfolio in Indonesia

<p>Nowadays, stock investment has been increasingly growing in society. In investing activities, there are risks that may be experienced by investors. However, sometimes many investors do not realize how much risk that they might suffer in the future. One way that can be done to measure this risk is to calculate the Value at Risk (VaR). This study aims to calculate the VaR value of digital bank stock portfolio in Indonesia. The calculation of VaR will be done using two methods, include the Historical Simulation and Monte Carlo Simulation method. From the calculation, VaR with Historical Simulation and Monte Carlo sequentially generate results of IDR 6,006,718 and IDR 10,797,904 for 99% confidence level, IDR 4,135,857 and IDR 5,376,949 for 95% confidence level, and IDR 3,219,885 and IDR 3,417,553 for 90% confidence level. Based on the results, it is found that VaR result is directly proportional to the confidence level used. Through the calculation results, it also found that VaR value with the Monte Carlo Simulation method are greater than those with the Historical Simulation method.</p>

Mean-Value-at-Risk Portfolio Optimization Based on Risk Tolerance Preferences and Asymmetric Volatility

Investors generally aim to obtain a high return from their stock portfolio. However, investors must realize that a high value-at-risk (VaR) is essential to calculate for this aim. One of the objects in the VaR calculation is the asymmetric return volatility of stocks, which causes an unbalanced decrease and increase in returns. Therefore, this study proposes a mean-value-at-risk (mean-VaR) stock portfolio optimization model based on stocks’ asymmetric return volatility and investors’ risk aversion preferences. The first stage is the determination of the mean of all stocks in the portfolio conducted using the autoregressive moving average Glosten–Jagannathan–Runkle generalized autoregressive conditional heteroscedasticity (ARMA-GJR-GARCH) models. Then, the second stage is weighting the capital of each stock based on the mean-VaR model with the investors’ risk aversion preferences. This is conducted using the Lagrange multiplier method. Then, the model is applied to stock data in Indonesia’s capital market. This application also analyzed the sensitivity between the mean, VaR, both ratios, and risk aversion. This research can be used for investors in the design and weighting of capital in a stock portfolio to ensure its asymmetrical effect is as small as possible.

Are the intraday volatility estimations more representative than the conventional measures? Evidence from the EURTRL FX.

This paper aims to assess the accuracy and representativeness of Value at Risk (VaR) estimation models for the highly volatile Turkish lira (TRY) and Euro (EUR) FX rate. We compare the performance of various VaR models commonly used in the financial and banking industry and examine the effectiveness of intraday models, particularly the Garman and Klass (1980) and the Parkinson (1980) approaches, in improving VaR estimation relative to conventional models such as Variance Covariance and Exponential Weighted Moving Average. Additionally, we highlight certain shortcomings of the VaR legislation proposed by Vasileiou (2016, 2017). Our findings demonstrate that intraday volatility estimations not only enhance the accuracy of VaR estimations, but also provide a more representative assessment of real risk. The results of this study have significant implications for scholars, regulators, portfolio managers, and investors seeking to better understand and manage risk in the TRY-EUR FX market.

VALUE AT RISK ANALYSIS ON BLUE CHIP STOCKS PORTFOLIO WITH GAUSSIAN COPULA

Value at Risk (VaR) is a risk measurement tool to calculate the estimated maximum investment loss with a certain confidence level and period. VaR calculations using financial data are often not normally distributed, so the copula method is used, which is flexible on the assumption of normality on stock return data. Previous research discussed Gaussian copula using stocks from the telecommunications sector. In this research, using Gaussian copula on Blue Chip stocks. Blue Chip stocks have a good reputation and have a stable growth rate so they have a lower risk. Therefore, the research objective is to analyze the VaR portfolio of Blue Chip stock with Gaussian copula. This research uses the daily stock closing prices of BBNI and BBTN from November 2, 2020 to October 27, 2022. The analysis results suggested that a VaR portfolio using Gaussian copula with a confidence level of 90%, 95%, and 99%, respectively are 2.24%, 2.88%, and 4.02%. The value shows the percentage of investment risk that may be obtained in the next one-day period. This result also indicates that the higher the confidence level, the greater the VaR.

The Gumbel Copula Method for Estimating Value at Risk: Evidence from Telecommunication Stocks in Indonesia during the COVID-19 Pandemic

The COVID-19 pandemic has had a substantial and far-reaching impact on global economic growth, extending its effects to Indonesia as well. Various sectors have witnessed a decline in stock returns as a consequence. Interestingly, the telecommunications sector has bucked this trend by experiencing an increase in stock returns, defying the negative implications of the pandemic. The relationship between returns and risk is inherently intertwined, necessitating a meticulous risk assessment. In response to this need, the Value at Risk (VaR) method has emerged as a rapidly growing and widely adopted risk measurement tool. Among the techniques employed for VaR estimation, the Monte Carlo simulation stands out due to its flexibility and comprehensiveness in accommodating factors such as time variance, volatility, returns, fat tails, and extreme scenarios. The Gumbel copula method, known for its heightened sensitivity to high-risk events, is utilized for VaR estimation on abnormal stock returns. This study aims to quantify the Value at Risk by leveraging the estimated Gumbel copula parameter for the return on the shares of PT. Indosat Ooredoo Hutchison Tbk, and PT. Smartfren Telecom Tbk during the COVID-19 pandemic. At a 90% confidence level, the VaR is determined to be 7.6%. Notably, this estimate closely aligns with the actual values, underscoring the reliability of the VaR estimation conducted using the Gumbel copula parameter estimator. Therefore, this model serves as a robust reference, particularly suitable when dealing with investment return data that deviate from the normal distribution, while considering the unique stock return characteristics within each dataset.