GARCH models for daily stock returns: Impact of estimation frequency on Value-at-Risk and Expected Shortfall forecasts

This study aims to apply value at risk (VaR) and expected shortfall (ES) as time-varying systematic and idiosyncratic risk factors to address the downside risk anomaly of various asset pricing models currently existing in the Pakistan stock exchange. The study analyses the significance of high minus low VaR and ES portfolios as a systematic risk factor in one factor, three-factor, and five-factor asset pricing model. Furthermore, the study introduced the six-factor model, deploying VaR and ES as the idiosyncratic risk factor. The theoretical and empirical alteration of traditional asset pricing models is the study’s contributions. This study reported a strong positive relationship of traditional market beta, value at risk, and expected shortfall. Market beta pertains its superiority in estimating the time-varying stock returns. Furthermore, value at risk and expected shortfall strengthen the effects of traditional beta impact on stock returns, signifying the proposed six-factor asset pricing model. Investment and profitability factors are redundant in conventional asset pricing models.

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Effects of asset frequency components on value-at-risk in emerging and developed markets

Brazilian Review of Econometrics ◽

10.12660/bre.v40n12020.77437 ◽

2020 ◽

Vol 40 (1) ◽

pp. 145

Author(s):

Milton Biage ◽

Pierre Joseph Nelcide

Keyword(s):

At Risk ◽

Stock Returns ◽

Value At Risk ◽

Financial Assets ◽

Back Testing ◽

Window Technique ◽

Rolling Window ◽

Frequency Components ◽

Daily Stock Returns ◽

Daily Returns

<p>Value-at-Risk was estimated using the technique of wavelet decomposition with goal to analyze the frequency components' impacts on variances of daily stock returns, and on forecasts. Daily returns of twenty-one shares of the Ibovespa and daily returns of twenty-two shares of the DJIA were used. The model was applied to the reconstructed returns to model and establish the prediction of conditional variance, applying the rolling window technique. The Value-at-Risk was then estimated, and the results showed that the DJIA shares showed more efficient market behavior than those of Ibovespa. The differences in behavior induces to affirm that VaRs, used in the analysis of financial assets from different markets with different governance premises, should be estimated by series of returns reconstructed by aggregations of components of different frequencies. A set of back-testing was applied to confront the estimated , which demonstrated that the estimation of models are consistent.</p>

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Semiparametric GARCH Models with Long Memory Applied to Value at Risk and Expected Shortfall

SSRN Electronic Journal ◽

10.2139/ssrn.3823895 ◽

2021 ◽

Author(s):

Sebastian Letmathe ◽

Yuanhua Feng ◽

André Uhde

Keyword(s):

At Risk ◽

Long Memory ◽

Value At Risk ◽

Expected Shortfall ◽

Garch Models

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Dynamic value at risk estimation for BELEX15

Advances in Methodology and Statistics ◽

10.51936/odxg4832 ◽

2011 ◽

Vol 8 (1) ◽

Author(s):

Emilija Nikolić-Đorić ◽

Dragan Đorić

Keyword(s):

At Risk ◽

Stock Returns ◽

Long Memory ◽

Value At Risk ◽

Stock Exchange ◽

Risk Estimation ◽

Value Theory ◽

Garch Models ◽

Measurement Models ◽

Standardized Residuals

This paper uses RiskMetrics, GARCH and IGARCH models to calculate daily VaR for Belgrade Stock Exchange index BELEX15 returns based on the normal and Student t innovation distribution. In the case of GARCH and IGARCH models VaR values are obtained applying Extreme Value Theory on the standardized residuals. The Kupiec's LR statistics was used to test the accuracy of risk measurement models. The main conclusions are: (1) when modelling value-at-risk it is very important to have a good model for volatility of stock returns; (2) both stationary and integrated GARCH models outperform RiskMetrics in estimating VaR; (3) although long memory volatility is present in the BELEX15 index, IGARCH models cannot outperform GARCH type models in VaR evaluations for this index.

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On the Volatility of Daily Stock Returns of Total Petroleum Company of Nigeria: Evidence from GARCH Models, Value-at-Risk and Backtesting

10.20944/preprints201812.0043.v1 ◽

2018 ◽

Author(s):

Ngozi G. Emenogu ◽

Monday Osagie Adenomon ◽

Nweze Nwaze Obinna

Keyword(s):

At Risk ◽

Stock Returns ◽

Confidence Level ◽

Value At Risk ◽

Stock Price ◽

Garch Models ◽

Correct Number ◽

Energy Company ◽

Petroleum Company ◽

Tests Of Independence

Total Nigeria Plc is a Marketing and Services subsidiary of Total; a multinational energy company operating in more than 130 countries and committed to providing sustainable products and services for its customers. For over 50 years, Total Nigeria  Plc  has  remained  the  leader  in  the  downstream  sector  of  the  Nigerian  oil  and  gas  industry. This study investigated the volatility of the stock price of Total Petroleum Nigeria plc using nine (9) GARCH models namely sGARCH, gjrGARCH, eGARCH, iGARCH, aPARCH, TGARCH, NGARCH, NAGARCH and AVGARCH. We also investigated the Value-at-Risk (VaR) and Backtesting of the Models. The aim actually of this study is to boost the confidence of the shareholders and investors of the Total Nigeria plc. To achieve this, daily stock price for Total petroleum Nigeria plc from secondary was collected from January 2nd 2001 to May 8th 2017. . The study used both normal and student t innovations, using Akaike Information Criterion (AIC) to select the best model, for normal innovations for log returns and cleansed log returns of Total plc, the eGARCH and sGARCH models performed best respectively, while NGARCH model performed best for student t innovation for both log returns and cleansed returns of Total plc. The persistence of the models are stable except in few cases where iGARCH, eGARCH where not stable. Also for student t innovation, the sGARCH and gjrGARCH fails to converge. The mean-reverting number of day for the returns of Total Nigeria plc differs from model to model. Evidence from the VaR Analysis revealed from the selected models revealed that the Risk of VaR losses is high at 99% confidence level, slightly high at 95% confidence level and better at 90% confidence level. Although The Duration-Based Tests of independence conducted revealed that the models are correctly specified since in all cases the null hypotheses were accepted. This means that the probability of an exception on any day did not depends on the outcome of the previous day. Finally, both the unconditional (Kupiec) and conditional (Christoffersen) coverage tests for the correct number of exceedances for both Total stock returns and cleansed returns. The tests revealed rejection of the models at 1% level of significance. This confirms that unconditional (Kupiec) and conditional (Christoffersen) coverage tests for the correct number of exceedances are reliable compared to the Duration-Based Tests of independence. Therefore we recommend that shareholders and investors in Total Nigeria plc are to remain and continue to investment in Total Nigeria plc because if there is any form of losses, the price of the stock has the potentials to improve in the future. Again, though the risk is high at 99% confidence level, this in line with the financial theory that states that an asset with high expected risk would pay higher return on the average.

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Previsão de value-at-risk e expected shortfall para mercados emergentes usando modelos FIGARCH

Brazilian Review of Finance ◽

10.12660/rbfin.v13n3.2015.53080 ◽

2015 ◽

Vol 13 (3) ◽

pp. 394

Author(s):

Alex Sandro Monteiro De Moraes ◽

Antonio Carlos Figueiredo Pinto ◽

Marcelo Cabus Klotzle

Keyword(s):

At Risk ◽

Long Memory ◽

Value At Risk ◽

Expected Shortfall ◽

Error Distribution ◽

Memory Models ◽

Garch Models ◽

Daily Data ◽

Short Memory ◽

Forecasting Volatility

This paper compares the performance of long-memory models (FIGARCH) with short-memory models (GARCH) in forecasting volatility for calculating value-at-risk (VaR) and expected shortfall (ES) for multiple periods ahead for six emerging markets stock indices. We used daily data from 1999 to 2014 and an adaptation of the Monte Carlo simulation to estimate VaR and ES forecasts for multiple steps ahead (1, 10 and 20 days ), using FIGARCH and GARCH models for four errors distributions. The results suggest that, in general, the FIGARCH models improve the accuracy of forecasts for longer horizons; that the error distribution used may influence the decision about the best model; and that only for FIGARCH models the occurrence of underestimation of the true VaR is less frequent with increasing time horizon. However, the results suggest that rolling sampled estimated FIGARCH parameters change less smoothly over time compared to the GARCH models.

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