Modelling and forecasting value at risk and expected shortfall for GCC stock markets: do long memory, structural breaks, asymmetry, and fat-tails matter? Forthcoming in North American Journal of Economics and Finance Financially supported by Fawzen Chair of Macroeconomics Forecasting Chaker Aloui College of Business Administration, King Saud University, KSA Ben Hamida Hela College of Economics and Administrative Sciences, Al Imam Muhammad Ibn Saud Islamic University , KSA Modelling and forecasting value at risk and expected shortfall for GCC stock markets: do long memory, structural breaks, asymmetry, and fat-tails matter? Contents o o o o o o o Introduction and research motivations Main research question Econometric framework Data and preliminary analysis Empirical results Some risk management implications Concluding remarks Introduction and research motivations GCC stock markets: some stylized facts Volatility clustering, asymmetry, structural breaks and long memory 1.0 100 ACF-sqared return (QATAR) squared return (Qatar) 75 0.5 50 25 0 50 100 10 0.75 2004 Density logarithmic return (Qatar) 2006 2008 2010 2012 2014 RQATAR 0.50 0 0.25 2004 2006 Distribution 10 2008 2010 2012 2014 10 -10 QQ plot 0 5 10 RQATAR ´ normal RQATAR 0 -5 0 -10 -10 -5 0 5 10 -4 -2 0 2 4 Main objectives and research question 1. Researching the relevance of LM, structural breaks, asymmetry, and fat-tails in modeling and forecasting the volatility of GCC stock markets; 2. Assessing the predictive ability of LM GARCH-class models under various return innovations’ distributions (normal, Student-t, and skewed student-t) 3. Analyzing the VaR and ES performance for short and long trading positions. 4. We connect the VaR analysis to Basel II Capital Accord requirements Do LM, structural changes, asymmetry, and heavy tails matter when quantifying risk using the VaR and ES tools? What are the main financial implications in terms of risk management? Econometric framework (1) Long memory GARCH-class models o ARFIMA model (mean process) o FIGARCH model (variance process) o FIAPARCH model (variance) process Densities o Student t distribtion o Skewed Student-t distribution Econometric framework (2) Value-at-risk and expected shortfall o The one-day-ahead VaR: o The expected shortfall: Statistical accuracy of model-based VaR’s estimations We employ two alternative tests, o Kupiec (1995) test and o Dynamic Quantile test (DQT) suggested by Engle and Manganelli (2002). Data and preliminary analysis Markets: Kingdom of Saudi Arabia (SASEIDX), Dubai (DFMGI Index) and Abu Dhabi (ADSMI Index), Oman (MSM30), Bahrain (BHSEASI), Kuwait (KWSEIDX) and Qatar (DSM). Source and sample period: Bloomberg daily stock indexes (January, 3nd 2003 to January 22nd, 2013). 2,620 observations The sample periods are varying across GCC markets and indexes are expressed in local currencies. We should note that the last 1,000 observations are reserved to the out-of-sample forecasts. Long memory vs. structural breaks Empirical results o Long memory We implement three alternative long-range memory tests: Lo’s (1991) test, the logperiodogram regression (GPH) of Geweke and Porter-Hudak (1983) and the GSP Robinson (1995) test. o Structural breaks We check whether the occurrence of LM is spurious and caused by some structural breaks. We refer to Shimotsu (2006)’s to test the null hypothesis of LM against structural We confirm the existence of LM in the squared returns and that conditional volatility of the GCC countries is not caused by the occurrence of structural breaks. The LM fact is not spurious for all the GCC stock markets. Results of Inclan and Tiao (1994)’s structural break test GCC stock market Saudi Arabia Kuwait Oman Qatar Dubai Abu Dhabi Bahrain Number of breaks Break dates 4 3 3 2 3 4 2 09/16/2003 - 04/18/2004 – 06/04/2006 – 09/18/2009 06/13/2003 - 03/09/2005 - 09/18/2009 05/13/2005 - 01/03/2008 - 09/20/2009 09/19/2008 - 01/02/2011 02/08/2005 – 08/16/2007 – 18/09/2008 05/03/2005- 02/08/2005 – 08/16/2007 – 18/09/2008 09/18/2008 – 01/21/2011 Saudi Arabia and Abu Dhabi stock markets exhibit four structural breaks in their unconditional variance behavior. Kuwait, Oman and Dubai display at least three structural breaks. 2008-2009 global financial crisis is a common break date for all the GCC stock markets. The Arab Spring on January 2011 is identified as a structural change in the unconditional variance behavior for at least two countries namely Bahrain and Qatar. Forecasting performance assessment We employ 1) the mean square error (MSE), 2) the mean absolute prediction error (MAPE) , 3) the logarithmic loss function (LL), and 4) the Mincer-Zarnowitz (1969) regression. Qatar Saudi Arabia Kuwait ARFIMAAR-FIAPARCH AR-FIAPARCH FIAPARCH with skew. St.- t with St. t with skew. St. Oman ARFIMAFIAPARCH with St. –t Dubai & Abu Dhabi AR-FIGARCH with sk. St.-t Bahrain AR-FIAPARCH with sk. St. Saudi Arabia and Oman , under skewed Student-t innovations distributions, the ARFIMAFIAPARCH model performs better than the other models for both short and long trading positions. The selected models under skewed student-t distribution provide the best forecasts for the VaR and ES. Some risk management implications: VaR and Basel II Accord capital requirements Under the Basel II Capital Accord, the VaR’s predictions of the banks should be reported to the appropriate authority at the beginning of the day, and are then compared to actual returns at the end of the day. These forecasts are used to compute the amount of capital requirements (daily capital charges) in order to provide a cushion against adverse market situations. DCC must be set at the higher of the previous day’s VaR or the average over the business day adjusted by a scaling factor with reference to three-zone approach. The scaling factor corresponds to the sum of 3 and a given multiplicative factor (k) as given in the table. The DCC is the penalty that the Basel II imposes on financial institutions employing models that lead to a greater number of violations than would be expected, given a specific confidence level of 99%. For a daily data, the DCC is given by: Zone Nb. of k violations Green 0 to 4 0.00 5 0.40 6 0.50 7 0.65 8 0.75 9 0.85 +10 1.00 Yellow Red LM GARCH-class models, VaR forecasts and DCC under Basel II rules The number of violations for all the LM-GARCH specifications and all GCC markets is always less than ten suggesting that these models do not lead to entry in the Basel II Accord critical zone (i.e. red zone). In terms of daily average capital charges, the FIAPARCH model under skewed Student density is the best model followed by the FIGARCH model under Student-t density as it yields in three cases out of four. The percentage of violations given by the FIAPARCH-N for three out of seven indexes is higher than that of the FIAPARCH model under skewed Student and Student densities indicating that the risk of going into the red zone defined by the Basel II rules is higher with the FIAPARCH-normal. The results of the various APARCH specifications are comparable in terms of DCC, but the APARCH model with skewed Student distribution generates less violations. Concluding remarks LM is particularly strong and plays dominant role in explaining the GCC stock market returns. The selection tests provide results confirming LM to the detriment of structural breaks. Only two markets, namely Saudi Arabia and Oman exhibit LM in both conditional mean and variance. We uncover the superiority of the FIAPARCH model under skewed Student-t innovation distribution for the in-sample forecasting exercise. For the out-of-sample forecasting, the FIAPARCH model provides the best predictive ability. The VaR seems to work in GCC stock markets and we believe that greater attention should be paid to LM properties, asymmetry and fat tails when quantifying risk. Some references Aloui, C. and Mabrouk, S. 2010.Value-at-risk estimations of energy commodities via long-memory, asymmetry and fat-tailed GARCH models. Energy Policy 38, 2326-2339. Conrad, C., Karanasos, M., Zeng, N., 2011. Multivariate fractionally integrated APARCH modeling of stock market volatility: a multicountry study. Journal of Empirical Finance 18, 147–159. Degiannakis, S, C. Floros and P. Dent. 2013. Forecasting value-at-risk and expected shortfall using fractionally integrated models of conditional volatility: international evidence. International Review of Financial Analysis 27, 21-33. Degiannakis, S. 2004. Volatility forecasting: evidence from a fractional integrated asymmetric power ARCH skewed-t model. Applied Financial Economics 14, 1333– 1342. Kupiec, P., 1995. Technique for verifying the accuracy of risk measurement models. Journal of Derivatives 2, 173-184.
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