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This study utilizes the seven bivariate generalized autoregressive conditional heteroskedasticity (GARCH) models to forecast the out-of-sample value-at-risk (VaR) of 21 stock portfolios, and seven currency-stock portfolios with three weight combinations, and then employs three accuracy tests and one efficiency test to evaluate the VaR forecast performance for the above models. The seven models are constructed by four types of bivariate variance-covariance specification and two approaches of parameters estimate. Four types of bivariate variance-covariance specification are the constant conditional correlation (CCC), asymmetric and symmetric dynamic conditional correlation (ADCC and DCC), and the BEKK, whereas the two types of approach include the standard and nonstandard approaches. Empirical results show that, regarding the accuracy tests, the VaR forecast performance of stock portfolios varies with the variance-covariance specifications and approaches of parameters estimate, whereas it doesn’t vary with the weight combinations of portfolios. Conversely, the VaR forecast performance of currency-stock portfolios is almost the same for all models and still doesn’t vary with the weight combinations of portfolios. Regarding the efficiency test via market risk capital, the NS-BEKK model is the most suitable model to be used in the stock and currency-stock portfolios for the bank risk manager irrespective of the weight combination of povalue-at-risk; accuracy test; efficiency testrtfolios.
- value-at-risk
- accuracy test
- efficiency test
- constant conditional correlation
- dynamic conditional correlation
- stock market
In this study, according to the procedure of parameters estimate or the number of parameter estimate of model (i.e., the approach of parameters estimate), the seven bivariate GARCH models: the S-CCC, NS-CCC, S-DCC, NS-DCC, NS-ADCC, S-BEKK, and NS-BEKK models can be classified into the following two categories: the standard CCC, DCC, and BEKK models (i.e., the S-CCC, S-DCC, and S-BEKK models); and the nonstandard CCC, DCC, ADCC, and BEKK models (i.e., the NS-CCC, NS-DCC, NS-ADCC, and NS-BEKK models). Or, according to the specification depicting the correlative relationship between two assets, they can be divided as the following four categories: the CCC model of Bollerslev (1990) (i.e., the S-CCC and NS-CCC models), the DCC model of Engle (2002) (i.e., the S-DCC and NS-DCC models), the ADCC model of Cappiello et al. (2006) (i.e., the NS-ADCC model), and the BEKK model defined in Engle and Kroner (1995) (i.e., the S-BEKK and NS-BEKK models). Subsequently, the above seven bivariate GARCH models are utilized to estimate the VaR of 21 bi-component stock portfolios, and seven bi-component currency-stock portfolios, and then three accuracy measures and one efficiency test are used to evaluate the out-of-sample VaR forecast performance of the above seven bivariate GARCH models. Further, regarding the results of accuracy tests, this study explores which bivariate variance-covariance specification, which parameter estimate approach has better VaR forecast performance, and whether the asymmetric DCC model has better forecast performance than its corresponding symmetric one.
According to the above issues, four categories of model performance competition are executed . The first category of model performance competition is used to inspect which approach of parameters estimate, the standard or nonstandard approach, has better VaR forecast performance, and it is executed by the performance competition between the standard approach and its corresponding nonstandard approach based on the same bivariate variance-covariance specification, and it includes three groups of model performance competition- the S-CCC vs. NS-CCC, the S-DCC vs. NS-DCC, and the S-BEKK vs. NS-BEKK. Notes 6 and 10 (respectively Notes 3 and 7) of Table 3 (respectively Table 4) shows the above comparison results based on failure rate (respectively mean VaR). Also, note 6 of Table 5 shows the summarized comparison results based on failure rate and mean VaR. Similarity, note 6 (respectively note 5) of Table 7 (respectively Table 8) shows the summarized comparison results based on LRuc, LRcc and DQ tests.
The second category of model performance competition is used to inspect which type of bivariate variance-covariance specification, the CCC, DCC or BEKK, has the best VaR forecast performance, and it is executed by the performance competition among the three types of bivariate variance-covariance specification (i.e., the CCC, DCC and BEKK) based on the same approach of parameters estimate, and it includes two groups of model performance competition- the S-CCC, S-DCC and S-BEKK; and the NS-CCC, NS-DCC and NS-BEKK. Notes 7 and 11 (respectively Notes 4 and 8) of Table 3 (respectively Table 4) shows the above comparison results based on failure rate (respectively mean VaR). Also, note 7 of Table 5 shows the summarized comparison results based on failure rate and mean VaR. Similarity, note 7 (respectively note 6) of Table 7 (respectively Table 8) shows the summarized comparison results based on LRuc, LRcc and DQ tests.
The third category of model performance competition is the performance competition among all the bivariate GARCH models except the NS-ADCC model in order to inspect which model has the best VaR forecast performance among the above six models (i.e. S-CCC, S-DCC, S-BEKK, NS-CCC, NS-DCC and NS-BEKK). Notes 8 and 12 (respectively Notes 5 and 9) of Table 3 (respectively Table 4) shows the above comparison results based on failure rate (respectively mean VaR). Also, note 8 of Table 5 shows the summarized comparison results based on failure rate and mean VaR. Similarity, note 8 (respectively note 7) of Table 7 (respectively Table 8) shows the summarized comparison results based on LRuc, LRcc and DQ tests.
The last category of model performance competition is used to inspect whether the asymmetric DCC model has better forecast performance than its corresponding symmetric one, and it is executed by the performance competition between the NS-DCC and NS-ADCC models. Notes 9 and 13 (respectively Notes 6 and 10) of Table 3 (respectively Table 4) shows the above comparison results based on failure rate (respectively mean VaR). Also, note 9 of Table 5 shows the summarized comparison results based on failure rate and mean VaR. Similarity, note 9 (respectively note 8) of Table 7 (respectively Table 8) shows the summarized comparison results based on LRuc, LRcc and DQ tests.
