||Forecasting Volatility and Capturing Downside Risk in Financial Markets under the Subprime Mortgage Crisis
||Department of Banking and Finance
Subprime mortgage crisis
Exchange Traded Fund
||This thesis applies alternative GARCH-type models to daily volatility forecasting with Value-at-Risk (VaR) application to the Taiwanese stock index futures and Standard & Poor’s Depositary Receipts (SPDRs) that suffered the global financial tsunami that occurred during 2008. Instead of using squared returns as a proxy for true volatility, this thesis adopts four volatility proxy measures, the PK-range, GK-range, RS-range, and RV, for use in the empirical exercise. The volatility forecast evaluation is conducted with a variety of volatility proxies according to both symmetric and asymmetric types of loss functions regarding forecasting accuracy. These models are also evaluated in terms of their ability to provide adequate VaR estimates with the inclusion of realized-volatility-based VaR model. Moreover, the predictive performance of the RV-based VaR model is compared with various GARCH-based VaR models according to both unconditional coverage test (Kupiec,1995) and utility-based loss functions with respect to risk management practice.
Empirical results indicate that the EGARCH model provides the most accurate daily volatility forecasts, whereas the performances of the standard GARCH model are relatively poor. Such evidence suggests that asymmetry in volatility dynamics should be taken into account for forecasting financial markets volatility. Moreover, I find a consistent result that the forecasting performance of models remains constant across various volatility proxies for both empirical data in most cases. In the area of risk management,the RV-VaR model tends to underestimate VaR and has been rejected for lacking correct unconditional coverage for the TAIFEX returns data, while the GARCH genre of models is capable of providing satisfactory and reliable daily VaR forecasts. In particular, the asymmetric EGARCH model is the most preferred. For SPDRs case, while all models have passed the back-test, the RV-VaR is considered the optimal VaR model both for a regulator and for a firm at alternative confidence levels during the whole year of 2008. The empirical findings presented here provide crucial implications for market practitioners, such as, policy makers, institutional risk managers, and common investors in risk management.
||TABLE OF CONTENTS
ABSTRACT IN CHINESE ii
ABSTRACT IN ENGLISH iii
LIST OF TABLES viii
LIST OF FIGURES ix
1.1 Research Background 1
1.1.1 Lessons from Long-Term Capital Management Crisis 1
1.1.2 The Subprime Mortgage Storm in America 4
1.1.3 The Expatiation of ETFs and Futures 7
1.2 Motivations 9
1.3 Objectives 12
1.4 Flow Chart 14
2.Literature Review 15
2.1 Volatility Forecasting 15
2.1.1 Volatility Proxy Measures 15
2.1.2 Related Literature Review 18
2.2 Applications to Risk Management: Value-at-Risk 22
2.2.1 The definition of Value-at-Risk 22
2.2.2 Related Literature Review 24
2.3 Contribution of the Thesis 34
3. Data Description and Preliminary Analysis 36
3.1 Data Description 36
3.1.1 Taiwanese Stock Index Futures 37
3.1.2 Standard and Poor's Depositary Receipts 37
3.2 Preliminary Analysis of Empirical Data 39
3.2.1 Descriptive Statistics 39
3.2.2 Descriptive Graphs 44
4. Econometric Frameworks 48
4.1 Various Adaptations of GARCH Models 48
4.1.1 GARCH (1,1) Model 48
4.1.2 GJR-GARCH Model 49
4.1.3 QGARCH Model 50
4.1.4 EGARCH Model 50
4.2 The Skewed Generalized T (SGT) Distribution 51
4.3 Alternative Volatility Proxies 53
4.4 Performance Evaluation for Volatility Forecasting Models 54
4.4.1 R-squared from the Mincer and Zarnowitz (1969) Regression 54
4.4.2 Symmetric Loss Functions 55
4.4.3 Asymmetric Loss Function 55
4.5 Model-Based VaRs and their Evaluations 56
4.5.1 The LR Test for Unconditional Coverage 56
4.5.2 The Utility-Based Loss Functions 57
22.214.171.124 Regulatory Loss Function (RLF) 57
126.96.36.199 Firm Loss Function (FLF) 58
5.Empirical Results and Analysis 59
5.1 Model estimates and diagnostic test 59
5.2 Analyzing Volatility forecasting performance of models62
5.2.1 R-squared from Mincer and Zarnowitz (1969) regression 62
5.2.2 Forecasting performance based on symmetric loss errors 63
5.2.3 Forecasting performance based on asymmetric loss errors 66
5.3 Analyzing predictive accuracy of the model-based VaR 75
5.3.1 VaR performance for various models at the 99% confidence level 75
5.3.2 VaR performance for various models at the 99.5% confidence level 81
6.Conclusions and Suggestions 87
LIST OF TABLES
Table 3.1 The Contract Specifications of the Taiwanese Stock Index Futures36
Table 3.2 The Specifications of the SPDRs 39
Table 3.3 Descriptive Statistics of Daily TAIFEX Futures and SPDRs Returns 43
Table 3.4 Descriptive Statistics of alternative volatility proxies for TAIFEX Futures and SPDRs 44
Table 5.1 Estimation results of various GARCH models 61
Table 5.2 The Mincer and Zarnowitz (1969) regression test results 62
Table 5.3 Out-of-sample forecasting performance based on symmetric loss errors:
The case for TAIFEX 64
Table 5.4 Out-of-sample forecasting performance based on symmetric loss errors:
The case for SPDRs 65
Table 5.5 Out-of-sample forecasting performance based on asymmetric loss errors:
The case for TAIFEX 68
Table 5.6 Out-of-sample forecasting performance based on asymmetric loss errors:
The case for SPDRs 69
Table 5.7 Value-at-Risk forecasting results for TAIFEX at the 99% confidence level78
Table 5.8 Value-at-Risk forecasting results for SPDRs at the 99% confidence level 78
Table 5.9 Value-at-Risk forecasting results for TAIFEX at the 99.5% confidence level 83
Table 5.10 Value-at-Risk forecasting results for SPDRs at the 99.5% confidence level 83
LIST OF FIGURES
Figure 3.1 Daily TAIFEX futures prices in level 41
Figure 3.2 Daily SPDRs prices in level 41
Figure 3.3 Daily TAIFEX futures returns 45
Figure 3.4 Daily SPDRs returns 45
Figure 3.5 Daily TAIFEX futures QQ-plot 46
Figure 3.6 Daily SPDRs QQ-plot 46
Figure 3.7 Daily TAIFEX futures returns density 47
Figure 3.8 Daily SPDRs returns density 47
Figure 5.1 PK versus various model-based volatility forecasts for TAIFEX 70
Figure 5.2 GK versus various model-based volatility forecasts for TAIFEX 71
Figure 5.3 RS versus various model-based volatility forecasts for TAIFEX 71
Figure 5.4 RV versus various model-based volatility forecasts for TAIFEX 72
Figure 5.5 PK versus various model-based volatility forecasts for SPDRs 72
Figure 5.6 GK versus various model-based volatility forecasts for SPDRs 73
Figure 5.7 RS versus various model-based volatility forecasts for SPDRs 73
Figure 5.8 RV versus various model-based volatility forecasts for SPDRs 74
Figure 5.9 Daily returns versus the EGARCH-based VaR forecasts at the 99% confidence level:The case of TAIFEX 80
Figure 5.10 Daily returns versus the RV-based VaR forecasts at the 99% confidence level:The case of SPDRs 80
Figure 5.11 Daily returns versus the EGARCH-based VaR forecasts at the 99.5% confidence level:The case of TAIFEX 85
Figure 5.12 Daily returns versus the RV-based VaR forecasts at the 99.5% confidence level:The case of SPDRs 85
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