| Literature DB >> 32837374 |
Khurram Shehzad1, Liu Xiaoxing1, Hayfa Kazouz2.
Abstract
This investigation employed the Asymmetric Power GARCH model and found that COVID-19 substantially harms the US and Japan's market returns. Moreover, COVID-19 has influenced the variance of the US, Germany, and Italy's stock markets more than the Global Financial Crises (GFC). However, GFC indicated a more significant impact on the financial volatility of the Nikkei 225 index and SSEC than COVID-19. The study confirmed the leverage effect for the S&P 500, Nasdaq Composite Index, DAX 30, Nikkei 225, FTSE MIB, and SSEC. The analysis authenticated that the health crisis that befell due to COVID-19 have imperatively originated the financial crisis globally; however, the Asian markets still make available better prospects for portfolio optimization.Entities:
Keywords: APGARCH model; COVID-19; Financial markets; Global Financial Crises; Leverage effect
Year: 2020 PMID: 32837374 PMCID: PMC7318935 DOI: 10.1016/j.frl.2020.101669
Source DB: PubMed Journal: Financ Res Lett ISSN: 1544-6131
Fig. 1Decline in stock market values due to COVID-19
Data source: Statista.com.
Nested ARCH and GARCH model limitations.
| Approach | Αi | χi | βi | |
|---|---|---|---|---|
| ARCH | independent | 0 | 0 | 2 |
| GARCH | independent | 0 | independent | 2 |
| GJR GARCH | αi(1+χi)2 | 4αiχi | 0 | 2 |
| GJR ARCH | αi(1+χi)2 | 4αiχi | independent | 2 |
| TARCH | independent | |χ|≤1 | 0 | 1 |
| Taylor ARCH | independent | 0 | 0 | 1 |
| Taylor GARCH | independent | 0 | independent | 1 |
| NARCH | independent | 0 | 0 | independent |
| Generalized TARCH | independent | |χ|≤1 | independent | 1 |
| Asymmetric ARCH | independent | |χ|≤1 | 0 | 2 |
| Asymmetric GARCH | independent | |χ|≤1 | independent | 2 |
| PGARCH | independent | 0 | independent | independent |
| APGARCH | independent | |χ|≤1 | independent | independent |
Summary statistics of stock returns.
| NKR | FMBR | SCR | NSR | SPR | DXR | |
|---|---|---|---|---|---|---|
| Mean | -0.313724 | -0.402455 | -0.147617 | -0.215405 | -0.147623 | -0.51546 |
| Std. Dev. | 2.445463 | 3.453028 | 1.769321 | 3.626117 | 2.977544 | 2.925632 |
| Skewness | 0.505023 | -2.31595 | -1.558152 | -0.510258 | -0.556915 | -0.875228 |
| Kurtosis | 4.942365 | 14.04434 | 8.030458 | 5.449286 | 7.903214 | 9.651646 |
| Jarque-Bera | 12.78127 | 424.3192 | 90.4602 | 19.36125 | 106.3956 | 130.0984 |
| Probability | 0.001677 | 0 | 0 | 0.000062 | 0 | 0 |
Unit root and Heteroskedasticity test
| ADF | PP | ARCH-LM | |||
|---|---|---|---|---|---|
| Variable | Level | 1st Diff. | Level | 1st Diff. | F-statistics |
| SPR | -66.03021*** | -22.63017*** | -66.25453*** | -828.5502*** | 426.7328*** |
| NSR | -64.45909*** | -64.63904*** | -65.08732*** | -816.2465*** | 466.3889*** |
| DXR | -56.48601*** | -22.39084*** | -56.48463*** | -785.2905*** | 48.2608*** |
| NKR | 44.8633*** | 21.9552*** | -53.6732*** | -721.3891*** | 329.7114*** |
| FMBR | -59.11521*** | -26.05068*** | -59.1209*** | -810.3178*** | 80.99362*** |
| SCR | -54.81653*** | -23.65203*** | -54.84421*** | -521.7985*** | 109.9907*** |
Note: *, **, and *** denotes the 10%, 5%, and 1% level of significance, respectively. Source: author's calculation.
Results of mean equation.
| Variable | Coefficient | Std. Err | Z-Statistics | Prob. |
|---|---|---|---|---|
| SPR | ||||
| ξ1 | -0.074166 | 0.051206 | -1.448404 | 0.1475 |
| ξ2 | -0.033553 | 0.03892 | 8.625601 | 0.0000 |
| ξ3 | 0.024108 | 0.031249 | 0.771508 | 0.4404 |
| ξ0 | 0.046116 | 0.013268 | 3.475718 | 0.0005 |
| NSR | ||||
| ξ1 | -0.07019 | 0.057106 | -2.91165 | 0.0359 |
| ξ2 | 0.068919 | 0.049588 | 1.389834 | 0.1646 |
| ξ3 | 0.029659 | 0.059823 | 0.49578 | 0.62 |
| ξ0 | 0.071684 | 0.016054 | 4.465119 | 00000 |
| DXR | ||||
| ξ1 | -0.074194 | 0.053305 | -1.391876 | 0.164 |
| ξ2 | 0.003962 | 0.05155 | 0.076855 | 0.9387 |
| ξ0 | 0.043952 | 0.017596 | 2.497806 | 0.0125 |
| NKR | ||||
| ξ1 | -0.105667 | 0.059912 | -1.763687 | 0.0778 |
| ξ2 | -0.046816 | 0.054285 | -0.862421 | 0.3885 |
| ξ0 | 0.052843 | 0.019775 | 2.672166 | 0.0075 |
| FMBR | ||||
| ξ1 | -0.114119 | 0.057484 | -1.985253 | 0.0471 |
| ξ2 | 0.017097 | 0.129362 | 0.132167 | 0.8949 |
| ξ0 | 0.017786 | 0.022873 | 0.777598 | 0.4368 |
| SCR | ||||
| ξ1 | 0.159696 | 0.081796 | 1.952361 | 0.0509 |
| ξ2 | 0.088564 | 0.093508 | 9.471250 | 0.0000 |
| ξ3 | -0.031935 | 0.049069 | -0.650818 | 0.5152 |
| ξ0 | 0.034007 | 0.02037 | 1.669487 | 0.095 |
Results of variance equation.
| Variable | Coefficient | Std. Err | Z-Statistics | Prob. |
|---|---|---|---|---|
| SPR | ||||
| ϑ0 | 0.037938 | 0.004409 | 8.604057 | 0 |
| α | 0.138593 | 0.01163 | 11.91649 | 0 |
| χ | 0.994209 | 0.069184 | 14.3704 | 0 |
| β | 0.861692 | 0.011788 | 73.09983 | 0 |
| Φ1 | 0.036573 | 0.009111 | 4.014814 | 0.0001 |
| Φ2 | 0.000766 | 0.006152 | 1.448201 | 0.0737 |
| Φ3 | -0.000543 | 0.005079 | -0.10683 | 0.9149 |
| 0.869052 | 0.098541 | 8.819156 | 0 | |
| Γ | 6.44113 | 0.707081 | 9.109459 | 0 |
| NSR | ||||
| ϑ0 | 0.049766 | 0.005443 | 9.142806 | 0 |
| α | 0.124476 | 0.008233 | 15.11968 | 0 |
| χ | 0.999998 | 0000000 | 4800000 | 0 |
| β | 0.861615 | 0.010638 | 80.99348 | 0 |
| Φ1 | 0.03738 | 0.009882 | 3.782666 | 0.0002 |
| Φ2 | 0.003984 | 0.007429 | 0.53633 | 0.5917 |
| Φ3 | 0.006086 | 0.00959 | 0.634627 | 0.5257 |
| 0.897292 | 0.095359 | 9.409617 | 0 | |
| Γ | 7.359537 | 0.910916 | 8.079272 | 0 |
| DXR | ||||
| ϑ0 | 0.034172 | 0.005377 | 6.355084 | 0 |
| α | 0.073512 | 0.008658 | 8.490796 | 0 |
| χ | 0.997048 | 0.084556 | 11.79154 | 0 |
| β | 0.922762 | 0.009217 | 100.1114 | 0 |
| Φ1 | 0.008138 | 0.004861 | 1.674201 | 0.0941 |
| Φ2 | 0.008571 | 0.010051 | 0.852748 | 0.3938 |
| 0.879833 | 0.134396 | 6.546564 | 0 | |
| Γ | 8.037546 | 0.937191 | 8.576207 | 0 |
| NKR | ||||
| ϑ0 | 0.05136 | 0.006832 | 7.518056 | 0 |
| α | 0.104771 | 0.010673 | 9.816201 | 0 |
| χ | 0.883281 | 0.081964 | 10.77651 | 0 |
| β | 0.883054 | 0.011243 | 78.54085 | 0 |
| Φ1 | 0.023895 | 0.007921 | 3.016814 | 0.0026 |
| Φ2 | -0.003074 | 0.006092 | -0.504632 | 0.6138 |
| 0.864164 | 0.111283 | 7.765457 | 0 | |
| Γ | 6.600645 | 0.658709 | 10.02058 | 0 |
| FMBR | ||||
| ϑ0 | 0.0346 | 0.004874 | 7.098794 | 0 |
| α | 0.090903 | 0.007194 | 12.63516 | 0 |
| χ | 0.999987 | 0.000001 | 4800000 | 0 |
| β | 0.898316 | 0.009178 | 97.87958 | 0 |
| Φ1 | 0.01981 | 0.00834 | 2.37527 | 0.0175 |
| Φ2 | 0.001447 | 0.006227 | -2.32424 | 0.0100 |
| 1.064429 | 0.118983 | 8.946031 | 0 | |
| Γ | 6.246663 | 0.689603 | 9.058344 | 0 |
| SCR | ||||
| ϑ0 | 0.011564 | 0.003894 | 2.969629 | 0.003 |
| α | 0.067482 | 0.009789 | 6.893807 | 0 |
| χ | 0.13211 | 0.069902 | 1.889922 | 0.0588 |
| β | 0.938788 | 0.007753 | 121.0913 | 0 |
| Φ1 | 0.024274 | 0.016066 | 1.510895 | 0.1308 |
| Φ2 | 0.000971 | 0.008832 | 10.99064 | 0.0000 |
| Φ3 | 0.003074 | 0.005022 | 0.612173 | 0.5404 |
| 1.382652 | 0.265928 | 5.199348 | 0 | |
| Γ | 4.475004 | 0.405198 | 11.04399 | 0 |
Fig. 2Conditional variance plots of each stock market.
Diagnostic parameters.
| Serial Correlation | Heteroskedasticity | |||
|---|---|---|---|---|
| Variables | Q statistics | |||
| SPR | 33.071 | 0.609 | 2.127126 | 0.1448 |
| NSR | 42.096 | 0.224 | 2.238769 | 0.1067 |
| DXR | 46.167 | 0.119 | 2.275491 | 0.1315 |
| NKR | 28.143 | 0.822 | 0.531143 | 0.4662 |
| FMBR | 37.113 | 0.417 | 0.117112 | 0.7322 |
| SCR | 44.462 | 0.157 | 1.353077 | 0.2448 |