# S&P 500 Index Price Spillovers around the COVID-19 Market Meltdown

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data

_{t}= ln(P

_{t}) − ln(P

_{t−1})) across each five-minute interval for seven asset classes (SPX, VIX, FX, OIL, GOLD, BTC, and TBILL) from 1 January 2020 to 12 May 2020, for a total of 7594 observations per asset class. The data are obtained from the Thomson Reuters Eikon terminal. We divided the data across three regime shifts during the 2020 market crash (Figure 1). The first period spans from 1 January–19 February, just before the 2020 market crash. We label this period the normal market regime. The second period spans from 20 February–23 March, representing the peak to trough of the 2020 market crash as measured by the SPX. We label this period as the market crash regime. The third period spans from 24 March–12 May, representing the recovery from the 2020 market crash trough. We label this period as the market recovery regime.

## 3. Methods

_{t}= [x

_{t}, y

_{t}]′ be a two-dimensional time series vector with t = 1, ..., T. It is assumed that z

_{t}has a finite-order VAR representation:

_{1}L − … − Θ

_{p}L

^{p}is a 2 × 2 lag polynomial with L

^{k}z

_{t}= z

_{t}

_{−k}. It is assumed that the vector ε

_{t}is white noise with E(ε

_{t}) = 0 and E(ε

_{t}ε

_{t}′) = ∑, where ∑ is a positive definite matrix. Next, let G be the lower triangular matrix of the Cholesky decomposition G′G = ∑

^{−1}, such that E(η

_{t}η

_{t}′) = I and η

_{t−}= Gε

_{t}. The system is assumed to be stationary, implying the following moving average representation:

_{t}can be expressed as:

_{1}, …, β

_{p}]’ and:

## 4. Empirical Results and Discussion

#### 4.1. Causality

#### 4.2. Determinants of Recovery

_{i}is the i

^{th}observation of the dependent variable, β

_{0}is an intercept, x

_{ij}is the i

^{th}observation of the j

^{th}explanatory variable, and β

_{j}is its corresponding coefficient, while ${\left|\right|\beta \left|\right|}_{1}$≡$\sum}_{j=1}^{p}\left|{\beta}_{j}\right|$ is the L1 norm and s is a tuning parameter. When s is relatively large enough, the constraint on β has no effect. The model becomes the standard least-squares regression. However, for smaller (but positive) values of s, the estimated parameters are shrunken versions of their least-squares counterparts, with some β

_{j}’s often equal to zero. A cross-validation (CV) method is typically used for estimating the optimal value for s (as well as for the parameter $\lambda $ below), and we will also follow this approach.

## 5. Conclusions, Limitations and Future Research

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Notes

1. | |

2. | For example, in an option pricing setting, Shafi et al. (2019) conclude that the S&P 500 index movements are negatively correlated with those of the VIX index. |

3. | For instance, a comprehensive discussion can be found in Næs et al. (2011). In short, investors trade stocks based upon their expectations of the future. Therefore, stock market activity may antcipate a market movement before the actual economy reacts. |

## References

- Al-Awadhi, Abdullah M., Khaled Alsaifi, Ahmad Al-Awadhi, and Salah Alhammadi. 2020. Death and contagious infectious diseases: Impact of the COVID-19 virus on stock market returns. Journal of Behavioral and Experimental Finance 27: 1–5. [Google Scholar] [CrossRef]
- Baig, Ahmed, Hassan Anjum Butt, Omair Haroon, and Syed Aun R. Rizvi. 2020. Deaths, panic, lockdowns and US equity markets: The case of COVID-19 pandemic. Finance Research Letters 38: 101701. [Google Scholar] [CrossRef]
- Billio, Monica, Mila Getmansky, Andrew W. Lo, and Loriana Pelizzon. 2012. Econometric measures of connectedness and systemic risk in the finance and insurance sectors. Journal of Financial Economics 104: 535–59. [Google Scholar] [CrossRef]
- Bing, Tao, and Hongkun Ma. 2021. COVID-19 pandemic effect on trading and returns: Evidence from the Chinese stock market. Economic Analysis and Policy 71: 384–96. [Google Scholar] [CrossRef]
- Breitung, Jorg, and Bertrand Candelon. 2006. Testing for short- and long-run causality: A frequency-domain approach. Journal of Econometrics 132: 363–78. [Google Scholar] [CrossRef]
- Corbet, Shaen, Yang Hou, Yang Hu, Brian Lucey, and Les Oxley. 2020. Aye corona! the contagion effects of being named corona during the covid-19 pandemic. Finance Research Letters 38: 101591. [Google Scholar] [CrossRef]
- Corbet, Shaen, Yang Hou, Yang Hu, Les Oxley, and Danyang Xu. 2021. Pandemic-related financial market volatility spillovers: Evidence from the Chinese covid-19 epicentre. International Review of Economics &. Finance 71: 55–81. [Google Scholar]
- Coronado, Semei, Rebeca Jiménez-Rodríguez, and Omar Rojas. 2017. An Empirical Analysis of the Relationships between Crude Oil, Gold and Stock Markets. The Energy Journal 39: 193–207. [Google Scholar] [CrossRef]
- Dai, Peng-Fei, Xiong Xiong, Zhifeng Liu, Toan Luu Duc Huynh, and Jianjun Sun. 2021. Preventing crash in stock market: The role of economic policy uncertainty during COVID-19. Financial Innovation 7: 1–15. [Google Scholar] [CrossRef]
- Demir, Ender, Mehmet Huseyin Bilgin, Gokhan Karabulut, and Asli Cansin Doker. 2020. The relationship between cryptocurrencies and COVID-19 pandemic. Eurasian Economic Review 10: 349–60. [Google Scholar] [CrossRef]
- Deng, Guichuan, Jing Shi, Yanli Li, and Yin Liao. 2021. The COVID-19 pandemic: Shocks to human capital and policy responses. Accounting and Finance. Available online: https://onlinelibrary.wiley.com/doi/10.1111/acfi.12770 (accessed on 28 April 2021).
- Duarte, Fernando, and Thomas Eisenbach. 2021. Fire-sale spillovers and systemic risk. Journal of Finance 76: 1251–94. [Google Scholar] [CrossRef]
- Friedman, Jerome, Trevor Hastie, Holger Hofling, and Robert Tibshirani. 2007. Pathwise coordinate optimization. The Annals of Applied Statistics 1: 302–32. [Google Scholar] [CrossRef][Green Version]
- Geweke, John. 1982. Measurement of linear dependence and feedback between multiple time series. Journal of the American Statistical Association 77: 304–24. [Google Scholar] [CrossRef]
- Granger, Clive W. J. 1969. Investigating causal relations by econometric models and cross-spectral methods. Econometrica: Journal of the Econometric Society 37: 424–38. [Google Scholar] [CrossRef]
- Granger, Clive W.J, Bwo-Nung Huangb, and Chin-Wei Yang. 2000. A bivariate causality between stock prices and exchange rates: Evidence from recent Asian flu. The Quarterly Review of Economics and Finance 40: 337–54. [Google Scholar] [CrossRef]
- Gu, Xin, Shan Ying, Weiqiang Zhang, and Yewei Tao. 2020. How do firms respond to COVID-19? First evidence from Suzhou, China. Emerging Markets Finance and Trade 56: 2181–97. [Google Scholar] [CrossRef]
- Gungoraydinoglu, Ali, Ilke Öztekin, and Özde Öztekin. 2021. The Impact of COVID-19 and Its Policy Responses on Local Economy and Health Conditions. Journal of Risk and Financial Management 14: 233. [Google Scholar] [CrossRef]
- Guo, Jin, and Tetsuji Tanaka. 2020. Dynamic Transmissions and Volatility Spillovers between Global Price and U.S. Producer Price in Agricultural Markets. Journal of Risk Financial Management 13: 83. [Google Scholar] [CrossRef]
- Guo, Hongfeng, Xinyao Zhao, Hang Yu, and Xin Zhang. 2021. Analysis of global stock markets’ connections with emphasis on the impact of COVID-19. Physica A: Statistical Mechanics and Its Applications 569: 125774. [Google Scholar] [CrossRef]
- Hastie, Trevor, Robert Tibshirani, and Jerome Friedman. 2009. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Series in Statistics. New York: Springer. [Google Scholar]
- Hastie, Trevor, Robert Tibshirani, and Martin Wainwright. 2015. Statistical Learning with Sparsity: The Lasso and Generalizations. Boca Raton: Chapman and Hall/CRC. [Google Scholar]
- Hoang, Thi Hong Van, and Qasim Raza Syed. 2021. Investor sentiment and volatility prediction of currencies and commodities during the COVID-19 pandemic. Asian Economics Letters, 1. [Google Scholar] [CrossRef]
- Hong, Yongmiao, Yanhui Liu, and Shouyang Wang. 2009. Granger causality in risk and detection of extreme risk spillover between financial markets. Journal of Econometrics 150: 271–87. [Google Scholar] [CrossRef][Green Version]
- Hosoya, Yuzo. 1991. The decomposition and measurement of the interdependence between second-order stationary process. Probability Theory and Related Fields 88: 429–44. [Google Scholar] [CrossRef]
- James, Nick. 2021. Dynamics, behaviours, and anomaly persistence in cryptocurrencies and equities surrounding COVID-19. Physica A: Statistical Mechanics and Its Applications 570: 125831. [Google Scholar] [CrossRef]
- Jiang, Yonghong, Gengyu Tian, and Bin Mo. 2020. Spillover and quantile linkage between oil price shocks and stock returns: New evidence from G7 countries. Financial Innovation 6: 1–26. [Google Scholar] [CrossRef]
- Keown, Callum. 2020. Gold and Stocks Have Been Moving Together for Weeks. Here’s What It Means. Barron’s. May 11. Available online: https://www.barrons.com/articles/gold-and-stocks-have-been-moving-together-for-weeks-heres-what-it-means-51589203866 (accessed on 20 June 2020).
- Kilian, Lutz, and Cheolbeom Park. 2009. The impact of oil price shocks on the U.S. stock market. International Economic Review 50: 1267–87. [Google Scholar] [CrossRef]
- Liu, Taixing, Beixiao Pan, and Zhichao Yin. 2020. Pandemic, mobile payment, and household consumption: Micro-evidence from China. Emerging Markets Finance and Trade 56: 2378–89. [Google Scholar] [CrossRef]
- Liu, Zhifeng, Toan Luu Duc Huynh, and Peng-Fei Dai. 2021. The impact of COVID-19 on the stock market crash risk in China. Research in International Business and Finance 57: 101419. [Google Scholar] [CrossRef]
- Maghyereh, Aktham, and Hussein Abdoh. 2020. Tail dependence between Bitcoin and financial assets: Evidence from a quantile cross-spectral approach. International Review of Financial Analysis 71: 101545. [Google Scholar] [CrossRef]
- Makin, Anthony J., and Allan Layton. 2021. The global fiscal response to COVID-19: Risks and repercussions. Economic Analysis and Policy 69: 340–49. [Google Scholar] [CrossRef]
- Marquez, Jaime, and Silvia Merler. 2020. A Note on the Empirical Relation between Oil Prices and the Value of the Dollar. Journal of Risk and Financial Management 13: 164. [Google Scholar] [CrossRef]
- McMillan, David G. 2020. Interrelation and spillover effects between stocks and bonds: Cross-market and cross-asset evidence. Studies in Economics and Finance 37: 561–82. [Google Scholar] [CrossRef]
- Mensi, Walid, Ferihane Zaraa Boubaker, Khamis Hamed Al-Yahyaee, and Sang Hoon Kang. 2018. Dynamic volatility spillovers and connectedness between global, regional, and GIPSI stock markets. Finance Research Letters 25: 230–38. [Google Scholar] [CrossRef]
- Næs, Randi, Johannes A. Skjeltorp, and Bernt Arne Ødegaard. 2011. Stock market liquidity and the business cycle. The Journal of Finance 66: 139–76. [Google Scholar] [CrossRef]
- Ortmann, Regina, Matthias Pelster, and Sascha Tobias Wengerek. 2020. COVID-19 and investor behavior. Finance Research Letters 37: 101717. [Google Scholar] [CrossRef]
- Padhan, Rakesh, and K. P. Prabheesh. 2021. The economics of COVID-19 pandemic: A survey. Economic Analysis and Policy 70: 220–37. [Google Scholar] [CrossRef] [PubMed]
- Park, June, and Eunbin Chung. 2021. Learning from past pandemic governance: Early response and public–Private partnerships in testing of COVID-19 in South Korea. World Development, 10. [Google Scholar] [CrossRef]
- Qin, Xiuhong, Guoliang Huang, Huayu Shen, and Mengyao Fu. 2020. COVID-19 pandemic and firm-level cash holding—Moderating effect of goodwill and goodwill impairment. Emerging Markets Finance and Trade 56: 2243–58. [Google Scholar] [CrossRef]
- Shafi, Khuram, Natasha Latif, Shafqat Ali Shad, and Zahra Idrees. 2019. High-frequency trading: Inverse relationship of the financial markets. Physica A: Statistical Mechanics and Its Applications 527: 121067. [Google Scholar] [CrossRef]
- Tisdell, Clement A. 2020. Economic, social and political issues raised by the COVID-19 pandemic. Economic Analysis and Policy 68: 17–28. [Google Scholar] [CrossRef]
- Xiong, Hao, Zuofeng Wu, Fei Hou, and RJun Zhang. 2020. Which firm-specific characteristics affect the market reaction of chinese listed companies to the COVID-19 pandemic? Emerging Markets Finance and Trade 56: 2231–42. [Google Scholar] [CrossRef]
- Xu, Liao, Jilong Chen, Xuan Zhang, and Jing Zhao. 2020. COVID-19, public attention and the stock market. Accounting and Finance. Available online: https://onlinelibrary.wiley.com/doi/full/10.1111/acfi.12734 (accessed on 1 May 2021).
- Yagi, Michiyuki, and Shunsuke Managi. 2021. Global supply constraints from the 2008 and COVID-19 crises. Economic Analysis and Policy 69: 514–28. [Google Scholar] [CrossRef]
- Zaremba, Adam, Renata Kizys, David Y. Aharon, and Ender Demir. 2020. Infected markets: Novel coronavirus, government interventions, and stock return volatility around the globe. Finance Research Letters 35: 1–7. [Google Scholar] [CrossRef] [PubMed]
- Zou, Hui. 2006. The adaptive lasso and its oracle properties. Journal of the American Statistical Association 101: 1418–29. [Google Scholar] [CrossRef][Green Version]

ΔSPX | ΔVIX | ΔFX | ΔOIL | ΔGOLD | ΔBTC | ΔTBILL | |
---|---|---|---|---|---|---|---|

Normal Market Regime | |||||||

Mean (×10^{−6}) | 9.210 | −97.90 | −2.470 | −29.50 | 7.800 | 71.00 | 0.168 |

Standard deviation (×10^{−4}) | 5.176 | 64.877 | 1.887 | 15.224 | 5.043 | 18.224 | 0.480 |

Median (×10^{−6}) | 27.00 | 0.000 | 0.000 | 0.000 | 11.50 | 51.70 | 0.000 |

Skewness | −0.266 | 0.320 | 0.305 | 0.067 | −0.588 | −0.269 | 0.010 |

Kurtosis | 5.100 | 7.627 | 8.556 | 7.209 | 16.530 | 13.905 | 2.864 |

Market Crash Regime | |||||||

Mean (×10^{−6}) | −3.840 | 267.70 | −3.440 | −162.10 | −30.50 | −14.10 | 0.623 |

Standard deviation (×10^{−4}) | 39.286 | 163.123 | 6.526 | 60.548 | 16.832 | 51.075 | 0.622 |

Median (×10^{−6}) | −183.70 | 583.00 | 0.000 | −198.90 | −1.610 | 29.40 | 0.000 |

Skewness | 0.525 | −0.668 | −0.157 | −0.174 | −0.140 | 0.389 | −0.598 |

Kurtosis | 6.569 | 13.178 | 8.974 | 26.917 | 7.249 | 20.609 | 11.879 |

Market Recovery Regime | |||||||

Mean (×10^{−6}) | 51.50 | −155.80 | 11.90 | 88.60 | 21.90 | 79.10 | −0.612 |

Standard deviation (×10^{−4}) | 19.155 | 63.263 | 4.465 | 1187.191 | 11.236 | 28.053 | 0.544 |

Median (×10^{−6}) | 85.50 | −307.30 | 0.000 | 0.000 | 51.20 | 82.70 | 0.000 |

Skewness | 0.280 | 0.330 | 0.746 | −23.636 | −0.352 | 0.420 | −0.131 |

Kurtosis | 10.041 | 4.843 | 9.422 | 1125.328 | 6.592 | 43.722 | 3.163 |

Normal Market Regime (1 January–19 February 2020) | Market Crash Regime (20 February–23 March 2020) | Market Recovery Regime (24 March–12 May 2020) | ||||
---|---|---|---|---|---|---|

Null Hypothesis | χ^{2} Statistic | Prob > χ^{2} | χ^{2} Statistic | Prob > χ^{2} | χ^{2} Statistic | Prob > χ^{2} |

ΔSPX does not cause ΔVIX at frequency ω | For ω > 1.9 | Reject | For all ω ∈ (0, π) | Reject | For ω < 1.3 | Reject |

ΔVIX does not cause ΔSPX at frequency ω | For all ω ∈ (0, π) | Do not reject | For ω < 1.5 | Reject | For all ω ∈ (0, π) | Do not reject |

ΔSPX does not cause ΔFX at frequency ω | For all ω ∈ (0, π) | Do not reject | For ω > 2.8 | Reject | For all ω ∈ (0, π) | Do not reject |

ΔFX does not cause ΔSPX at frequency ω | For all ω ∈ (0, π) | Do not reject | For all ω ∈ (0, π) | Do not reject | For all ω ∈ (0, π) | Do not reject |

ΔSPX does not cause ΔOIL at frequency ω | For ω < 0.3, 1.7 < ω < 2.0, 2.2 < ω < 2.3 | Reject | For all ω ∈ (0, π) | Do not reject | For all ω ∈ (0, π) | Do not reject |

ΔOIL does not cause ΔSPX at frequency ω | For all ω ∈ (0, π) | Do not reject | For ω < 0.1, 0.5 < ω < 0.6, 1.8 < ω < 1.9, 2.3 < ω < 2.5, 2.9 < ω < 3.0 | Reject | For 1.4 < ω < 1.5 | Reject |

ΔSPX does not cause ΔGOLD at frequency ω | For 1.1 < ω < 1.4 | Reject | For ω < 0.3, 0.6 < ω < 0.9, 2.3 < ω < 2.4, ω > 2.9 | Reject | For 2.2 < ω < 2.5 | Reject |

ΔGOLD does not cause ΔSPX at frequency ω | For all ω ∈ (0, π) | Do not reject | For ω > 2.6 | Reject | For 0.9 < ω < 1.1 | Reject |

ΔSPX does not cause ΔBTC at frequency ω | For all ω ∈ (0, π) | Do not reject | For 0.9 < ω < 2.2 | Reject | For all ω ∈ (0, π) | Do not reject |

ΔBTC does not cause ΔSPX at frequency ω | For all ω ∈ (0, π) | Do not reject | For all ω ∈ (0, π) | Reject | For all ω ∈ (0, π) | Reject |

ΔSPX does not cause ΔTBILL at frequency ω | For 2.4 < ω < 2.5, ω > 3.0 | Reject | For 1.2 < ω < 1.5, ω > 2.7 | Reject | For all ω ∈ (0, π) | Do not reject |

ΔTBILL does not cause ΔSPX at frequency ω | For all ω ∈ (0, π) | Do not reject | For all ω ∈ (0, π) | Do not reject | For ω < 0.9, 1.5 < ω < 1.7 | Reject |

LASSO | Adaptive LASSO | |||
---|---|---|---|---|

Rank | Variable | Coefficient | Variable | Coefficient |

1 | ΔVIX | −0.9169 | ΔVIX | −0.9289 |

2 | ΔFX | 0.0584 | ΔFX | 0.0655 |

3 | ΔGOLD | 0.0557 | ΔGOLD | 0.0628 |

4 | ΔTBILL | 0.0178 | ΔTBILL | 0.0234 |

5 | ΔBTC | 0.0000 | ΔBTC | 0.0000 |

6 | ΔOIL | 0.0000 | ΔOIL | 0.0000 |

R^{2} | 0.6273 | 0.6272 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lento, C.; Gradojevic, N. S&P 500 Index Price Spillovers around the COVID-19 Market Meltdown. *J. Risk Financial Manag.* **2021**, *14*, 330.
https://doi.org/10.3390/jrfm14070330

**AMA Style**

Lento C, Gradojevic N. S&P 500 Index Price Spillovers around the COVID-19 Market Meltdown. *Journal of Risk and Financial Management*. 2021; 14(7):330.
https://doi.org/10.3390/jrfm14070330

**Chicago/Turabian Style**

Lento, Camillo, and Nikola Gradojevic. 2021. "S&P 500 Index Price Spillovers around the COVID-19 Market Meltdown" *Journal of Risk and Financial Management* 14, no. 7: 330.
https://doi.org/10.3390/jrfm14070330