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Renyi entropy and mutual information measurement of market expectations and investor fear during the COVID-19 pandemic

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  • Lahmiri, Salim
  • Bekiros, Stelios

Abstract

The COVID-19 pandemic has seriously affected world economies. In this regard, it is expected that information level and sharing between equity, digital currency, and energy markets has been altered due to the pandemic outbreak. Specifically, the resulting twisted risk among markets is presumed to rise during the abnormal state of world economy. The purpose of the current study is twofold. First, by using Renyi entropy, we analyze the multiscale entropy function in the return time series of Bitcoin, S&P500, WTI, Brent, Gas, Gold, Silver, and investor fear index represented by VIX. Second, by estimating mutual information, we analyze the information sharing between these markets. The analyses are conducted before and during the COVID-19 pandemic. The empirical results from Renyi entropy indicate that for all market indices, randomness and disorder are more concentrated in less probable events. The empirical results from mutual information showed that the information sharing network between markets has changed during the COVID-19 pandemic. From a managerial perspective, we conclude that during the pandemic (i) portfolios composed of Bitcoin and Silver, Bitcoin and WTI, Bitcoin and Gold, Bitcoin and Brent, or Bitcoin and S&P500 could be risky, (ii) diversification opportunities exist by investing in portfolios composed of Gas and Silver, Gold and Silver, Gold and Gas, Brent and Silver, Brent and Gold, or Bitcoin and Gas, and that (iii) the VIX exhibited the lowest level of information disorder at all scales before and during the pandemic. Thus, it seems that the pandemic has not influenced the expectations of investors. Our results provide an insight of the response of stocks, cryptocurrencies, energy, precious metal markets, to expectations of investors in the aftermath of the COVID-19 pandemic in terms of information ordering and sharing.

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  • Lahmiri, Salim & Bekiros, Stelios, 2020. "Renyi entropy and mutual information measurement of market expectations and investor fear during the COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304811
    DOI: 10.1016/j.chaos.2020.110084
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    References listed on IDEAS

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    1. Assaf, Ata & Bhandari, Avishek & Charif, Husni & Demir, Ender, 2022. "Multivariate long memory structure in the cryptocurrency market: The impact of COVID-19," International Review of Financial Analysis, Elsevier, vol. 82(C).
    2. Lahmiri, Salim & Bekiros, Stelios & Bezzina, Frank, 2022. "Evidence of the fractal market hypothesis in European industry sectors with the use of bootstrapped wavelet leaders singularity spectrum analysis," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    3. Assaf, Ata & Mokni, Khaled & Youssef, Manel, 2023. "COVID-19 and information flow between cryptocurrencies, and conventional financial assets," The Quarterly Review of Economics and Finance, Elsevier, vol. 89(C), pages 73-81.
    4. Choi, Insu & Kim, Woo Chang, 2024. "Practical forecasting of risk boundaries for industrial metals and critical minerals via statistical machine learning techniques," International Review of Financial Analysis, Elsevier, vol. 94(C).
    5. Alves, P.R.L., 2022. "Quantifying chaos in stock markets before and during COVID-19 pandemic from the phase space reconstruction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 480-499.
    6. Salim Lahmiri, 2025. "Wavelet Entropy for Efficiency Assessment of Price, Return, and Volatility of Brent and WTI During Extreme Events," Commodities, MDPI, vol. 4(2), pages 1-10, March.
    7. Sarit Maitra, 2023. "Impact of Economic Uncertainty, Geopolitical Risk, Pandemic, Financial & Macroeconomic Factors on Crude Oil Returns -- An Empirical Investigation," Papers 2310.01123, arXiv.org, revised Oct 2023.
    8. Lahmiri, Salim & Bekiros, Stelios, 2021. "The effect of COVID-19 on long memory in returns and volatility of cryptocurrency and stock markets," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    9. Xia, Yufei & Han, Zhiyin & Zheng, Qiong & Yang, Xiaoli, 2024. "The (in)effectiveness of financial consumer protection: Quasi-experimental evidence from consumer finance in China," Pacific-Basin Finance Journal, Elsevier, vol. 88(C).
    10. Daniel Stefan Armeanu & Stefan Cristian Gherghina & Jean Vasile Andrei & Camelia Catalina Joldes, 2023. "Evidence from the nonlinear autoregressive distributed lag model on the asymmetric influence of the first wave of the COVID-19 pandemic on energy markets," Energy & Environment, , vol. 34(5), pages 1433-1470, August.
    11. Ebenezer Boateng & Emmanuel Asafo-Adjei & John Gartchie Gatsi & ªtefan Cristian Gherghina & Liliana Nicoleta Simionescu, 2022. "Multifrequency-based non-linear approach to analyzing implied volatility transmission across global financial markets," Oeconomia Copernicana, Institute of Economic Research, vol. 13(3), pages 699-743, September.
    12. Caferra, Rocco, 2022. "Sentiment spillover and price dynamics: Information flow in the cryptocurrency and stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    13. Maghyereh, Aktham & Abdoh, Hussein & Awartani, Basel, 2022. "Have returns and volatilities for financial assets responded to implied volatility during the COVID-19 pandemic?," Journal of Commodity Markets, Elsevier, vol. 26(C).
    14. Ryuji Ishizaki & Masayoshi Inoue, 2024. "Short-term Kullback–Leibler divergence analysis to extract unstable periods in financial time series," Evolutionary and Institutional Economics Review, Springer, vol. 21(2), pages 227-236, September.
    15. Assaf, Ata & Mokni, Khaled & Yousaf, Imran & Bhandari, Avishek, 2023. "Long memory in the high frequency cryptocurrency markets using fractal connectivity analysis: The impact of COVID-19," Research in International Business and Finance, Elsevier, vol. 64(C).
    16. Moinak Maiti & Parthajit Kayal, 2022. "Asymmetric Information Flow between Exchange Rate, Oil, and Gold: New Evidence from Transfer Entropy Approach," JRFM, MDPI, vol. 16(1), pages 1-14, December.

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