Document Type : Research Article


1 Department of Mangement and Accounting, Allameh Tabataba’i University, Tehran, Iran

2 Faculty of Economics, University of Tehran, Tehran, Iran

3 Telfer School of Management, University of Ottawa, Ottawa, Canada

4 Department of Technology and Society, The State University of New York, Incheon, Republic of Korea

5 Azman Hashim International Business School, Universiti Teknologi Malaysia, Johor, Malaysia


In recent years, cryptocurrency has attracted more attention and is a new option in the economy and the financial sector. The purpose of this study is to the volatility and “herd behavior” of the cryptocurrency, gold, and stock markets in the US. This research is aimed at investor “herd behavior” and how it correlates with the volatility of three assets: the Standard & Poor's 500 indexes, Bitcoin, and gold. Also, A new formula by applying the conditional standard deviation (risk), maximum return, minimum return, and average return to quantify the herding bias is designed in this research. In this study, the generalized autoregressive conditional heteroscedasticity model (GARCH) and the autoregressive moving average model (ARMA) were both employed. Research results show that Bitcoin is 3.3 times as volatile as the S&P 500 and 4.6 times as volatile as gold. The results of this novel equation also show that the herding bias of Bitcoin is more than 26 times higher than the global average and 10 times higher than the S&P 500. Also, it’s important to consider the energy consumption and sustainability of investments when evaluating their long-term viability and risk. In some cases, investments in companies with strong sustainability practices and low carbon footprints may be seen as lower risk. Since Bitcoin relies on a network of computers to validate transactions based on proof of work and it is an energy consumption consensus mechanism, investment in Bitcoin may be seen as a higher risk.


[1] M. A. AbdElaal, Modeling and forecasting time varying stock return volatility in the Egyptian stock market, International Research Journal of Finance and Economics, 78.
[2] N. S. N. Ainia and L. Lutfi, The influence of risk perception, risk tolerance, overconfidence,
and loss aversion towards investment decision making, Journal of Economics, Business, &
Accountancy Ventura, 21(3), 401-413.
[3] T. Bollerslev, Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31(3), 307-327.
[4] S. Bogdan, S. Baresa, and S. Curcic, Diversification Benefits of Gold and Other Precious
Metals in an Investment Portfolio, ICAMSS19, 21.
[5] J. Cerovi Smolovi, M. Lipovina-Boovi, and S. Vujoevi, GARCH models in value at risk
estimation: empirical evidence from the Montenegrin stock exchange, Economic ResearchEkonomska Istraivanja, 30(1), 477-498.
[6] W. Coffie, G. Tackie, I. Bedi, and F. A. Otchere, Alternative Models for the Conditional
Heteroscedasticity and the Predictive Accuracy of Variance Models-Empirical Evidence from
East and North Africa Stock Markets, Journal of Accounting and Finance, 17(2), 100-116.
[7] K. Daniel, R. J. Hodrick, and Z. Lu, The carry trade: Risks and drawdowns, National
Bureau of Economic Research.
[8] P. Della Corte, A. Jeanneret, and E. Patelli, A credit-based theory of the currency
risk premium, Available at SSRN 3413785.
[9] P. Della Corte, L. Sarno, and I. Tsiakas, An economic evaluation of empirical exchange
rate models, The Review of Financial Studies, 22(9), 3491-3530.
[10] A. K. Dhamija and V. K. Bhalla, Financial time series forecasting: comparison of neural
networks and ARCH models, International Research Journal of Finance and Economics, 49,
[11] C. Dritsaki,An empirical evaluation in GARCH volatility modeling: Evidence from the
Stockholm stock exchange, Journal of Mathematical Finance, 7(2), 366-390.
[12] F. C. Drost and C. A. J. Klaassen, Efficient estimation in semiparametric GARCH
models, Journal of Econometrics, 81(1), 193-221.
[13] R. F. Engle and G. Gonzalez-Rivera, Semiparametric ARCH models, Journal of Business
& Economic Statistics, 9(4), 345-359.
[14] M. Farajnezhad, S. Ramakrishnan, and M. Shehni Karam Zadeh, Analyses the Effect
of Monetary Policy Transmission on the Inequality in OECD Countries, Journal of Environmental Treatment Techniques, Volume 8, Issue 2, Pages: 589-596.
[15] L. R. Glosten, R. Jagannathan, and D. Runkle, On the relationship between GARCH
and symmetric stable process: Finding the source of fat tails in data, Journal of Finance,
48(5), 1779-1802.
[16] Z.-Y. Guo, GARCH models with fat-tailed distributions and the Hong Kong stock market
[17] Z.-Y. Guo, Models with short-term variations and long-term dynamics in risk management
of commodity derivatives, ZBW-Leibniz Information Centre for Economics.
[18] P. Hall and Q. Yao, Inference in ARCH and GARCH models with heavy-tailed errors,
Econometrica, 71(1), 285-317.
[19] A. Intaz, D. Subhrabaran, and R. Niranjan, Stock market volatility, firm size, and returns: A study of automobile sector of National Stock Exchange in India, International
Journal of Innovative Research & Development, 5(4), 272-281.
[20] F. Kamalov, L. Smail, and I. Gurrib, Forecasting with deep learning: S&P 500 index,
In 2020 13th International Symposium on Computational Intelligence and Design (ISCID),
[21] N. A. Kyriazis, Herding behavior in digital currency markets: An integrated survey and
empirical estimation, Heliyon, 6(8), e04752.
[22] J. Kurka, Do cryptocurrencies and traditional asset classes influence each other?, Finance
Research Letters, 31, 38-46.
[23] S. Ling and M. McAleer, Asymptotic theory for a vector ARMA-GARCH model, Econometric Theory, 19(2), 280-310.
[24] O. Linton, Adaptive estimation in ARCH models, Econometric Theory, 9(4), 539-569.
[25] H.-C. Liu and J.-C. Hung, Forecasting S&P-100 stock index volatility: The role of volatility
asymmetry and distributional assumption in GARCH models, Expert Systems with Applications, 37(7), 4928-4934.
[26] M. Mehrara and S. Tajdini, Comparison of profitability of speculation in the foreign exchange market and investment in the Tehran Stock Exchange during Iran’s currency crisis
using conditional Sharpe ratio, Advances in Mathematical Finance and Applications, 5(3),
[27] D. B. Nelson and C. Q. Cao, Inequality constraints in the univariate GARCH model,
Journal of Business & Economic Statistics, 10(2), 229-235.
[28] A.-C. Petric and S. Stancu, Empirical Results of Modeling EUR/RON Exchange Rate
using ARCH, GARCH, EGARCH, TARCH, and PARCH models, Romanian Statistical Review, 1.
[29] F. Prado, M. C. Minutolo, and W. Kristjanpoller, Forecasting based on an ensemble
autoregressive moving average-adaptive neuro-fuzzy inference system-neural network-genetic
algorithm framework, Energy, 197, 117159.
[30] G. Spaargaren and A. P. Mol, Carbon flows, carbon markets, and low-carbon lifestyles:
reflecting on the role of markets in climate governance, Environmental Politics, 22(1), 174-
[31] S. Spyrou, Herding in financial markets: a review of the literature, Review of Behavioral
Finance, 5(2), 175-194.
[32] S. Tajdini, M. Mehrara, and R. Tehrani, Double-sided balanced conditional Sharpe ratio,Cogent Economics & Finance, 7(1), 1630931.
[33] S. Tajdini, M. Mehrara, and R. Tehrani, Hybrid Balanced Justified Treynor ratio,Managerial Finance.
[34] S. Tajdini, A. Hamooni, J. Maghsoudi, F. Jafari, and M. Lotfi Ghahroud, Trade War
and the Balanced Trade-Monetary Theory,Journal of Mathematics and Modeling in Finance,
1(2), 93-110.
[35] A. Talaiekhozani, M. Lotfi Ghahroud, and S. Rezania, Estimation of carbon monoxide,
sulfur oxides, nitrogen oxides, volatile organic compounds, and particulate matters emission
due to cryptocurrency miners activity in Iran,Earth, 2(3), 667-673.
[36] M. Youssef, What drives herding behavior in the cryptocurrency market?,Journal of Behavioral Finance, 23(2), 230-239.