# Bitcoin as an Investment and Hedge Alternative. A DCC MGARCH Model Analysis

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Proto-Money

#### 2.2. Bitcoin

#### 2.3. Adoption History

#### 2.4. Austrian Economics

#### 2.5. Keynesian Economics

#### 2.6. Electricity Usage and Scaling

#### 2.7. Bitcoin and Traditional Assets as a Hedge Tool

## 3. COVID19 and the Future

#### 3.1. Stores of Value

#### 3.2. Debt, Modern Monetary Theory and Bitcoin

#### 3.3. United States Dollar (USD), Gold and the Future

## 4. Data and Methodology

#### 4.1. Data

#### 4.2. Models Autoregressive Conditional Heteroskedasticity (ARCH) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH)

#### 4.3. Model Used: Dynamic Conditional Correlation (DCC)-GARCH and r

- ${r}_{t}=$ n × 1 vector log returns of n assets at time t.
- ${\alpha}_{t}$ = n × 1 vector of mean corrected returns of n assets at time t, i.e., E [${\alpha}_{t}$] = 0.
- ${\mu}_{t}$ = n × 1 vector of the expected value of the conditional ${r}_{t}$.
- ${H}_{t}=$ n × n matrix of conditional variances of ${\alpha}_{t}$ at time t.
- ${H}_{t}^{1/2}=$ any n × n matrix at time t such that ${H}_{t}$ is the conditional variance matrix of ${\alpha}_{t}.$
- ${H}_{t}^{1/2}$ may be obtained by a Cholesky factorization of ${H}_{t}$.
- ${D}_{t}$ = n × n diagonal matrix of conditional standard deviations of ${\alpha}_{t}$ at time t.
- ${R}_{t}$ = n × n conditional correlation matrix of ${\alpha}_{t}$ at time t.
- ${Z}_{t}$ = n × 1 vector of iid errors such that E [${Z}_{t}$] = 0 and E [${Z}_{t}{Z}_{t}^{T}$] = I.

- (1)
- ${H}_{t}$ has to be positive definite as it is a covariance matrix. To ensure ${H}_{t}$ will be a positive definite, ${R}_{t}$ has to be positive definite (${D}_{t}$ is positive definite since all the diagonal elements are positive).
- (2)
- All the elements in the correlation matrix ${R}_{t}$ have to be equal or less than 1 by definition.

## 5. Expectations

#### Returns, Volatility, Correlation

## 6. Results

#### 6.1. Volume Results

#### 6.2. DCC-GARCH Model

- AR1 = coefficient of the mean model.
- alpha1 = coefficient to the squared residuals.
- beta1 = coefficient to the lagged variance.

#### 6.3. Interpretation

#### 6.4. Correlation Interpretation

- Black = Last realised correlations.
- Orange = Forecasted correlation.

#### 6.5. Individual Assets

- Green = Last estimated conditional variance.
- Orange = Forecast of conditional variance.
- Black = Squared residuals of the last 20 observations.
- Sigma Volatility forecasts (10 periods).

#### 6.6. Interpretation of Individual Figures

## 7. Summary of Results

## 8. Conclusions, Limitations and Recommendations

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Acharya, Sunayan, and Jessica Dunn. 2014. Overstock. com ventures into digital currencies. Journal of Business Cases and Applications 12: 1. [Google Scholar]
- Amadeo, Kimberly, and J. Michael Boyle. 2020. US national debt by year compared to GDP and major events. The Balance 1: 1. Available online: https://www.thebalance.com/national-debt-by-year-compared-to-gdp-and-major-events-3306287 (accessed on 10 August 2021).
- Andersen, Torben G., and Tim Bollerslev. 1988. Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. International Economic Review 39: 885–905. [Google Scholar] [CrossRef]
- Andersson-Säll, Tim, and Johan Lindskog. 2019. A Study on the DCC Garch Model’s Forecasting Ability with value at risk applications on the Scandinavian foreign exchange market. Available online: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-375201 (accessed on 8 July 2021).
- Antonakakis, Nikolaos, and Julia Darby. 2013. Forecasting volatility in developing countries’ nominal exchange returns. Applied Financial Economics 23: 1675–91. [Google Scholar] [CrossRef]
- Alotaibi, Sara Jeza. 2021. Using Blockchain for Smart Contracts. In Innovative and Agile Contracting for Digital Transformation and Industry IGI Global 4: 208–221. [Google Scholar]
- Bauwens, Luc, Sébastien Laurent, and Jeroen VK Rombouts. 2006. Multivariate GARCH models: A survey. Journal of Applied Econometrics 21: 79–109. [Google Scholar] [CrossRef] [Green Version]
- Bianchi, Daniele, Luca Rossini, and Matteo Iacopini. 2020. Stablecoins and cryptocurrency returns: Evidence from large bayesian vars. SSRN. [Google Scholar] [CrossRef]
- Bohte, Rick, and Luca Rossini. 2019. Comparing the forecasting of cryptocurrencies by bayesian time-varying volatility models. Journal of Risk and Financial Management 12: 150. [Google Scholar] [CrossRef] [Green Version]
- Borradaile, Glencora. 2021. Defend Dissent. Corvallis: Oregon State University. [Google Scholar]
- Bouri, Elie, Peter Molnár, Georges Azzi, David Roubaud, and Lars Ivar Hagfors. 2017. On the hedge and safe haven properties of Bitcoin: Is it really more than a diversifier? Finance Research Letters 20: 192–98. [Google Scholar] [CrossRef]
- Bouri, Elie, Syed Jawad Hussain Shahzad, David Roubaud, Ladislav Kristoufek, and Brian Lucey. 2020. Bitcoin, gold, and commodities as safe havens for stocks: New insight through wavelet analysis. The Quarterly Review of Economics and Finance 77: 156–64. [Google Scholar] [CrossRef]
- Boyapati, Vijay. 2018. The Bullish Case for Bitcoin. Available online: https://vijayboyapati.medium.com/the-bullish-case-for-bitcoin-6ecc8bdecc1 (accessed on 3 July 2021).
- Breedlove, Robert. 2019. An Open Letter to Ray Dalio: Bitcoin. Available online: https://breedlove22.medium.com/an-open-letter-to-ray-dalio-re-bitcoin-4b07c52a1a98 (accessed on 7 July 2021).
- Brownlees, Christian T., Robert F. Engle, and Bryan T. Kelly. 2011. A practical guide to volatility forecasting through calm and storm. SSRN. [Google Scholar] [CrossRef] [Green Version]
- Catania, Leopoldo, Stefano Grassi, and Francesco Ravazzolo. 2019. Forecasting cryptocurrencies under model and parameter instability. International Journal of Forecasting 35: 485–501. [Google Scholar] [CrossRef]
- Cermak, Vavrinec. 2017. Can bitcoin become a viable alternative to fiat currencies? An empirical analysis of bitcoin’s volatility based on a GARCH model. In An Empirical Analysis of Bitcoin’s Volatility Based on a GARCH Model. New York: Skidmore College. [Google Scholar]
- Chen, Weili, Jun Wu, Zibin Zheng, Chuan Chen, and Yuren Zhou. 2019. Market manipulation of bitcoin: Evidence from mining the Mt. Gox transaction network. Paper presented at IEEE INFOCOM 2019-IEEE Conference on Computer Communications, Paris, France, April 29–May 2; pp. 964–72. [Google Scholar]
- Clegg, Alastair G. 2014. Could Bitcoin Be a Financial Solution for Developing Economies. Birmingham: University of Birmingham, vol. 1, pp. 2013–14. [Google Scholar]
- Connors, Louisa, and William Mitchell. 2017. Framing modern monetary theory. Journal of Post Keynesian Economics 40: 239–59. [Google Scholar] [CrossRef]
- Corbet, Shaen, Brian Lucey, Andrew Urquhart, and Larisa Yarovaya. 2019. Cryptocurrencies as a financial asset: A systematic analysis. International Review of Financial Analysis 62: 182–99. [Google Scholar] [CrossRef] [Green Version]
- Cuñado, Jorge Hernando, Jorge Colvin Díez, and Javier Antonio Enríquez Román. 2020. Engie: Business Model Transformation. Harvard Deusto Business Research 9: 152–67. [Google Scholar] [CrossRef]
- Datta, Anwitaman, Sonja Buchegger, Le-Hung Vu, Thorsten Strufe, and Krzysztof Rzadca. 2010. Decentralized online social networks. In Handbook of Social Network Technologies and Applications. Boston: Springer, pp. 349–78. [Google Scholar]
- Davidson, Laura, and Walter E. Block. 2015. Bitcoin, the Regression Theorem, and the emergence of a new medium of exchange. Quarterly Journal of Austrian Economics 18: 311. [Google Scholar]
- De Grauwe, Paul. 1988. Exchange rate variability and the slowdown in growth of international trade. Staff Papers 35: 63–84. [Google Scholar] [CrossRef]
- Dutta, Anupam, Debojyoti Das, R. K. Jana, and Xuan Vinh Vo. 2020. COVID-19 and oil market crash: Revisiting the safe haven property of gold and Bitcoin. Resources Policy 69: 101816. Available online: https://www.sciencedirect.com/science/article/abs/pii/S0301420720308485 (accessed on 10 August 2021). [CrossRef]
- Dyhrberg, Anne Haubo. 2016a. Bitcoin, gold and the dollar–A GARCH volatility analysis. Finance Research Letters 16: 85–92. [Google Scholar] [CrossRef] [Green Version]
- Dyhrberg, Anne Haubo. 2016b. Hedging capabilities of bitcoin. Is it the virtual gold? Finance Research Letters 16: 139–44. [Google Scholar] [CrossRef] [Green Version]
- Elliott, Colin P. 2015. The Crisis of AD 33: Past and present. Journal of Ancient History 3: 267–81. [Google Scholar] [CrossRef]
- Engel, Charles, and Kenneth D. West. 2005. Exchange rates and fundamentals. Journal of Political Economy 113: 485–517. [Google Scholar] [CrossRef] [Green Version]
- Engle, Robert F. 1982. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the Econometric Society, 987–1007. [Google Scholar] [CrossRef]
- Engle, Robert. 2002. Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business & Economic Statistics 20: 339–50. [Google Scholar]
- Frino, Alex, Steven Lecce, and Reuben Segara. 2011. The impact of trading halts on liquidity and price volatility: Evidence from the Australian Stock Exchange. Pacific-Basin Finance Journal 19: 298–307. [Google Scholar] [CrossRef]
- Fröhlich, Michael, Maurizio Raphael Wagenhaus, Albrecht Schmidt, and Florian Alt. 2021. Don’t Stop Me Now! Exploring Challenges of First-Time Cryptocurrency Users. Paper presented at Designing Interactive Systems Conference, Online, June 21–July 1; pp. 138–48. [Google Scholar]
- Fukami, Aya, Radina Stoykova, and Zeno Geradts. 2021. A new model for forensic data extraction from encrypted mobile devices. Forensic Science International: Digital Investigation 38: 301169. [Google Scholar]
- Garman, Mark B., and Michael J. Klass. 1980. On the estimation of security price volatilities from historical data. Journal of business 53: 67–78. [Google Scholar] [CrossRef]
- Ghalanos, Alexios. 2019. The RMGARCH Models: Background and Properties. Version 1.3–0. Available online: https://mran.microsoft.com (accessed on 19 June 2021).
- Griffin, John M., and Amin Shams. 2020. Is Bitcoin really untethered? The Journal of Finance 75: 1913–64. [Google Scholar] [CrossRef]
- Grinberg, Reuben. 2011. Bitcoin: An innovative alternative digital currency. Hastings Science & Technology Law Journal 4: 160. [Google Scholar]
- Gronwald, Marc. 2014. The Economics of Bitcoins—Market Characteristics and Price Jumps. Available online: https://ssrn.com/abstract=2548999 (accessed on 2 June 2021).
- Hansen, Peter R., and Asger Lunde. 2005. A forecast comparison of volatility models: Does anything beat a GARCH (1, 1)? Journal of Applied Econometrics 20: 873–89. [Google Scholar] [CrossRef] [Green Version]
- Hatemi-J., Abdulnasser, Mohamed A. Hajji, Elie Bouri, and Rangan Gupta. 2019. The Benefits of Diversification between Bitcoin, Bonds, Equities and the US Dollar: A Matter of Portfolio Construction. No. 201959. Pretoria: University of Pretoria. [Google Scholar]
- Hayek, Friedrich August. 1976. Choice in Currency: A Way to Stop Inflation. Auburn: Ludwig von Mises Institute. [Google Scholar]
- Hossain, Md Jamal, Mohd Tahir Ismail, Sadia Akter, and Mohammad Raquibul Hossain. 2020. Which will serve better as a hedge or diversifier Gold or Bitcoin? Paper presented at 2020 International Conference on Decision Aid Sciences and Application (DASA), Online, November 8–9; pp. 1052–55. [Google Scholar]
- Jareño, Francisco, María de la O González, Marta Tolentino, and Karen Sierra. 2020. Bitcoin and gold price returns: A quantile regression and NARDL analysis. Resources Policy 67: 101666. [Google Scholar] [CrossRef]
- Jiang, Yonghong, Jiayi Lie, Jieru Wang, and Jinqi Mu. 2021. Revisiting the roles of cryptocurrencies in stock markets: A quantile coherency perspective. Economic Modelling 95: 21–34. [Google Scholar] [CrossRef]
- Jones, Paul, and Lorenzo Giorgianni. 2020. The Great Monetary Inflation. Market Outlook—Macro Perspective. Available online: coinvertit.com (accessed on 15 May 2021).
- Kelly, Brian. 2014. The Bitcoin Big Bang: How Alternative Currencies Are about to Change the World. Hoboken: John Wiley & Sons. [Google Scholar]
- Kim, Jung. 2021. Most Traded National Currencies for Bitcoin. Coinhills. Available online: https://www.coinhills.com/market/currency/ (accessed on 13 March 2021).
- Klein, Tony, Hien Pham Thu, and Thomas Walther. 2018. Bitcoin is not the New Gold–A comparison of volatility, correlation, and portfolio performance. International Review of Financial Analysis 59: 105–16. [Google Scholar] [CrossRef]
- Kliber, Agata, Paweł Marszałek, Ida Musiałkowska, and Katarzyna Świerczyńska. 2019. Bitcoin: Safe haven, hedge or diversifier? Perception of bitcoin in the context of a country’s economic situation—A stochastic volatility approach. Physica A: Statistical Mechanics and Its Applications 524: 246–57. [Google Scholar] [CrossRef]
- Knafo, Samuel. 2006. The gold standard and the origins of the modern international monetary system. Review of International Political Economy 13: 78–102. [Google Scholar] [CrossRef]
- Küfeoglu, Sinan, and Mahmut Özkuran. 2019. Energy Consumption of Bitcoin Mining. Available online: repository.cam.ac.uk (accessed on 2 July 2021).
- Kurtz, Marcus J., and Andrew Schrank. 2007. Growth and governance: Models, measures, and mechanisms. The Journal of Politics 69: 538–54. [Google Scholar] [CrossRef]
- Lamport, Leslie, Robert Shostak, and Marshall Pease. 2019. The Byzantine generals problem. Concurrency: The Works of Leslie Lamport 1: 203–26. [Google Scholar]
- Laurent, Sébastien, Jeroen V.K. Rombouts, and Francesco Violante. 2012. On the forecasting accuracy of multivariate GARCH models. Journal of Applied Econometrics 27: 934–55. [Google Scholar] [CrossRef] [Green Version]
- Lavoie, Marc. 2014. Post-Keynesian Economics: New Foundations. Cheltenham: Edward Elgar Publishing. [Google Scholar]
- Leerssen, Joep. 2021. Culture, humanities, evolution: The complexity of meaning-making over time. Philosophical Transactions of the Royal Society B 376: 20200043. [Google Scholar] [CrossRef]
- Luther, William J., and Alexander W. Salter. 2017. Bitcoin and the bailout. The Quarterly Review of Economics and Finance 66: 50–56. [Google Scholar] [CrossRef]
- Maddox, Alexia, and Luke J. Heemsbergen. 2021. Digging in Crypto-Communities’ Future-Making: From Dark to Doge. M/C Journal 24. [Google Scholar] [CrossRef]
- Masters, Jered. 2019. Impact of the 2020 Bitcoin Halving: A Mathematical, Social, and Econometric Analysis, Bitcoin 2020 Having Impact Analysis. Bentley: Curtin University. [Google Scholar]
- Mokni, Khaled, Elie Bouri, Ahdi Noomen Ajmi, and Xuan Vinh Vo. 2021. Does Bitcoin Hedge Categorical Economic Uncertainty? A Quantile Analysis. Thousand Oaks: SAGE Open. [Google Scholar]
- Nabilou, Hossein. 2020. Testing the waters of the Rubicon: The European Central Bank and central bank digital currencies. Journal of Banking Regulation 21: 299–314. [Google Scholar] [CrossRef]
- Nakamoto, Satoshi. 2009. Bitcoin: A peer-to-peer electronic cash system Bitcoin: A Peer-to-Peer Electronic Cash System. Bitcoin. org. Available online: https://bitcoin.org/en/bitcoin-paper (accessed on 19 March 2021).
- Nugroho, Bayu Adi. 2021. Dynamic risk-based optimization on cryptocurrencies. Journal of Capital Markets Studies. [Google Scholar] [CrossRef]
- Orskaug, Elisabeth. 2009. Multivariate DCC Garch Model: With Various Error Distributions. Master’s Dissertation, Aalborg University, Aalborg, Denmark. [Google Scholar]
- Peterson, Timothy. 2018. Metcalfe’s Law as a Model for Bitcoin’s Value. Alternative Investment Analyst Review Q 7: 9–18. [Google Scholar] [CrossRef]
- Philipson, Sarah. 2020. Consumers and enterprises as actors on the market. Harvard Deusto Business Research 9: 168–80. [Google Scholar] [CrossRef]
- Ponticelli, Jacopo, and Hans Joachim Voth. 2011. Austerity and Anarchy: Budget Cuts and Social Unrest in Europe, 1919–2008. Masters dissertation, Pompeu Fabra University, Barcelona, Spain; p. 10230. [Google Scholar]
- Poon, Ser-Huang. 2005. A Practical Guide to Forecasting Financial Market Volatility. Hoboken: John Wiley & Sons. [Google Scholar]
- Putnam, Blu. 2020. The Fed’s Balance Sheet Will Continue to Grow in 2021. Chicago: CME Group. [Google Scholar]
- Regaieg, Rym, Wajdi Moussa, and Nidhal Mgadmi. 2020. Can We Reckon Bitcoin as a Hedge, a Safe Haven or a Diversifier for US Dollars? Global Business Review. [Google Scholar] [CrossRef]
- Rosales, Antulio. 2021. Unveiling the power behind cryptocurrency mining in Venezuela: A fragile energy infrastructure and precarious labor. Energy Research & Social Science 79: 102167. [Google Scholar]
- Rozas, David, Antonio Tenorio-Fornés, Silvia Díaz-Molina, and Samer Hassan. 2021. When Ostrom Meets Blockchain: Exploring the Potentials of Blockchain for Commons Governance. Thousand Oaks: SAGE Open. [Google Scholar]
- Scott, Brett, John Loonam, and Vikas Kumar. 2017. Exploring the rise of blockchain technology: Towards distributed collaborative organizations. Strategic Change 26: 423–28. [Google Scholar] [CrossRef]
- Selmi, Refk, Walid Mensi, Shawkat Hammoudeh, and Jamal Bouoiyour. 2018. Is Bitcoin a hedge, a safe haven or a diversifier for oil price movements? A comparison with gold. Energy Economics 74: 787–801. [Google Scholar] [CrossRef]
- Senge, Peter M., Bryan Smith, Nina Kruschwitz, Joe Laur, and Sara Schley. 2008. The Necessary Revolution: How Individuals and Organizations Are Working together to Create a Sustainable World. Redfern: Currency. [Google Scholar]
- Shahzad, Syed Jawad Hussain, Elie Bouri, David Roubaud, Ladislav Kristoufek, and Brian Lucey. 2019. Is Bitcoin a better safe-haven investment than gold and commodities? International Review of Financial Analysis 63: 322–30. [Google Scholar] [CrossRef]
- Smales, Lee A. 2019. Bitcoin as a safe haven: Is it even worth considering? Finance Research Letters 30: 385–93. [Google Scholar] [CrossRef]
- Stensås, Anders, Magnus Frostholm Nygaard, Khine Kyaw, and Sirimon Treepongkaruna. 2019. Can Bitcoin be a diversifier, hedge or safe haven tool? Cogent Economics & Finance 7: 1593072. [Google Scholar]
- Stevens, Amy, and James Allen-Robertson. 2021. Encrypting human rights: The intertwining of resistant voices in the UK state surveillance debate. Big Data & Society 8: 2053951720985304. [Google Scholar]
- Stross, Randall. 2012. What’s Coming Out of Silicon Valley. The New York Times, June 19. [Google Scholar]
- Szabo, Nick. 2002. Shelling Out. Satoshi Nakamoto Institute. Available online: https://nakamotoinstitute.org/shelling-out (accessed on 23 February 2021).
- Takaishi, Tetsuya. 2020. Rough volatility of Bitcoin. Finance Research Letters 32: 101379. [Google Scholar] [CrossRef]
- Takemoto, Yoshifumi, and Sophie Knight. 2014. Mt. Gox files for bankruptcy, hit with lawsuit. Reuters Accessed January 4: 2018. [Google Scholar]
- Tsertsvadze, Vano, and Lali Khurtsia. 2015. Drugs, Silk Road, Bitcoins. WASET World Academy 17: 3612–15. [Google Scholar]
- Umar, Muhammad, Chi-Wei Su, Syed Kumail Abbas Rizvi, and Xue-Feng Shao. 2021. Bitcoin: A safe haven asset and a winner amid political and economic uncertainties in the US? Technological Forecasting and Social Change 167: 120680. [Google Scholar] [CrossRef]
- Wang, Gangjin, Yanping Tang, Chi Xie, and Shou Chen. 2019. Is bitcoin a safe haven or a hedging asset? Evidence from China. Journal of Management Science and Engineering 4: 173–88. [Google Scholar] [CrossRef]
- Wang, Gang-Jin, Xin-yu Ma, and Hao-yu Wu. 2020. Are stablecoins truly diversifiers, hedges, or safe havens against traditional cryptocurrencies as their name sug-gests? Research in International Business and Finance 54: 101225. [Google Scholar] [CrossRef]
- Wray, L. Randall. 2015. Modern Money Theory: A Primer on Macroeconomics for Sovereign Monetary Systems, 2nd ed. New York: Springer. [Google Scholar]
- Yermack, David. 2015. Is Bitcoin a Real Currency? An Economic Appraisal. In Handbook of Digital Currency. Amsterdam: Academic Press, pp. 31–43. [Google Scholar]
- Zhang, Yue-Jun, Elie Bouri, Rangan Gupta, and Shu-Jiao Ma. 2021. Risk spillover between Bitcoin and conventional financial markets: An expectile-based approach. The North American Journal of Economics and Finance 55: 101296. [Google Scholar] [CrossRef]
- Zhao, Haidong, and Lini Zhang. 2021. Financial literacy or investment experience: Which is more influential in cryptocurrency investment? International Journal of Bank Marketing. [Google Scholar] [CrossRef]

**Figure 8.**GBTC squared residuals (Black) of the last 20 observations, forecasted conditional variance (Yellow), estimated conditional variance (Green).

**Figure 10.**GLD squared residuals (Black) of the last 20 observations, forecasted (Yellow) conditional variance, estimated conditional variance (Green).

**Figure 12.**VOO squared residuals (Black) of the last 20 observations, forecasted (Yellow) conditional variance, estimated conditional variance (Green).

**Table 1.**Dynamic conditional correlation generalized autoregressive conditional heteroskedasticity (DCC GARCH) FIT.

Variable | Coefficient (Standard Error) |
---|---|

Distribution and Model | Mvnorm (Multi Variate Normal Distribution) and DCC (Dynamic Conditional Correlation) (1.1) |

No. of parameters | 20 |

[VAR (Vector Auto Regression) GARCH DCC (Dynamic Conditional Correlation) UncQ] | [0 + 15 + 2 + 3] |

No. of Series | 3 |

No. of Observations | 756 |

Log likelihood | 6128.491 |

Av. Log likelihood | 8.11 |

Information Criteria | |

Akaike | −16.160 |

Bayes | −16.038 |

Shibata | −16.161 |

Hannah Quinn | −16.113 |

Variable | GBTC (Grayscale Bitcoin Trust Fund) | VOO (Vanguard 500 Index Fund) | GLD (Gold) |
---|---|---|---|

Mu (mean) | 0.002025 | 0.001096 | 0.000135 |

AR1 (coefficient of the mean model) | −0.020731 | −0.069730 | −0.019810 |

Omega | 0.000345 | 0.000004 | 0.000004 |

Alpha1 (coefficient to the squared residuals) | 0.119798 | 0.235647 | 0.105659 |

Beta1 (coefficient to the lagged variance) | 0.775774 | 0.756135 | 0.859825 |

Dcca1 | 0.028476 | 0.028476 | 0.028476 |

Dccb1 | 0.951253 | 0.951253 | 0.951253 |

Tickers | GBTC | VOO | GLD |
---|---|---|---|

GBTC | 1.00000000 | 0.07248292 | 0.11428288 |

VOO | 0.07248292 | 1.00000000 | 0.08309941 |

GLD | 0.11428288 | 0.08309941 | 1.00000000 |

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**

Rudolf, K.O.; Ajour El Zein, S.; Lansdowne, N.J.
Bitcoin as an Investment and Hedge Alternative. A DCC MGARCH Model Analysis. *Risks* **2021**, *9*, 154.
https://doi.org/10.3390/risks9090154

**AMA Style**

Rudolf KO, Ajour El Zein S, Lansdowne NJ.
Bitcoin as an Investment and Hedge Alternative. A DCC MGARCH Model Analysis. *Risks*. 2021; 9(9):154.
https://doi.org/10.3390/risks9090154

**Chicago/Turabian Style**

Rudolf, Karl Oton, Samer Ajour El Zein, and Nicola Jackman Lansdowne.
2021. "Bitcoin as an Investment and Hedge Alternative. A DCC MGARCH Model Analysis" *Risks* 9, no. 9: 154.
https://doi.org/10.3390/risks9090154