Bitcoin as an Investment and Hedge Alternative. A DCC MGARCH Model Analysis
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
- n × 1 vector log returns of n assets at time t.
- = n × 1 vector of mean corrected returns of n assets at time t, i.e., E [] = 0.
- = n × 1 vector of the expected value of the conditional .
- n × n matrix of conditional variances of at time t.
- any n × n matrix at time t such that is the conditional variance matrix of
- may be obtained by a Cholesky factorization of .
- = n × n diagonal matrix of conditional standard deviations of at time t.
- = n × n conditional correlation matrix of at time t.
- = n × 1 vector of iid errors such that E [] = 0 and E [] = I.
- (1)
- has to be positive definite as it is a covariance matrix. To ensure will be a positive definite, has to be positive definite ( is positive definite since all the diagonal elements are positive).
- (2)
- All the elements in the correlation matrix 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
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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 |
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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
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 StyleRudolf, 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