# Cryptocurrencies, Diversification and the COVID-19 Pandemic

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## Abstract

**:**

## 1. Introduction

## 2. Research Methods

#### 2.1. Basic Measures

#### 2.2. Copula Models

#### 2.3. Generalised Measure of Correlation (GMC)

## 3. Results

#### 3.1. Characteristics of the Base Series

#### 3.2. Simple Tests of Correlation

#### 3.3. Regression Analysis in Period 2

#### 3.4. Non-Linear Non-Parametric Measures of Association in Period 1

#### 3.5. Non-Linear Non-Parametric Measures of Association in Period 2

#### 3.6. Generalised Measure of Correlation (GMC) Analysis

## 4. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Note

1 | I thank an anonymous reviewer for emphasising the importance of the explanation of this point. |

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**Figure 1.**Plots of the series pre-COVID-19. (

**a**) Plot price series levels pre-COVID-19. (

**b**) Plot of returns pre-COVID-19.

**Figure 2.**Plots of the series post-COVID-19. (

**a**) Price series levels post-COVID-19. (

**b**) Plot of returns post-COVID-19.

**Figure 3.**Kernel Density Estimates of Copula fitted to Ajusted Return Series Period 1 Pre-COVID-19. (

**a**) Panel A: BITRET and SPRET. (

**b**) Panel B: ETRET and SPRET. (

**c**) Panel C: BITRET and ETRET.

**Figure 4.**Kernel density estimates of copula fitted to adjusted return series Period 2 COVID-19. (

**a**) BITRET and SPRET. (

**b**) ETRET and SPRET. (

**c**) BITRET and ETRET.

Pre-COVID-19 Period 1107 Observations | |||

Series | Test Statistic | Critical Value 1% | Significance |

Bitcoin | 0.906587 | 0.218 | p-value < 0.01 |

Ethereum | 1.98551 | 0.218 | p-value < 0.01 |

S&P500 Index | 0.89212 | 0.218 | p-value < 0.01 |

Post-COVID-19 Period 388 Observations | |||

Series | Test Statistic | Critical Value 1% | Significance |

Bitcoin | 0.570669 | 0.217 | p-value < 0.01 |

Ethereum | 1.007 | 0.217 | p-value < 0.01 |

S&P500 Index | 0.819212 | 0.217 | p-value < 0.01 |

Pre-COVID-19 | |||||||

Variable | Mean | Median | Minimum | Maximum | Standard Deviation | Skewness | Kurtosis |

BitRet | 0.0030644 | 0.0028579 | −0.23874 | 0.22512 | 0.045864 | −0.066529 | 4.3715 |

EthRet | 0.0037798 | −0.00076875 | −1.3643 | 0.50969 | 0.088035 | −2.7868 | 55.437 |

SPRet | 0.00040215 | 0.00055609 | −0.041843 | 0.048403 | 0.0086027 | −0.56605 | 4.11 |

Doornik-Hansen | Shapiro-Wilk | Lilliefors | Jarque-Bera | ||||

BitRet | 384.5 *** | 0.918 *** | 0.115 *** | 881.5 *** | |||

EthRet | 3174.1 *** | 0.779 *** | 0.126 *** | 143,056 *** | |||

SPRet | 23,591.6 *** | 0.5134 *** | 0.185 *** | 5,267,300 *** | |||

Post-COVID-19 Sample Period Descriptive Statistics Return Series | |||||||

Variable | Mean | Median | Minimum | Maximum | Standard Deviation | Skewness | Kurtosis |

BitRet | 0.0041152 | 0.0034694 | −0.46473 | 0.19153 | 0.051090 | −2.0163 | 18.759 |

EthRet | 0.0067657 | 0.0040564 | −0.55073 | 0.23070 | 0.065380 | −1.4801 | 13.968 |

SPRet | 0.00080243 | 0.0017851 | −0.12765 | 0.089683 | 0.018271 | −1.0116 | 12.402 |

Doornik-Hansen | Shapiro-Wilk | Lilliefors | Jarque-Bera | ||||

BitRet | 261.5 *** | 0.854 *** | 0.121 *** | 5952 *** | |||

EthRet | 285.5 *** | 0.888 *** | 0.098 *** | 3295.9 *** | |||

SPRet | 379.8 *** | 0.811 *** | 0.144 *** | 2552.7 *** |

BITRET Regression on ETRET | ||||

OLS, using observations 2015-08-10–2019-12-31 (T = 1106) | ||||

Dependent variable: BITRET | ||||

Coefficient | Std. Error | t-ratio | p-value | |

const | 0.00225718 | 0.00125961 | 1.792 | 0.0734 |

ETRET | 0.213561 | 0.0143013 | 14.93 | 0.0000 |

Mean dependent var | 0.003064 | S.D. dependent var | 0.045864 | |

Sum squared resid | 1.933742 | S.E. of regression | 0.041852 | |

${R}^{2}$ | 0.168043 | Adjusted ${R}^{2}$ | 0.167290 | |

$F(1,1104)$ | 222.9924 | p-value(F) | 4.58 × 10${}^{-46}$ | |

$\widehat{\rho}$ | 0.042830 | Durbin–Watson | 1.886082 | |

RESET test for specification— | ||||

Null hypothesis: specification is adequate | ||||

Test statistic: $F(2,1102)$ = 54.6266 | ||||

with p-value = P($F(2,1102)$ 54.6266) = 2.39666 × 10${}^{-23}$ | ||||

Regression with Squared ETRET added | ||||

OLS, using observations 2015-08-10–2019-12-31 (T = 1106) | ||||

Dependent variable: BITRET | ||||

Coefficient | Std. Error | t-ratio | p-value | |

const | 0.00147166 | 0.00126693 | 1.162 | 0.2457 |

ETRET | 0.235129 | 0.0152147 | 15.45 | 0.0000 |

sq_ETRET | 0.0907500 | 0.0229085 | 3.961 | 0.0001 |

Mean dependent var | 0.003064 | S.D. dependent var | 0.045864 | |

Sum squared resid | 1.906616 | S.E. of regression | 0.041576 | |

${R}^{2}$ | 0.179714 | Adjusted ${R}^{2}$ | 0.178227 | |

$F(2,1103)$ | 120.8264 | p-value(F) | 3.56 × 10${}^{-48}$ | |

$\widehat{\rho}$ | 0.056203 | Durbin–Watson | 1.882833 |

BITRET Regressed on S&P500 Index Returns | ||||

OLS, using observations 2015-08-10–2019-12-31 (T = 1106) | ||||

Dependent variable: BITRET | ||||

Coefficient | Std. Error | t-ratio | p-value | |

const | 0.00306575 | 0.00137975 | 2.222 | 0.0265 |

SPRET | −0.0127336 | 0.107227 | −0.1188 | 0.9055 |

Mean dependent var | 0.003064 | S.D. dependent var | 0.045864 | |

Sum squared resid | 2.324301 | S.E. of regression | 0.045884 | |

${R}^{2}$ | 0.000013 | Adjusted ${R}^{2}$ | −0.000893 | |

$F(1,1104)$ | 0.014102 | p-value(F) | 0.905492 | |

$\widehat{\rho}$ | 0.020015 | Durbin–Watson | 1.958382 | |

RESET test for specification— | ||||

Null hypothesis: specification is adequate | ||||

Test statistic: $F(2,1102)$ = 0.94016 | ||||

with p-value = P($F(2,1102)$ 0.94016) = 0.390878 | ||||

Regression of ETRET on S&P500 Index Return Period 1 | ||||

OLS, using observations 2015-08-10–2019-12-31 (T = 1106) | ||||

Dependent variable: ETRET | ||||

Coefficient | Std. Error | t-ratio | p-value | |

const | 0.00378385 | 0.00264840 | 1.429 | 0.1534 |

SPRET | −0.0380504 | 0.205821 | −0.1849 | 0.8534 |

Mean dependent var | 0.003780 | S.D. dependent var | 0.088035 | |

Sum squared resid | 8.563712 | S.E. of regression | 0.088074 | |

${R}^{2}$ | 0.000031 | Adjusted ${R}^{2}$ | −0.000875 | |

$F(1,1104)$ | 0.034177 | p-value(F) | 0.853364 | |

$\widehat{\rho}$ | 0.006020 | Durbin–Watson | 1.769479 | |

RESET test for specification— | ||||

Null hypothesis: specification is adequate | ||||

Test statistic: $F(2,1102)$ = 1.04091 | ||||

with p-value = P($F(2,1102)$ 1.04091) = 0.353479 |

Paired Series | Kendall’s Tau | Z-Score | Two-Tailed Probability |
---|---|---|---|

BITRET and SPRET | −0.00908414 | 0.689712 | 0.4904 |

ETRET and SPRET | 0.01384959 | 0.689712 | 0.4904 |

ETRET and BITRET | 0.35508334 | 17.6852 | 0.0000 |

BITRET Regression on ETRET | ||||

OLS, using observations 2020-01-02–2021-07-23 (T = 388) | ||||

Dependent variable: BITRET | ||||

Coefficient | Std. Error | t-ratio | p-value | |

const | 0.00737211 | 0.00237119 | 3.109 | 0.0020 |

ETRET | 0.200777 | 0.0365130 | 5.499 | 0.0000 |

sq_ETRET | −1.07101 | 0.142508 | −7.515 | 0.0000 |

Mean dependent var | 0.004115 | S.D. dependent var | 0.051090 | |

Sum squared resid | 0.759745 | S.E. of regression | 0.044423 | |

${R}^{2}$ | 0.247872 | Adjusted ${R}^{2}$ | 0.243965 | |

$F(2,385)$ | 63.44057 | p-value(F) | 1.54 × 10${}^{-24}$ | |

$\widehat{\rho}$ | −0.074587 | Durbin–Watson | 2.147612 | |

Return Regressions Post-COVID-19 BITRET Regression on SPRET | ||||

OLS, using observations 2020-01-02–2021-07-23 (T = 388) | ||||

Dependent variable: BITRET | ||||

Coefficient | Std. Error | t-ratio | p-value | |

const | 0.00558160 | 0.00248122 | 2.250 | 0.0250 |

SPRET | 0.915062 | 0.134756 | 6.790 | 0.0000 |

sq_SPRET | −6.59678 | 1.95763 | −3.370 | 0.0008 |

Mean dependent var | 0.004115 | S.D. dependent var | 0.051090 | |

Sum squared resid | 0.849030 | S.E. of regression | 0.046960 | |

${R}^{2}$ | 0.159483 | Adjusted ${R}^{2}$ | 0.155116 | |

$F(2,385)$ | 36.52566 | p-value(F) | 2.99 × 10${}^{-15}$ | |

$\widehat{\rho}$ | −0.060347 | Durbin–Watson | 2.118522 | |

Regression of ETRET on SPRET Period 2 COVID-19 | ||||

OLS, using observations 2020-01-02–2021-07-23 (T = 388) | ||||

Dependent variable: ETRET | ||||

Coefficient | Std. Error | t-ratio | p-value | |

const | 0.00924389 | 0.00322452 | 2.867 | 0.0044 |

SPRET | 0.967587 | 0.175126 | 5.525 | 0.0000 |

sq_SPRET | −9.75624 | 2.54408 | −3.835 | 0.0001 |

Mean dependent var | 0.006766 | S.D. dependent var | 0.065380 | |

Sum squared resid | 1.433917 | S.E. of regression | 0.061028 | |

${R}^{2}$ | 0.133186 | Adjusted ${R}^{2}$ | 0.128683 | |

$F(2,385)$ | 29.57768 | p-value(F) | 1.12 × 10${}^{-12}$ | |

$\widehat{\rho}$ | 0.008506 | Durbin–Watson | 1.979712 |

Paired Series | Kendall’s Tau | Z-Score | Two-Tailed Probability |
---|---|---|---|

BITRET and SPRET | 0.14576840 | 4.28722 | 0.000 |

ETRET and SPRET | 0.05975119 | 1.75712 | 0.079 |

ETRET and BITRET | 0.11017875 | 3.24039 | 0.001 |

BITRET and SPRET | |||

Kernel Copula Density estimate tau = −0.0065 | |||

Observations = 1107 | Method: Transformation local likelihood, log-quadratic (nearest-neighbor) | ||

Band width alpha = 0.5363016 | |||

logLik: 3.27 | AIC: 20.48 | cAIC: 20.83 | BIC: 88.12 |

Effective number of parameters: 13.5 | |||

Kendall −0.0065 | Spearman −0.0096 | Blomquist −0.0109 | Gini −0.0102 |

vd_waerden −0.0008 | minfo 0.00165 | linfoot 0.0574 | |

ETRET and SPRET | |||

Kernel Copula Density estimate tau=0.014 | |||

Observations = 1107 | Method: Transformation local likelihood, log-quadratic (nearest-neighbor) | ||

Bandwidth: alpha = 0.5363016 | |||

logLik: 4.49 | AIC: 18.21 | cAIC: 18.57 | BIC: 86.33 |

Effective number of parameters: 13.6 | |||

Kendall 0.0143 | Spearman 0.0218 | Blomquist 0.0113 | Gini 0.0151 |

vd_waerden 0.0270 | minfo 0.0016 | Linfoot 0.0567 | |

BITRET and ETRET | |||

Kernel Copula Density estimate tau=0.35 | |||

Observations = 1608 | Method: Transformation local likelihood, log-quadratic (nearest-neighbor) | ||

Bandwidth: alpha = 0.1920285 | |||

logLik: 378.95 | AIC: −699.29 | cAIC: −698.16 | BIC: −541.55 |

Effective number of parameters: 29.3 | |||

Kendall 0.3535 | Spearman 0.4873 | Blomqvist 0.3535 | gini 0.4007 |

vd_waerden 0.5027 | minfo 0.2137 | linfoot 0.5897 |

BITRET and SPRET | |||

Kernel Copula Density estimate tau = 0.15 | |||

Observations = 388 | Method: Transformation local likelihood, log-quadratic (nearest-neighbor) | ||

Bandwidth: alpha = 0.5803161 | |||

logLik: 18.98 | AIC: −15.07 | cAIC: −14.31 | BIC: 30.26 |

Effective number of parameters: 11.24 | |||

Kendall 0.1546 | Spearman 0.2316 | Blomquist 0.1450 | Gini 0.1758 |

Van der Waerden 0.2536 | Minfo 0.0390 | Linfoot 0.2738 | |

ETRET and SPRET | |||

Kernel Copula Density estimate tau = 0.075 | |||

Observations = 388 | Method: Transformation local likelihood, log-quadratic (nearest-neighbor) | ||

Band width alpha = 0.5886832 | |||

LogLik: 15.49 | AIC: −7.52 | cAIC: −6.72 | BIC: 38.93 |

Effective number of parameters: 11.73 | |||

Kendall 0.0753 | Spearman 0.1125 | Blomquist 0.0491 | Gini 0.0768 |

Van der Waerden 0.1457 | Minfo 0.0203 | Linfoot 0.1995 | |

BITRET and ETRET | |||

Kernel Copula Density estimate tau = 0.013 | |||

Observations = 388 | Method: Transformation local likelihood, log-quadratic (nearest-neighbor) | ||

Bandwidth: alpha = 0.4297086 | |||

logLik: 39.05 | AIC: −47.77 | cAIC: −46.45 | BIC: 12.29 |

Effective number of parameters: 15.16 | |||

Kendall 0.1301 | Spearman 0.1886 | Blomquist 0.1217 | Gini 0.1493 |

Van der Waerden 0.2167 | Minfo 0.0559 | Linfoot 0.3253 |

Period 1: Pre-COVID-19 | |||

SPRET | BITRET | ETRET | |

SPRET | 1.000 | −0.4542502 | −0.4695773 |

BITRET | −0.5563881 | 1.000 | 0.8003115 |

ETRET | −0.7299776 | 0.8324365 | 1.000 |

Period 2: Post-COVID-19 | |||

SPRET | BITRET | ETRET | |

SPRET | 1.000 | 0.6758405 | 0.8140017 |

BITRET | 0.6898318 | 1.000 | 0.7194903 |

ETRET | 0.6840218 | 0.7671989 | 1.000 |

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**MDPI and ACS Style**

Allen, D.E.
Cryptocurrencies, Diversification and the COVID-19 Pandemic. *J. Risk Financial Manag.* **2022**, *15*, 103.
https://doi.org/10.3390/jrfm15030103

**AMA Style**

Allen DE.
Cryptocurrencies, Diversification and the COVID-19 Pandemic. *Journal of Risk and Financial Management*. 2022; 15(3):103.
https://doi.org/10.3390/jrfm15030103

**Chicago/Turabian Style**

Allen, David E.
2022. "Cryptocurrencies, Diversification and the COVID-19 Pandemic" *Journal of Risk and Financial Management* 15, no. 3: 103.
https://doi.org/10.3390/jrfm15030103