# Precious Metals Comovements in Turbulent Times: COVID-19 and the Ukrainian Conflict

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Methodology

#### 3.1. Unconditional Correlation Coefficient

#### 3.2. Multidimensional Scaling Analysis

- Step 1:
- Define an ($N\times N$) matrix, $\mathit{A}$, using the squared dissimilarities between all pairs of financial returns ($i$,$j$):$$\mathit{A}=\left[-\frac{1}{2}d{\left(\mathsf{\rho}\right)}_{ij}^{2}\right]$$
- Step 2:
- Form a positive semi-definite matrix, $\mathit{B}$, with zero-sum rows and columns, using a centering matrix, $\mathit{H}$, and where the center of coordinate points is set at the origin.$$\mathit{B}=\mathit{HAH}\mathrm{where}\mathit{H}=\mathit{I}-{N}^{-1}{\mathbf{11}}^{T}.$$
- Step 3:
- Derive the spectral decomposition of $\mathit{B}$, where $\mathit{\Lambda}$ and $\mathit{V}$ are the matrices of ordered eigenvalues (${e}_{1}\ge {e}_{2}\ge \dots \ge {e}_{N}$) and normalized eigenvectors (${V}_{i}{V}_{{}_{i}}^{T}=1$), respectively,$$\mathit{B}={\mathit{V}\mathit{\Lambda}\mathit{V}}^{T}\mathrm{where}\mathit{\Lambda}=diag({e}_{1},\dots ,{e}_{N})\mathrm{and}\mathit{V}=({V}_{1},\dots ,{V}_{N}).$$
- Step 4:
- Use the following coordinate matrix, $\mathit{X}$, to represent the $N$ objects in $N$ dimensions:$$\mathit{X}={\mathit{V}\mathit{\Lambda}}^{1/2}.$$

## 4. Results and Discussion

#### 4.1. Results

#### 4.2. Tests for Normality, Variance Stabilization and Sample Size Adjustment

#### 4.3. Discussion

## 5. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

US Stocks | Gold | Palladium | Platinum | Silver | |
---|---|---|---|---|---|

US stocks | 1 | –0.115 | 0.473 | 0.364 | 0.182 |

Gold | –0.115 | 1 | 0.372 | 0.640 | 0.785 |

Palladium | 0.473 | 0.372 | 1 | 0.622 | 0.498 |

Platinum | 0.364 | 0.640 | 0.622 | 1 | 0.668 |

Silver | 0.182 | 0.785 | 0.498 | 0.668 | 1 |

US Stocks | Gold | Palladium | Platinum | Silver | |
---|---|---|---|---|---|

US stocks | 1 | 0.300 | 0.305 | 0.711 | 0.589 |

Gold | 0.300 | 1 | 0.316 | 0.398 | 0.710 |

Palladium | 0.305 | 0.316 | 1 | 0.425 | 0.342 |

Platinum | 0.711 | 0.398 | 0.425 | 1 | 0.713 |

Silver | 0.589 | 0.710 | 0.342 | 0.713 | 1 |

US Stocks | Gold | Palladium | Platinum | Silver | |
---|---|---|---|---|---|

US stocks | 1 | 0.015 | 0.248 | 0.330 | 0.210 |

Gold | 0.015 | 1 | 0.343 | 0.558 | 0.758 |

Palladium | 0.248 | 0.343 | 1 | 0.534 | 0.432 |

Platinum | 0.330 | 0.558 | 0.534 | 1 | 0.685 |

Silver | 0.210 | 0.758 | 0.432 | 0.685 | 1 |

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US Stocks | Gold | Palladium | Platinum | Silver | |
---|---|---|---|---|---|

Stable period | |||||

Mean | 0.579 | 0.003 | 0.014 | –0.003 | 0.002 |

Median | 0.993 | 0.001 | 0.019 | –0.005 | –0.011 |

Stand. Dev. | 2.888 | 0.034 | 0.062 | 0.045 | 0.063 |

Min | –11.468 | –0.068 | –0.170 | –0.122 | –0.162 |

Max | 6.748 | 0.116 | 0.168 | 0.120 | 0.172 |

Turbulent period | |||||

Mean | 0.493 | 0.007 | 0.001 | 0.006 | 0.012 |

Median | 1.178 | 0.000 | –0.001 | 0.018 | 0.008 |

Stand. Dev. | 4.913 | 0.034 | 0.091 | 0.066 | 0.084 |

Min | –21.940 | –0.053 | –0.170 | –0.210 | –0.168 |

Max | 7.663 | 0.068 | 0.196 | 0.123 | 0.318 |

Correlation | Conditional | Unconditional | ||
---|---|---|---|---|

Period | Stable | Turbulent | Full | Full |

US stocks—Gold | –0.115 | 0.300 ** | 0.025 | 0.015 |

US stocks—Palladium | 0.473 * | 0.305 ** | 0.399 * | 0.248 * |

US stocks—Platinum | 0.364 * | 0.711 * | 0.511 * | 0.330 * |

US stocks—Silver | 0.182 * | 0.589 * | 0.344 * | 0.210 * |

1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|

Absolute eigenvalues | |||||

Stable—conditional correlation | 0.788 | 0.868 | 0.916 | 0.916 | 1.000 |

Turbulent—conditional correlation | 0.465 | 0.924 | 0.979 | 0.979 | 1.000 |

Full—conditional correlation | 0.691 | 0.935 | 0.988 | 1.000 | 1.000 |

Squared eigenvalues | |||||

Stable—conditional correlation | 0.975 | 0.985 | 0.989 | 0.989 | 1.000 |

Turbulent—conditional correlation | 0.502 | 0.992 | 0.998 | 0.999 | 1.000 |

Full—conditional correlation | 0.884 | 0.995 | 0.999 | 1.000 | 1.000 |

Shapiro—Wilk | Kolmogorov—Smirnov | |
---|---|---|

US stocks | <0.001 | <0.001 |

Gold | 0.381 | <0.001 |

Palladium | 0.630 | <0.001 |

Platinum | 0.061 | <0.001 |

Silver | 0.001 | <0.001 |

Correlation | Conditional | Unconditional | ||
---|---|---|---|---|

Period | Stable | Turbulent | Full | Full |

US stocks—Gold | –0.420–0.103 | 0.004–0.526 | –0.268–0.188 | –0.139–0.107 |

US stocks—Palladium | 0.288–0.598 | 0.037–0.633 | 0.232–0.537 | 0.148–0.344 |

US stocks—Platinum | 0.158–0.487 | 0.436–0.898 | 0.355–0.691 | 0.224–0.505 |

US stocks—Silver | –0.001–0.350 | 0.369–0.764 | 0.174–0.481 | 0.107–0.320 |

Correlation | Conditional | Unconditional | ||
---|---|---|---|---|

Period | Stable | Turbulent | Full | Full |

US stocks—Gold | –0.048 | 0.329 * | 0.071 | 0.047 |

US stocks—Palladium | 0.498* | 0.239 | 0.390 * | 0.270 * |

US stocks—Platinum | 0.406* | 0.698 * | 0.523 * | 0.376 * |

US stocks—Silver | 0.204* | 0.671 * | 0.374 * | 0.258 * |

Correlation | Conditional | Unconditional | ||
---|---|---|---|---|

Period | Stable | Turbulent | Full | Full |

US stocks—Gold | –0.067 | 0.300 ** | 0.198 ** | 0.098 |

US stocks—Palladium | 0.243 | 0.305 ** | 0.289 * | 0.146 ** |

US stocks—Platinum | 0.335 * | 0.711 * | 0.619 * | 0.360 * |

US stocks—Silver | –0.021 | 0.589 * | 0.474 * | 0.255 * |

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## Share and Cite

**MDPI and ACS Style**

Michis, A.A.
Precious Metals Comovements in Turbulent Times: COVID-19 and the Ukrainian Conflict. *J. Risk Financial Manag.* **2023**, *16*, 280.
https://doi.org/10.3390/jrfm16050280

**AMA Style**

Michis AA.
Precious Metals Comovements in Turbulent Times: COVID-19 and the Ukrainian Conflict. *Journal of Risk and Financial Management*. 2023; 16(5):280.
https://doi.org/10.3390/jrfm16050280

**Chicago/Turabian Style**

Michis, Antonis A.
2023. "Precious Metals Comovements in Turbulent Times: COVID-19 and the Ukrainian Conflict" *Journal of Risk and Financial Management* 16, no. 5: 280.
https://doi.org/10.3390/jrfm16050280