Research on Bitcoin and Gold Price Correlation Using Copula Functions

Introduction

Since the inception of Bitcoin in 2008, the cryptocurrency market has expanded exponentially, encompassing over 4,000 digital currencies. Among these, Bitcoin stands out for its extreme volatility—its price surged from $172.7 to $28,841.57 within years, highlighting significant investment risks. Concurrently, gold remains a traditional safe-haven asset. This study explores their price correlation using Copula functions, addressing gaps in existing literature that primarily rely on linear models or Granger causality, which fail to capture nonlinear financial dynamics effectively.

Copula Functions: Theory and Application

1. Overview of Copula Functions

Introduced by Sklar (1959), Copula theory decouples joint distributions into marginal distributions and a dependence structure. This allows modeling of nonlinear, asymmetric relationships common in financial markets. Key types include:

• Gaussian Copula: Symmetric but limited to linear correlations.

• Archimedean Copulas (Gumbel, Clayton, Frank): Capture tail dependencies.

  • Gumbel: Upper-tail sensitive (e.g., rapid price surges).
  • Clayton: Lower-tail sensitive (e.g., crash resilience).
  • Frank: Symmetric, suitable for general dependence.

2. Dependence Metrics

• Kendall’s Tau: Measures concordance (e.g., 0.026 implies weak positive ties).
• Spearman’s Rho: Ranks correlation (0.04 confirms mild synergy).

Empirical Analysis

1. Data and Methodology

• Dataset: Daily Bitcoin (CoinMarketCap) and gold (CSMAR) prices (2010–2020).

• Method:

  1. Log-return transformation.
  2. GARCH models for volatility clustering.
  3. Copula selection via Euclidean distance minimization.

2. Key Findings

• Gumbel Copula best fit (Euclidean distance: 0.0174), confirming asymmetric upper-tail dependence.

• Bitcoin-gold correlation: weakly positive (τ = 0.026), suggesting:

  • Long-term co-movement.
  • Short-term divergence during crises.

Conclusion and Implications

1. Investors: Hedge portfolios with both assets; Bitcoin’s volatility complements gold’s stability.
2. Policymakers: Monitor asymmetric tail risks in cryptocurrency regulations.

👉 Explore real-time Bitcoin-gold correlation trends

FAQs

Q1: Can Bitcoin replace gold in portfolios?
A: Partially—it offers higher returns but with greater risk.

Q2: Why use Copulas over traditional models?
A: They capture nonlinear, tail-dependent relationships missed by linear methods.

Q3: How often should investors rebalance Bitcoin-gold allocations?
A: Quarterly, given their low but evolving correlation.

Funded by the National Social Science Fund of China (Project 17BJY235).

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