Abstract
This study examines risk co-dependence and portfolio Value-at-Risk (VaR) for major cryptocurrencies—Bitcoin (BTC), Ethereum (ETH), Litecoin (LTC), and Ripple (XRP)—from January 2016 to December 2021. Using the Generalized Autoregressive Score (GAS) model, we identify strong dynamic interdependence among these assets, particularly during volatile periods like the 2018 crypto crash and COVID-19 pandemic. Empirical results demonstrate that the GAS model outperforms traditional DCC-GARCH in handling volatility and correlation shifts, offering superior probabilistic forecasts and risk management insights.
Introduction
Cryptocurrencies have emerged as decentralized digital assets, independent of traditional banking systems. Bitcoin’s 2009 inception paved the way for thousands of cryptocurrencies, with prices experiencing extreme volatility—notably during the 2018 bubble and 2020 COVID-19 sell-off. While existing literature focuses on univariate volatility or static correlations, this study leverages the multivariate GAS model to analyze dynamic risk dependencies and portfolio VaR.
Key Contributions:
- First application of GAS to cryptocurrency volatility and correlation forecasting.
- Comprehensive comparison with DCC-GARCH, highlighting GAS’s robustness during market turbulence.
- Evidence that cryptocurrencies lack the "leverage effect" seen in traditional markets, possibly due to differing investor demographics.
Methodology
1. Multivariate GAS Model
The GAS(1,1) framework updates time-varying parameters (volatilities, correlations) using the score of a multivariate Student-t distribution:
θ_{t+1} = κ + A \cdot s_t + B \cdot θ_tWhere:
- θ_t: Parameters (location, scale, correlation, shape).
- s_t: Scaled score function of the log-likelihood.
2. DCC-GARCH Model
A benchmark for comparison:
Q_t = D_t R_t D_tWhere:
- D_t: Diagonal matrix of GARCH(1,1) volatilities.
- R_t: Dynamic correlation matrix.
Empirical Findings
Data Overview
- Period: 2016–2021, split into in-sample (2016–2018) and out-of-sample (2019–2021).
- Assets: ETH, LTC, BTC, XRP (winsorized returns).
Key Statistics:
- Positive mean returns, leptokurtic distributions (JB test rejects normality).
- Strong ARCH effects confirm volatility clustering.
In-Sample Results
- Volatility Estimates: GAS provides smoother volatility paths vs. DCC’s erratic spikes (Figs. 3–6).
Correlations:
- GAS: Stable positive correlations post-2018 (Fig. 7).
- DCC: Sensitive to extreme events (e.g., ETH-XRP drop during SEC lawsuit, 2021).
Out-of-Sample Performance
Forecast Accuracy:
- Volatility: GAS superior via MSE; mixed results for QLIKE (Table 5).
- Correlation: GAS significantly outperforms (DM test p < 0.05).
- Density Forecasts: GAS excels in Energy Score and Variogram Score (Table 6).
VaR Forecasting
- Portfolio VaR: GAS accurately forecasts 1% and 5% VaR for equal-weighted portfolios (Figs. 15–16).
- Backtests: DCC overestimates risk during crises (e.g., March 2020).
Conclusion
- The GAS model captures dynamic cryptocurrency interdependencies more effectively than DCC-GARCH.
- Cryptocurrencies exhibit unique volatility patterns (no leverage effect), influenced by market structure.
- GAS’s robustness during crises (e.g., COVID-19) makes it ideal for multivariate risk management.
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FAQs
Q: Why does the GAS model outperform DCC-GARCH?
A: GAS uses likelihood scores to adapt parameters dynamically, while DCC relies on lagged squared returns, leading to overreactions.
Q: Are cryptocurrencies suitable for portfolio diversification?
A: Yes, but correlations rise during crises (e.g., 2018 crash), reducing diversification benefits.
Q: How does the SEC lawsuit affect XRP’s risk profile?
A: XRP showed weaker correlations with other cryptos during legal uncertainty, highlighting event-driven risks.