The global outbreak of the COVID-19 pandemic in early 2020 triggered not only a public health crisis but also profound disruptions in financial markets. As traditional economies contracted and central banks rolled out unprecedented monetary easing, investors increasingly turned to alternative assets for value preservation. Among these, Bitcoin emerged as a prominent contender, often dubbed "digital gold" due to its decentralized nature and finite supply. This article investigates the volatility and risk characteristics of Bitcoin’s return rate before and after the onset of the pandemic, using advanced econometric models including ARCH, GARCH, and APARCH. The analysis spans daily closing prices from September 1, 2015, to August 31, 2021, with January 23, 2020—the day Wuhan was locked down—serving as the structural breakpoint.
Understanding Bitcoin in a Post-Pandemic Financial Landscape
Bitcoin, introduced by Satoshi Nakamoto in 2008, operates on blockchain technology and functions as a decentralized digital currency. Unlike fiat money, it is not issued or backed by any government or central authority. Over the years, its price has exhibited extreme volatility: surging past $18,000 in 2017, dropping below $3,000, then rebounding dramatically to exceed $60,000 by late 2020. This rollercoaster performance underscores its speculative nature.
During the pandemic, global uncertainty drove capital toward perceived safe-haven assets. While gold appreciated by about 25%, Bitcoin surged over 300%, reinforcing its image as a potential hedge against macroeconomic instability. However, this rapid ascent raises critical questions: Is Bitcoin truly a store of value, or merely a high-risk speculative instrument? How did its return volatility behave during one of the most turbulent economic periods in recent history?
Core Econometric Models: ARCH, GARCH, and APARCH
To analyze Bitcoin’s return volatility, we employ three key models that capture time-varying variance and asymmetric responses to market shocks.
ARCH Model: Capturing Volatility Clustering
The Autoregressive Conditional Heteroskedasticity (ARCH) model, developed by Engle (1982), allows the conditional variance of returns to depend on past squared residuals. In simpler terms, large changes in price tend to be followed by more large changes—positive or negative—a phenomenon known as volatility clustering.
Mathematically, an ARCH(q) model assumes:
$$ \sigma_t^2 = \omega + \alpha_1 \varepsilon_{t-1}^2 + \dots + \alpha_q \varepsilon_{t-q}^2 $$
where $\sigma_t^2$ is the conditional variance at time $t$, $\varepsilon_t$ is the error term (residual), and $\omega > 0$, $\alpha_i \geq 0$.
This model effectively captures short-term volatility dynamics but becomes cumbersome when many lags are needed.
GARCH Model: Enhancing Long-Term Forecasting
The Generalized ARCH (GARCH) model, proposed by Bollerslev (1986), extends the ARCH framework by incorporating lagged conditional variances into the variance equation. A GARCH(p, q) model is expressed as:
$$ \sigma_t^2 = \omega + \sum_{i=1}^q \alpha_i \varepsilon_{t-i}^2 + \sum_{j=1}^p \beta_j \sigma_{t-j}^2 $$
The inclusion of past variances makes GARCH more parsimonious and better suited for modeling persistent volatility. The sum of $\alpha + \beta$ indicates the persistence of shocks—values close to 1 suggest long-lasting effects.
APARCH Model: Accounting for Leverage Effects
While GARCH models assume symmetric responses to positive and negative shocks, financial assets often react more strongly to bad news than good—a phenomenon known as the leverage effect. The Asymmetric Power ARCH (APARCH) model addresses this limitation by allowing different impacts based on shock sign and magnitude.
The APARCH(1,1) model is defined as:
$$ \sigma_t^\delta = \omega + \alpha (\left| \varepsilon_{t-1} \right| - \gamma \varepsilon_{t-1})^\delta + \beta \sigma_{t-1}^\delta $$
Here, $\gamma$ measures asymmetry: if $\gamma > 0$, negative shocks generate higher volatility than positive ones of equal size.
Empirical Analysis: Data and Methodology
Data Collection and Return Calculation
Our dataset comprises 2,192 daily closing prices of Bitcoin from September 1, 2015, to August 31, 2021. Prices were sourced from major cryptocurrency exchanges. Daily returns ($r_t$) are computed using logarithmic differences:
$$ r_t = \ln(P_t) - \ln(P_{t-1}) $$
where $P_t$ denotes the closing price at time $t$.
We split the sample at January 23, 2020—marking the start of widespread pandemic-related market disruptions—to compare pre- and post-outbreak behavior.
All analyses were conducted using RStudio and Excel.
Descriptive Statistics and Distributional Properties
Summary statistics reveal that Bitcoin’s daily return has a mean of 0.002432 and a standard deviation of 0.040470. The distribution is negatively skewed (−0.52), indicating more frequent small gains and occasional large drops. The excess kurtosis of 5.56 confirms fat tails, meaning extreme events occur more often than predicted by a normal distribution.
A Jarque-Bera test yields a p-value near zero, rejecting normality at conventional significance levels. A Q-Q plot visually reinforces this deviation, showing significant departures in both tails.
Stationarity and Autocorrelation Tests
ADF unit root tests confirm stationarity in both subsamples (p < 0.01), satisfying a key requirement for GARCH modeling. Autocorrelation Function (ACF) and Partial ACF plots show rapid decay within confidence bounds, further supporting stationarity.
However, squared returns exhibit strong autocorrelation—evidence of volatility clustering—justifying the use of GARCH-type models.
Model Estimation Results
ARCH Effect Detection
An ARCH-LM test detects significant ARCH effects in both periods (p < 0.01). Residual plots confirm that while raw residuals show no serial correlation, their squares do—indicating time-varying volatility.
A line chart of squared residuals reveals clear volatility clustering: quiet periods alternate with bursts of high variability.
GARCH(1,1) Model Performance
We fit multiple GARCH specifications and select GARCH(1,1) based on lowest AIC/BIC values for both pre- and post-pandemic samples.
Estimation results show:
- Pre-pandemic: $\alpha = 0.14$, $\beta = 0.83$, $\alpha + \beta = 0.97$
- Post-pandemic: $\alpha = 0.16$, $\beta = 0.80$, $\alpha + \beta = 0.96$
Both sums are less than but very close to 1, implying high persistence—shocks decay slowly over time but eventually fade. This confirms that Bitcoin’s volatility reacts enduringly to new information.
Standardized residual diagnostics indicate no remaining autocorrelation or ARCH effects, validating model adequacy.
APARCH(1,1) Reveals Asymmetric Reactions
Fitting an APARCH(1,1) model uncovers crucial asymmetries:
- Pre-pandemic: Leverage coefficient $\gamma = -0.08$ (p > 0.05)—not statistically significant.
- Post-pandemic: $\gamma = 0.15$ (p < 0.05)—positive and significant.
This means negative shocks (e.g., worsening pandemic news) had a disproportionately larger impact on volatility after the outbreak began. Investors became more sensitive to downside risks during times of systemic stress.
Key Findings and Interpretation
Based on our analysis, three major conclusions emerge:
- Persistent Volatility Clustering: Bitcoin exhibits strong ARCH/GARCH effects throughout both periods, confirming that past volatility helps predict future swings—a hallmark of speculative assets.
- High Shock Persistence: With $\alpha + \beta ≈ 0.97$, shocks have long memory in Bitcoin markets. Although their influence gradually diminishes, they do not vanish quickly—suggesting prolonged market sensitivity after major events.
- Emergence of Leverage Effect Post-Pandemic: Prior to 2020, positive and negative shocks affected volatility similarly. Afterward, negative news amplified volatility significantly more—a behavioral shift likely driven by increased institutional participation and risk awareness during crises.
These findings align with broader market trends: as Bitcoin transitioned from a niche asset to a mainstream investment vehicle during the pandemic, its risk profile evolved accordingly.
Frequently Asked Questions (FAQ)
Q: What does a high GARCH persistence parameter mean for investors?
A: A persistence value near 1 implies that volatility shocks last for extended periods. For traders, this means higher risk exposure following market turbulence and underscores the importance of dynamic risk management strategies.
Q: Why did Bitcoin develop a leverage effect only after the pandemic started?
A: Increased media coverage, regulatory scrutiny, and institutional involvement heightened investor sensitivity to negative developments. Market maturity led to asymmetric reactions where bad news triggers stronger sell-offs.
Q: Can Bitcoin still be considered a “digital gold” given its volatility?
A: While its scarcity mimics gold, Bitcoin’s price behavior remains far more volatile and speculative. It may serve as a hedge in certain environments but lacks the stability typically associated with traditional safe havens.
Q: How reliable are GARCH models for forecasting crypto volatility?
A: GARCH models perform well in capturing historical volatility patterns and clustering effects. However, they may underpredict sudden structural breaks (e.g., regulatory bans). Combining them with machine learning or EVT models can improve robustness.
Q: Does this study support using Bitcoin in diversified portfolios?
A: Yes—with caution. Its low correlation with traditional assets offers diversification benefits, but high volatility requires careful position sizing and hedging mechanisms.
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Conclusion
This study provides empirical evidence that the pandemic fundamentally altered Bitcoin’s risk dynamics. While persistent volatility existed before 2020, the emergence of a significant leverage effect afterward highlights a maturing yet still highly reactive market. Investors should recognize that although Bitcoin offers potential as an alternative asset class, it behaves more like a speculative instrument than a stable store of value during crises.
As digital assets continue to evolve within global financial systems, understanding their volatility structure through rigorous modeling remains essential for informed decision-making.
Core Keywords: Bitcoin, rate of return, COVID-19, ARCH effect, GARCH model, APARCH model