BTC vs MARA: Returns, Risk & Volatility (2021)

Written by Gale Finance Team

Reviewed by Sid Kalla CFA Charterholder

Analysis period: 2021-01-01 to 2021-12-31

BTC Total Return

↑ +44.8%

MARA Total Return

↑ +198.5%

Relative Performance of BTC vs MARA (Normalized to 100)

BTC MARA

Normalized to 100 at start date for comparison

Key Takeaways

Total Return: BTC delivered a +44.8% total return, while MARA returned +198.5% over the same period. MARA outperformed on total returns.
Risk-Adjusted Return (Sharpe Ratio): MARA had a higher Sharpe (1.43 vs 0.81), indicating better risk-adjusted performance.
Volatility (Annualized): MARA was more volatile, with 138.5% annualized volatility, versus 80.3% for BTC.
Maximum Drawdown: BTC's maximum drawdown was -53.1%, while MARA experienced a deeper drawdown of -65.2%.
Tail Risk (VaR & Expected Shortfall): At the 5% level (daily log returns), BTC's VaR was -6.63% and its Expected Shortfall (CVaR) was -9.38%; MARA's were -12.56% and -16.90%. VaR is the cutoff; Expected Shortfall is the average move on the worst days.
Skew & Kurtosis: Skew: BTC -0.10 vs MARA 0.32. Excess kurtosis: BTC 1.48 vs MARA 1.98. Negative skew leans downside; higher excess kurtosis means fatter tails.
Tail Days & Extremes: 2σ tail days (down/up): BTC 10/11, MARA 3/7. Worst day: BTC -13.77% (2021-05-19) vs MARA -27.03% (2021-11-15). Best day: BTC +18.75% (2021-02-08) vs MARA +42.41% (2021-02-08).
Risk ratios: Sortino - BTC: 1.20 vs. MARA: 2.42 , Calmar - BTC: N/A vs. MARA: N/A , Sterling - BTC: N/A vs. MARA: N/A , Treynor - BTC: N/A vs. MARA: N/A , Ulcer Index - BTC: N/A vs. MARA: N/A

Bitcoin vs Marathon Digital Correlation

0.61 Average Correlation

Bitcoin and Marathon Digital were strongly correlated in 2021. With a correlation of 0.61, these assets tended to move together, limiting diversification benefits.

For portfolio construction, this strong correlation means holding both BTC and MARA provides limited risk reduction — they're likely to decline together in downturns.

Metric	Value
Current (30-day)	0.70
Average (full period)	0.61
Minimum	0.37
Maximum	0.84

Correlation measures how closely two assets move together. Values near +1 indicate strong co-movement, near 0 indicates independence, and negative values indicate inverse movement.

Investment Comparison

If you invested $10,000 in each asset on January 1, 2021:

BTC $14,483.477 +44.8%

MARA $29,845.595 +198.5%

Difference: $15,362.118 (MARA ahead)

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Bitcoin and Marathon Digital: Risk Analysis

Bitcoin experienced its maximum drawdown of -53.1% from 2021-04-13 to 2021-07-20. It has not yet recovered to its previous peak.

Marathon Digital experienced its maximum drawdown of -65.2% from 2021-04-05 to 2021-05-13. It has not yet recovered to its previous peak.

Smaller drawdowns and faster recoveries indicate lower downside risk and greater resilience during market stress.

Sharpe Ratio of BTC and MARA

BTC Sharpe Ratio

↑ 0.81

MARA Sharpe Ratio

↑ 1.43

Sharpe ratio measures return per unit of risk (volatility). A higher Sharpe indicates better risk-adjusted performance. MARA had a higher Sharpe (1.43 vs 0.81), indicating better risk-adjusted performance.

A Sharpe above 1.0 is generally considered good, above 2.0 is excellent. Negative Sharpe means the asset underperformed the risk-free rate. Calculated on each asset's full 365-day lookback of available prices and annualized using the asset calendar (365 for crypto, 252 trading days for equities/ETFs/metals).

Sortino Ratio of BTC and MARA

BTC Sortino Ratio

↑ 1.20

MARA Sortino Ratio

↑ 2.42

Sortino ratio measures return per unit of downside risk. Unlike Sharpe, it only counts downside deviation (returns below the target return). MARA had better downside-adjusted returns.

A higher Sortino is better. It's useful when upside volatility is common (crypto is the obvious example). Downside deviation: BTC 54.1% vs MARA 81.6%. Calculated on each asset's full 365-day lookback of available prices, using the daily risk-free rate as the target return, and annualized using the asset calendar (365 for crypto, 252 trading days for equities/ETFs/metals).

Tail Risk & Distribution Shape (2021): Bitcoin vs. Marathon Digital

This section looks at the shape of daily returns, not just the average. Tail stats are computed per asset on its own daily series (crypto includes weekends). We use daily log returns $\ln\left(\frac{P_t}{P_{t-1}}\right)$ so multi-day moves add cleanly.

Definitions: Value at Risk (VaR), Expected Shortfall, skew, kurtosis, and fat tails.

Metric (2021)	BTC	MARA
5% VaR (daily log return)	-6.63%	-12.56%
5% Expected Shortfall (CVaR)	-9.38% (worst 19 days)	-16.90% (worst 13 days)
Skew	-0.10	0.32
Excess kurtosis	1.48	1.98
2σ tail days (down / up)	10 / 11	3 / 7
Worst day	-13.77% (2021-05-19)	-27.03% (2021-11-15)
Best day	+18.75% (2021-02-08)	+42.41% (2021-02-08)

Downside co-moves (2σ) — 2021

Computed on shared dates only (n=251). A “2σ downside move” means a shared-close log return more than 2 standard deviations below that asset’s own mean on this shared-date series. Dates below show simple returns (%) for readability.

When MARA has a big down day, BTC also does

33.3%

1 / 3 days

When BTC has a big down day, MARA also does

11.1%

1 / 9 days

Show downside tail dates

Dates below are shared-date observations. The “Date” is the period end (close). Tail thresholds are computed on log returns, but the table shows simple returns (%) for readability. Returns are computed from the previous shared close to this one (for example, Friday → Monday includes weekend moves).

Days when both BTC and MARA had a big down day (2σ)

Date (interval)	BTC	MARA
2021-02-23	-9.93%	-23.04%

Days when BTC had a big down day

Date (interval)	BTC	MARA
2021-01-08 → 2021-01-11	-12.82%	-11.48%
2021-01-21	-13.28%	-8.87%
2021-02-23	-9.93%	-23.04%
2021-04-16 → 2021-04-19	-9.50%	-8.68%
2021-05-12	-13.32%	-11.95%
2021-05-14 → 2021-05-17	-12.72%	-3.12%
2021-05-19	-13.77%	-5.57%
2021-06-18 → 2021-06-21	-11.49%	-3.77%
2021-09-17 → 2021-09-20	-9.36%	-5.44%

Days when MARA had a big down day

Date (interval)	BTC	MARA
2021-02-23	-9.93%	-23.04%
2021-04-14	-0.62%	-15.75%
2021-11-12 → 2021-11-15	-0.93%	-27.03%

Read this as “how ugly the ugly days get”, not as a precise forecast. One-year samples are small, so tail estimates are inherently noisy.

Full Comparison of Bitcoin vs. Marathon Digital (2021)

Metric	BTC	MARA
Total Return	+44.8%	+198.5%
Annualized Volatility	80.3%	138.5%
Sharpe Ratio	0.81	1.43
Sortino Ratio	1.20	2.42
Calmar Ratio	N/A	N/A
Sterling Ratio	N/A	N/A
Treynor Ratio	N/A	N/A
Ulcer Index	N/A	N/A
Max Drawdown	-53.1%	-65.2%
Avg Correlation to S&P 500	N/A	N/A
5% VaR (daily log return)	-6.63%	-12.56%
5% Expected Shortfall (CVaR)	-9.38%	-16.90%
Skew	-0.10	0.32
Excess kurtosis	1.48	1.98
2σ tail days (down / up)	10 / 11	3 / 7

Audit this calculation

Formulas, inputs, and conventions used to compute the metrics on this page.

Inputs & conventions

Shared window for pair metrics: 2021-01-01 → 2021-12-31 (last shared close).
Rolling correlation sample (shared closes): N/A
Annualization (days/year): BTC: 365 days/year; MARA: 252 days/year.
Risk-free rate: Uses the 3-month U.S. Treasury yield (FRED: DGS3MO), averaged over each asset’s window:

BTC: 4.50%.

MARA: 4.50%.
Volatility drag (rule of thumb): Estimated from annualized volatility (simple returns). For the log-return framing, see Log returns.

BTC: ≈ -32.2%/yr

MARA: ≈ -95.9%/yr
Data alignment: No forward fill. Correlation and tail co-moves are computed on shared closes only.
For cross-calendar pairs (e.g., crypto vs stocks), weekend/holiday moves roll into the next shared close.
Return conventions: Volatility/Sharpe/Sortino use simple daily returns. Tail-risk uses daily log returns for distribution stats (but tables show simple returns). Log returns.

Formulas

Daily simple return

r_t = \frac{P_t}{P_{t-1}} - 1

Volatility

\sigma_{ann} = \sigma(r_t)\sqrt{A}

Volatility drag (approx.)

\text{drag} \approx \tfrac{1}{2}\sigma_{ann}^2

Sharpe Ratio

S = \frac{A\,\bar{r} - r_f}{\sigma(r_t)\sqrt{A}}

Sortino Ratio

So = \frac{A\,\bar{r} - r_f}{\sqrt{\mathbb{E}[\min(0,\,r_t - r_f/A)^2]}\,\sqrt{A}}

Maximum Drawdown

MDD = \min_t\left(\frac{P_t}{\max_{s \le t} P_s} - 1\right)

Average Correlation

\rho = \frac{\operatorname{cov}(r^A,\,r^B)}{\sigma_A\,\sigma_B}

Log returns

\ell_t = \ln\left(\frac{P_t}{P_{t-1}}\right)

Notation

$P_t$: Price on day t.
$r_t$: Simple daily return.
$\ell_t$: Log daily return.
$\bar{r}$: Average daily return.
$\sigma(r_t)$: Standard deviation of daily returns.
$A$: Annualization factor (days/year).
$r_f$: Annual risk-free rate.

Bitcoin vs Marathon Digital: Frequently Asked Questions

Which had higher volatility: BTC or MARA?

MARA showed higher volatility at 138.5% annualized, compared to 80.3% for BTC During 2021. Higher volatility meant larger price swings in both directions.

Did BTC provide diversification when held with MARA?

BTC and MARA were strongly correlated in 2021, with an average correlation of 0.61. This strong correlation limited diversification benefits.

How bad are the worst 5% days for BTC vs MARA?

During 2021, BTC's 5% VaR was -6.63% and its 5% Expected Shortfall was -9.38% (worst 19 days). MARA's were -12.56% and -16.90% (worst 13 days).

Do BTC and MARA crash together on bad days?

On shared dates (n=251), when MARA has a 2σ down day, BTC also does 33.3% (1/3 days). In the other direction, when BTC has one, MARA also does 11.1% (1/9 days).

Which had better risk-adjusted returns: BTC or MARA?

MARA showed better risk-adjusted performance with a Sharpe ratio of 1.43 versus BTC's 0.81 During 2021.

Could BTC and MARA have been combined in a portfolio?

Yes, though allocation sizing mattered. Their strong correlation provided limited risk reduction since they tended to move together. MARA's higher volatility (138.5%) meant even small allocations can materially impact overall portfolio risk.

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