BTC vs HOOD: Returns, Risk & Volatility (2022)

Written by Gale Finance Team

Reviewed by Sid Kalla CFA Charterholder

Analysis period: 2022-01-01 to 2022-12-31

BTC Total Return

↓ -64.3%

HOOD Total Return

↓ -55.9%

Relative Performance of BTC vs HOOD (Normalized to 100)

BTC HOOD

Normalized to 100 at start date for comparison

Key Takeaways

Total Return: BTC delivered a -64.3% total return, while HOOD returned -55.9% over the same period. HOOD outperformed on total returns.
Risk-Adjusted Return (Sharpe Ratio): Both Sharpe ratios were negative (HOOD -0.64 vs BTC -1.38), meaning both underperformed the risk-free rate; HOOD was less negative.
Volatility (Annualized): HOOD was more volatile, with 82.9% annualized volatility, versus 63.8% for BTC.
Maximum Drawdown: HOOD's maximum drawdown was -62.6%, while BTC experienced a deeper drawdown of -66.7%.
Tail Risk (VaR & Expected Shortfall): At the 5% level (daily log returns), BTC's VaR was -5.80% and its Expected Shortfall (CVaR) was -9.10%; HOOD's were -8.51% and -10.76%. VaR is the cutoff; Expected Shortfall is the average move on the worst days.
Skew & Kurtosis: Skew: BTC -0.59 vs HOOD 0.48. Excess kurtosis: BTC 4.67 vs HOOD 3.10. Negative skew leans downside; higher excess kurtosis means fatter tails.
Tail Days & Extremes: 2σ tail days (down/up): BTC 12/9, HOOD 3/8. Worst day: BTC -15.97% (2022-06-13) vs HOOD -19.04% (2022-11-08). Best day: BTC +14.54% (2022-02-28) vs HOOD +24.88% (2022-05-13).
Risk ratios: Sortino - BTC: -1.81 vs. HOOD: -0.96 , Calmar - BTC: N/A vs. HOOD: N/A , Sterling - BTC: N/A vs. HOOD: N/A , Treynor - BTC: N/A vs. HOOD: N/A , Ulcer Index - BTC: N/A vs. HOOD: N/A

Bitcoin vs Robinhood Correlation

0.48 Average Correlation

Bitcoin and Robinhood were moderately correlated in 2022. With a correlation of 0.48, these assets showed moderate co-movement, offering some diversification when held together.

For portfolio construction, this moderate correlation offers some diversification benefit, though the assets still tend to move together during major market moves.

Metric	Value
Current (30-day)	0.49
Average (full period)	0.48
Minimum	0.24
Maximum	0.83

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, 2022:

BTC $3,573.667 -64.3%

HOOD $4,414.317 -55.9%

Difference: $840.649 (HOOD ahead)

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Bitcoin and Robinhood: Risk Analysis

Bitcoin experienced its maximum drawdown of -66.7% from 2022-03-29 to 2022-11-21. It has not yet recovered to its previous peak.

Robinhood experienced its maximum drawdown of -62.6% from 2022-01-03 to 2022-06-16. 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 HOOD

BTC Sharpe Ratio

↓ -1.38

HOOD Sharpe Ratio

↓ -0.64

Sharpe ratio measures return per unit of risk (volatility). A higher Sharpe indicates better risk-adjusted performance. Both Sharpe ratios were negative (HOOD -0.64 vs BTC -1.38), meaning both underperformed the risk-free rate; HOOD was less negative.

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 HOOD

BTC Sortino Ratio

↓ -1.81

HOOD Sortino Ratio

↓ -0.96

Sortino ratio measures return per unit of downside risk. Unlike Sharpe, it only counts downside deviation (returns below the target return). HOOD 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 48.6% vs HOOD 55.3%. 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 (2022): Bitcoin vs. Robinhood

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 (2022)	BTC	HOOD
5% VaR (daily log return)	-5.80%	-8.51%
5% Expected Shortfall (CVaR)	-9.10% (worst 19 days)	-10.76% (worst 13 days)
Skew	-0.59	0.48
Excess kurtosis	4.67	3.10
2σ tail days (down / up)	12 / 9	3 / 8
Worst day	-15.97% (2022-06-13)	-19.04% (2022-11-08)
Best day	+14.54% (2022-02-28)	+24.88% (2022-05-13)

Downside co-moves (2σ) — 2022

Computed on shared dates only (n=250). 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 HOOD has a big down day, BTC also does

66.7%

2 / 3 days

When BTC has a big down day, HOOD also does

25.0%

2 / 8 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 HOOD had a big down day (2σ)

Date (interval)	BTC	HOOD
2022-11-08	-10.01%	-19.04%
2022-11-09	-14.35%	-13.76%

Days when BTC had a big down day

Date (interval)	BTC	HOOD
2022-01-21	-10.38%	-5.19%
2022-05-06 → 2022-05-09	-15.94%	-6.13%
2022-06-10 → 2022-06-13	-22.68%	-7.43%
2022-06-16	-9.71%	-2.27%
2022-08-19	-10.06%	-8.95%
2022-09-13	-9.27%	-5.45%
2022-11-08	-10.01%	-19.04%
2022-11-09	-14.35%	-13.76%

Days when HOOD had a big down day

Date (interval)	BTC	HOOD
2022-05-11	-6.73%	-12.08%
2022-11-08	-10.01%	-19.04%
2022-11-09	-14.35%	-13.76%

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. Robinhood (2022)

Metric	BTC	HOOD
Total Return	-64.3%	-55.9%
Annualized Volatility	63.8%	82.9%
Sharpe Ratio	-1.38	-0.64
Sortino Ratio	-1.81	-0.96
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	-66.7%	-62.6%
Avg Correlation to S&P 500	N/A	N/A
5% VaR (daily log return)	-5.80%	-8.51%
5% Expected Shortfall (CVaR)	-9.10%	-10.76%
Skew	-0.59	0.48
Excess kurtosis	4.67	3.10
2σ tail days (down / up)	12 / 9	3 / 8

Audit this calculation

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

Inputs & conventions

Shared window for pair metrics: 2022-01-01 → 2022-12-31 (last shared close).
Rolling correlation sample (shared closes): N/A
Annualization (days/year): BTC: 365 days/year; HOOD: 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%.

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

BTC: ≈ -20.4%/yr

HOOD: ≈ -34.4%/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 Robinhood: Frequently Asked Questions

Which had higher volatility: BTC or HOOD?

HOOD showed higher volatility at 82.9% annualized, compared to 63.8% for BTC During 2022. Higher volatility meant larger price swings in both directions.

Did BTC provide diversification when held with HOOD?

BTC and HOOD were moderately correlated in 2022, with an average correlation of 0.48. This offered some diversification benefit, though they still tended to move together during major market moves.

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

During 2022, BTC's 5% VaR was -5.80% and its 5% Expected Shortfall was -9.10% (worst 19 days). HOOD's were -8.51% and -10.76% (worst 13 days).

Do BTC and HOOD crash together on bad days?

On shared dates (n=250), when HOOD has a 2σ down day, BTC also does 66.7% (2/3 days). In the other direction, when BTC has one, HOOD also does 25.0% (2/8 days).

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

Both assets posted negative Sharpe ratios During 2022 (HOOD -0.64 vs BTC -1.38), meaning both underperformed the risk-free rate; HOOD was less negative.

Could BTC and HOOD have been combined in a portfolio?

Yes, though allocation sizing mattered. Their moderate correlation offered some diversification benefits. HOOD's higher volatility (82.9%) meant even small allocations can materially impact overall portfolio risk.

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