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Bitcoin vs Gold (BTC vs XAU): Returns, Risk & Volatility (2022)

Published:

Last updated:

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

Gale Finance Team
Written by Gale Finance Team
Sid Kalla
Reviewed by Sid Kalla CFA Charterholder
BTC Total Return
↓ -64.3%
XAU Total Return
↑ +1.2%

Relative Performance of BTC vs XAU (Normalized to 100)

BTC XAU

Normalized to 100 at start date for comparison

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Key Takeaways

  • Total Return: BTC delivered a -64.3% total return, while XAU returned +1.2% over the same period. XAU outperformed on total returns.
  • Risk-Adjusted Return (Sharpe Ratio): Both Sharpe ratios were negative (XAU -0.15 vs BTC -1.42), meaning both underperformed the risk-free rate; XAU was less negative.
  • Volatility (Annualized): BTC was more volatile, with 63.5% annualized volatility, versus 14.8% for XAU.
  • Maximum Drawdown: XAU's maximum drawdown was -20.8%, 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%; XAU's were -1.61% and -1.98%. VaR is the cutoff; Expected Shortfall is the average move on the worst days.
  • Skew & Kurtosis: Skew: BTC -0.60 vs XAU 0.04. Excess kurtosis: BTC 4.67 vs XAU 0.78. Negative skew leans downside; higher excess kurtosis means fatter tails.
  • Tail Days & Extremes: 2σ tail days (down/up): BTC 12/9, XAU 5/9. Worst day: BTC -15.97% (2022-06-13) vs XAU -2.83% (2022-03-09). Best day: BTC +14.54% (2022-02-28) vs XAU +3.13% (2022-11-04).
  • Risk ratios: Sortino - BTC: -1.86 vs. XAU: -0.21 , Calmar - BTC: -0.98 vs. XAU: 0.06 , Sterling - BTC: -1.05 vs. XAU: -0.16 , Treynor - BTC: -0.59 vs. XAU: -0.18 , Ulcer Index - BTC: 46.11% vs. XAU: 12.21%
Scorecard:BTC vs XAU: 10-Year Historical
Assets:Bitcoin (BTC)·Gold (XAU)
Related:BNB vs Bitcoin·Bitcoin vs Coinbase·Bitcoin vs Ethereum
Live:BTC vs XAU (rolling)

Investment Comparison

If you invested $10,000 in each asset on January 1, 2022:

BTC $3,573.667 -64.3%
XAU $10,123.021 +1.2%

Difference: $6,549.354 (XAU ahead)

Bitcoin vs Gold Correlation

Average Correlation
weakly correlated
0.17
Current (30-day) 0.36
30-day rolling range -0.46 to +0.65

Bitcoin and Gold were weakly correlated in 2022. With a correlation of 0.17, these assets showed meaningful independence, offering diversification benefits when held together.

For portfolio construction, this weak correlation suggests that combining BTC and XAU could reduce overall portfolio variance. However, correlations can increase during market stress.

Metric Value
Current (30-day) 0.36
Average (full period) 0.17
Minimum (30-day rolling) -0.46
Maximum (30-day rolling) 0.65

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. Current, minimum, and maximum figures are 30-day rolling correlations on shared daily returns.

Drawdown

Maximum Drawdown
BTC
-66.7%
XAU
-20.8%

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.

Gold experienced its maximum drawdown of -20.8% from 2022-03-08 to 2022-09-26. It has not yet recovered to its previous peak.

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

Risk-adjusted ratios

Sharpe Ratio of BTC and XAU

Sharpe Ratio: BTC vs. XAU

Return per total volatility

Sharpe gives us excess return per unit of risk. Upside and downside volatility both count as risk.

Higher is better
Excess return Annualized volatility 0 75% vol 63.5% · excess -90.1% vol 14.8% · excess -2.2%
excess return / total volatility
Formula Sharpe=E[R]−RfσR\displaystyle \mathrm{Sharpe} = \frac{\mathbb{E}[R] - R_f}{\sigma_R}

Sharpe ratio measures return per unit of risk (volatility). A higher Sharpe indicates better risk-adjusted performance. Both Sharpe ratios were negative (XAU -0.15 vs BTC -1.42), meaning both underperformed the risk-free rate; XAU 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 XAU

Sortino Ratio: BTC vs. XAU

Return per downside volatility

Sortino keeps the return-over-risk idea, but only returns below the target rate count as volatility.

Higher is better
Frequency (days) Daily return (%) target -17.2% +15.8% 96 0
excess return / downside volatility
Formula Sortino=E[R]−Rfσdown\displaystyle \mathrm{Sortino} = \frac{\mathbb{E}[R] - R_f}{\sigma_{\mathrm{down}}}

Sortino ratio measures return per unit of downside risk. Unlike Sharpe, it only counts downside deviation (returns below the target return). XAU 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 48.4% vs XAU 10.5%. 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).

Calmar Ratio of BTC and XAU

Calmar Ratio: BTC vs. XAU

CAGR per worst drawdown

Calmar compares CAGR against the single deepest peak-to-trough loss over the period.

Higher is better
0% BTC -65.4% -66.9% XAU +1.2% -20.8%
CAGR / max drawdown
Formula Calmar=CAGR∣MaxDD∣\displaystyle \mathrm{Calmar} = \frac{\mathrm{CAGR}}{|\mathrm{MaxDD}|}

Calmar ratio compares CAGR to maximum drawdown. Higher Calmar means more return per unit of worst drawdown. XAU posted the higher Calmar ratio.

Calmar is computed on each asset's full 365-day lookback and uses the max drawdown over that same window.

Sterling Ratio of BTC and XAU

Sterling Ratio: BTC vs. XAU

Return per average drawdown

Sterling smooths the drawdown penalty by using average drawdown events instead of only the worst one.

Higher is better
0% -18% -35% -53% -70% 10% drawdown threshold
excess annual return / average deep drawdown
Formula Sterling=CAGR−RfD‾>10%\displaystyle \mathrm{Sterling} = \frac{\mathrm{CAGR} - R_f}{\overline{D}_{>10\%}}

Sterling ratio measures excess return per unit of average drawdown (typically drawdowns worse than 10%). XAU posted the higher Sterling ratio.

Sterling uses average drawdown events deeper than 10% and subtracts the risk-free rate to report excess return.

Treynor Ratio of BTC and XAU

Treynor Ratio: BTC vs. XAU

Excess return per market beta

Treynor divides excess annualized return by beta — the sensitivity of the asset to broad-market moves. The slope shown is each asset’s beta vs SPY.

Higher is better
Asset return Market return 0 0 β 1.48 β 0.12
excess return / market beta
Formula Treynor=E[R]−Rfβ\displaystyle \mathrm{Treynor} = \frac{\mathbb{E}[R] - R_f}{\beta}

Treynor ratio measures excess return per unit of market risk (beta) instead of total volatility. XAU posted the higher Treynor ratio.

Treynor uses beta vs the S&P 500 (SPY) on shared dates and the average 3-month Treasury rate as the risk-free rate.

Ulcer Index of BTC and XAU

Ulcer Index: BTC vs. XAU

Drawdown pain

Ulcer Index is a risk index, not a return-over-risk ratio. Lower means smaller and shorter drawdowns.

Lower is better
0% -18% -35% -53% -70%
root-mean-square drawdown
Formula UI=E[Dt2]\displaystyle \mathrm{UI} = \sqrt{\mathbb{E}[D_t^2]}

Ulcer Index captures drawdown depth and duration. Lower Ulcer Index means less drawdown pain. XAU had the lower Ulcer Index (less drawdown pain).

Ulcer Index is computed from each asset's drawdown series over the full lookback window.

Tail Risk & Distribution Shape (2022): Bitcoin vs. Gold

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⁡(PtPt−1)\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.

Tail Risk & Distribution Shape: BTC vs. XAU (2022)

Actual daily return tails

The bars are real daily log-return observations from the article window. Darker bars are observations at or beyond each asset’s 5% VaR cutoff.

Observed returns
BTC VaR 5% ES 5% XAU VaR 5% ES 5% -20.1% 0% +20.1% Daily log return
VaR marks the 5th percentile loss cutoff; Expected Shortfall averages the observations beyond that cutoff.
Formula VaR5%=Q0.05(rt),ES5%=E[rt∣rt≤VaR5%]\displaystyle \mathrm{VaR}_{5\%}=Q_{0.05}(r_t),\quad \mathrm{ES}_{5\%}=\mathbb{E}[r_t\mid r_t\le \mathrm{VaR}_{5\%}]
Metric (2022) BTC XAU
5% VaR (daily log return) -5.80% -1.61%
5% Expected Shortfall (CVaR) -9.10% (worst 19 days) -1.98% (worst 13 days)
Skew -0.60 0.04
Excess kurtosis 4.67 0.78
2σ tail days (down / up) 12 / 9 5 / 9
Worst day -15.97% (2022-06-13) -2.83% (2022-03-09)
Best day +14.54% (2022-02-28) +3.13% (2022-11-04)

Downside co-moves (2σ) — 2022

Computed on shared dates only (n=257). 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.

Downside co-move map: BTC vs. XAU (2σ)

Shared-close daily returns

Dots mark actual downside days: asset-colored dots are one-sided downside moves, and red dots are joint downside days. Grey dots add sampled shared-return context when available. The shaded lower-left zone shows where both BTC and XAU crossed their own 2σ downside threshold.

2σ
-2σ XAU -2σ BTC Joint downside zone -3.3% 0% +3.3% +29.3% 0% -29.3% XAU daily log return BTC daily log return
Shared daily return 257
BTC Downside threshold -8.55%
XAU Downside threshold -1.86%
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 XAU had a big down day (2σ)

Date (interval) BTC XAU
2022-06-10 → 2022-06-13 -22.68% -2.80%

Days when BTC had a big down day

Date (interval) BTC XAU
2022-01-21 -10.38% -0.43%
2022-05-06 → 2022-05-09 -15.94% -1.44%
2022-06-10 → 2022-06-13 -22.68% -2.80%
2022-06-16 -9.71% +1.25%
2022-08-19 -10.06% -0.67%
2022-09-13 -9.27% -1.28%
2022-11-08 -10.01% +2.21%
2022-11-09 -14.35% -0.31%

Days when XAU had a big down day

Date (interval) BTC XAU
2022-03-09 +8.38% -2.83%
2022-03-15 -0.83% -1.92%
2022-06-10 → 2022-06-13 -22.68% -2.80%
2022-07-05 -0.20% -2.39%
2022-09-15 -2.67% -1.94%

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. Gold (2022)

Metric BTC XAU
Total Return -64.3% +1.2%
Annualized Volatility 63.5% 14.8%
Sharpe Ratio -1.42 -0.15
Sortino Ratio -1.86 -0.21
Calmar Ratio -0.98 0.06
Sterling Ratio -1.05 -0.16
Treynor Ratio -0.59 -0.18
Ulcer Index 46.11% 12.21%
Max Drawdown -66.7% -20.8%
Avg Correlation to S&P 500 N/A N/A
5% VaR (daily log return) -5.80% -1.61%
5% Expected Shortfall (CVaR) -9.10% -1.98%
Skew -0.60 0.04
Excess kurtosis 4.67 0.78
2σ tail days (down / up) 12 / 9 5 / 9
Audit this calculation

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

Inputs & conventions

Shared window for pair metrics
2022-01-03 → 2022-12-30 (last shared close).
Rolling correlation sample (shared closes)
228 rolling 30-day values (from 257 shared daily returns).
Annualization (days/year)
BTC: 365 days/year; XAU: 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% over 2022-01-01 → 2022-12-31.
  • XAU: 4.50% over 2022-01-03 → 2022-12-30.
Volatility drag (rule of thumb)
Estimated from annualized volatility (simple returns). For the log-return framing, see Log returns.
  • BTC: ≈ -20.2%/yr
  • XAU: ≈ -1.1%/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
rt=PtPt−1−1r_t = \frac{P_t}{P_{t-1}} - 1
Volatility
σann=σ(rt)A\sigma_{ann} = \sigma(r_t)\sqrt{A}
Volatility drag (approx.)
drag≈12σann2\text{drag} \approx \tfrac{1}{2}\sigma_{ann}^2
Sharpe Ratio
S=A rˉ−rfσ(rt)AS = \frac{A\,\bar{r} - r_f}{\sigma(r_t)\sqrt{A}}
Sortino Ratio
So=A rˉ−rfE[min⁡(0, rt−rf/A)2] ASo = \frac{A\,\bar{r} - r_f}{\sqrt{\mathbb{E}[\min(0,\,r_t - r_f/A)^2]}\,\sqrt{A}}
Maximum Drawdown
MDD=min⁡t(Ptmax⁡s≤tPs−1)MDD = \min_t\left(\frac{P_t}{\max_{s \le t} P_s} - 1\right)
Average Correlation
ρ=cov⁡(rA, rB)σA σB\rho = \frac{\operatorname{cov}(r^A,\,r^B)}{\sigma_A\,\sigma_B}
Log returns
ℓt=ln⁡(PtPt−1)\ell_t = \ln\left(\frac{P_t}{P_{t-1}}\right)
Notation
PtP_t
Price on day t.
rtr_t
Simple daily return.
ℓt\ell_t
Log daily return.
rˉ\bar{r}
Average daily return.
σ(rt)\sigma(r_t)
Standard deviation of daily returns.
AA
Annualization factor (days/year).
rfr_f
Annual risk-free rate.

Bitcoin vs Gold: Frequently Asked Questions

Which had higher volatility: BTC or XAU?

BTC showed higher volatility at 63.5% annualized, compared to 14.8% for XAU During 2022. Higher volatility meant larger price swings in both directions.

Did BTC provide diversification when held with XAU?

BTC and XAU were weakly correlated in 2022, with an average correlation of 0.17. This weak correlation suggested meaningful diversification benefits when held together.

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

During 2022, BTC's 5% VaR was -5.80% and its 5% Expected Shortfall was -9.10% (worst 19 days). XAU's were -1.61% and -1.98% (worst 13 days).

Do BTC and XAU crash together on bad days?

On shared dates (n=257), when XAU has a 2σ down day, BTC also does 20.0% (1/5 days). In the other direction, when BTC has one, XAU also does 12.5% (1/8 days).

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

Both assets posted negative Sharpe ratios During 2022 (XAU -0.15 vs BTC -1.42), meaning both underperformed the risk-free rate; XAU was less negative.

Could BTC and XAU have been combined in a portfolio?

Yes, though allocation sizing mattered. Their weak correlation could have meaningfully reduced overall portfolio variance. BTC's higher volatility (63.5%) meant even small allocations can materially impact overall portfolio risk.

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