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MicroStrategy vs Bitcoin (MSTR vs BTC): Returns, Risk & Volatility (2023)

Published:

Last updated:

Analysis period: 2023-01-01 to 2023-12-31

Gale Finance Team
Written by Gale Finance Team
Sid Kalla
Reviewed by Sid Kalla CFA Charterholder
MSTR Total Return
↑ +335.5%
BTC Total Return
↑ +152.2%

Relative Performance of MSTR vs BTC (Normalized to 100)

MSTR BTC

Normalized to 100 at start date for comparison

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Key Takeaways

  • Total Return: MSTR delivered a +335.5% total return, while BTC returned +152.2% over the same period. MSTR outperformed on total returns.
  • Risk-Adjusted Return (Sharpe Ratio): MSTR had a higher Sharpe (2.34 vs 2.25), indicating better risk-adjusted performance.
  • Volatility (Annualized): MSTR was more volatile, with 73.1% annualized volatility, versus 43.9% for BTC.
  • Maximum Drawdown: BTC's maximum drawdown was -20.1%, while MSTR experienced a deeper drawdown of -35.7%.
  • Tail Risk (VaR & Expected Shortfall): At the 5% level (daily log returns), MSTR's VaR was -6.58% and its Expected Shortfall (CVaR) was -8.68%; BTC's were -3.11% and -4.52%. VaR is the cutoff; Expected Shortfall is the average move on the worst days.
  • Skew & Kurtosis: Skew: MSTR 0.26 vs BTC 0.69. Excess kurtosis: MSTR 0.40 vs BTC 2.93. Negative skew leans downside; higher excess kurtosis means fatter tails.
  • Tail Days & Extremes: 2σ tail days (down/up): MSTR 8/9, BTC 10/17. Worst day: MSTR -9.81% (2023-05-08) vs BTC -7.10% (2023-08-17). Best day: MSTR +16.22% (2023-03-13) vs BTC +10.31% (2023-10-23).
  • Risk ratios: Sortino - MSTR: 4.03 vs. BTC: 3.93 , Calmar - MSTR: 9.68 vs. BTC: 7.75 , Sterling - MSTR: 12.92 vs. BTC: 8.04 , Treynor - MSTR: 0.75 vs. BTC: 1.81 , Ulcer Index - MSTR: 15.11% vs. BTC: 8.62%
Assets:Bitcoin (BTC)
Related:Marathon Digital vs MicroStrategy·MicroStrategy vs Bitcoin·MicroStrategy vs iShares Bitcoin Trust ETF
Live:MSTR vs BTC (rolling)

Investment Comparison

If you invested $10,000 in each asset on January 1, 2023:

MSTR $43,553.993 +335.5%
BTC $25,224.861 +152.2%

Difference: $18,329.132 (MSTR ahead)

MicroStrategy vs Bitcoin Correlation

Average Correlation
strongly correlated
0.73
Current (30-day) 0.74
30-day rolling range +0.50 to +0.88

MicroStrategy and Bitcoin were strongly correlated in 2023. With a correlation of 0.73, these assets tended to move together, limiting diversification benefits.

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

Metric Value
Current (30-day) 0.74
Average (full period) 0.73
Minimum (30-day rolling) 0.50
Maximum (30-day rolling) 0.88

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
MSTR
-35.7%
BTC
-20.1%

MicroStrategy experienced its maximum drawdown of -35.7% from 2023-02-15 to 2023-03-10. It has not yet recovered to its previous peak.

Bitcoin experienced its maximum drawdown of -20.1% from 2023-07-13 to 2023-09-11. 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 MSTR and BTC

Sharpe Ratio: MSTR vs. BTC

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 0 100% vol 73.1% · excess +171.0% vol 43.9% · excess +98.8%
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. MSTR had a higher Sharpe (2.34 vs 2.25), 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 MSTR and BTC

Sortino Ratio: MSTR vs. BTC

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 -10.9% +17.3% 98 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). MSTR 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: MSTR 42.4% vs BTC 25.1%. 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 MSTR and BTC

Calmar Ratio: MSTR vs. BTC

CAGR per worst drawdown

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

Higher is better
0% MSTR +345.0% -35.6% BTC +155.4% -20.1%
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. MSTR 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 MSTR and BTC

Sterling Ratio: MSTR vs. BTC

Return per average drawdown

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

Higher is better
0% -9% -19% -28% -37% 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%). MSTR 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 MSTR and BTC

Treynor Ratio: MSTR vs. BTC

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 2.28 β 0.55
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. BTC 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 MSTR and BTC

Ulcer Index: MSTR vs. BTC

Drawdown pain

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

Lower is better
0% -9% -19% -28% -37%
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. BTC 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 (2023): MicroStrategy vs. Bitcoin

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: MSTR vs. BTC (2023)

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
MSTR VaR 5% ES 5% BTC VaR 5% ES 5% -17.3% 0% +17.3% 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 (2023) MSTR BTC
5% VaR (daily log return) -6.58% -3.11%
5% Expected Shortfall (CVaR) -8.68% (worst 13 days) -4.52% (worst 19 days)
Skew 0.26 0.69
Excess kurtosis 0.40 2.93
2σ tail days (down / up) 8 / 9 10 / 17
Worst day -9.81% (2023-05-08) -7.10% (2023-08-17)
Best day +16.22% (2023-03-13) +10.31% (2023-10-23)

Downside co-moves (2σ) — 2023

Computed on shared dates only (n=249). 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: MSTR vs. BTC (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 MSTR and BTC crossed their own 2σ downside threshold.

2σ
-2σ BTC -2σ MSTR Joint downside zone -10.3% 0% +10.3% +15.3% 0% -15.3% BTC daily log return MSTR daily log return
Shared daily return 249
MSTR Downside threshold -8.48%
BTC Downside threshold -5.46%
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 MSTR and BTC had a big down day (2σ)

Date (interval) MSTR BTC
2023-03-09 -9.41% -6.24%
2023-05-05 → 2023-05-08 -9.81% -6.23%
2023-06-02 → 2023-06-05 -8.53% -5.47%

Days when MSTR had a big down day

Date (interval) MSTR BTC
2023-02-09 -9.76% -4.88%
2023-02-17 → 2023-02-21 -8.21% -0.53%
2023-03-09 -9.41% -6.24%
2023-03-10 -8.92% -0.86%
2023-03-22 -9.70% -3.08%
2023-05-05 → 2023-05-08 -9.81% -6.23%
2023-05-11 -8.80% -2.25%
2023-06-02 → 2023-06-05 -8.53% -5.47%

Days when BTC had a big down day

Date (interval) MSTR BTC
2023-03-09 -9.41% -6.24%
2023-05-05 → 2023-05-08 -9.81% -6.23%
2023-06-02 → 2023-06-05 -8.53% -5.47%
2023-08-17 -6.19% -7.10%
2023-12-08 → 2023-12-11 -7.27% -6.62%

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 MicroStrategy vs. Bitcoin (2023)

Metric MSTR BTC
Total Return +335.5% +152.2%
Annualized Volatility 73.1% 43.9%
Sharpe Ratio 2.34 2.25
Sortino Ratio 4.03 3.93
Calmar Ratio 9.68 7.75
Sterling Ratio 12.92 8.04
Treynor Ratio 0.75 1.81
Ulcer Index 15.11% 8.62%
Max Drawdown -35.7% -20.1%
Avg Correlation to S&P 500 N/A N/A
5% VaR (daily log return) -6.58% -3.11%
5% Expected Shortfall (CVaR) -8.68% -4.52%
Skew 0.26 0.69
Excess kurtosis 0.40 2.93
2σ tail days (down / up) 8 / 9 10 / 17
Audit this calculation

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

Inputs & conventions

Shared window for pair metrics
2023-01-03 → 2023-12-29 (last shared close).
Rolling correlation sample (shared closes)
220 rolling 30-day values (from 249 shared daily returns).
Annualization (days/year)
MSTR: 252 days/year; BTC: 365 days/year.
Risk-free rate
Uses the 3-month U.S. Treasury yield (FRED: DGS3MO), averaged over each asset’s window:
  • MSTR: 4.50% over 2023-01-03 → 2023-12-29.
  • BTC: 4.50% over 2023-01-01 → 2023-12-30.
Volatility drag (rule of thumb)
Estimated from annualized volatility (simple returns). For the log-return framing, see Log returns.
  • MSTR: ≈ -26.7%/yr
  • BTC: ≈ -9.6%/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.

MicroStrategy vs Bitcoin: Frequently Asked Questions

Which had higher volatility: MSTR or BTC?

MSTR showed higher volatility at 73.1% annualized, compared to 43.9% for BTC During 2023. Higher volatility meant larger price swings in both directions.

Did MSTR provide diversification when held with BTC?

MSTR and BTC were strongly correlated in 2023, with an average correlation of 0.73. This strong correlation limited diversification benefits.

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

During 2023, MSTR's 5% VaR was -6.58% and its 5% Expected Shortfall was -8.68% (worst 13 days). BTC's were -3.11% and -4.52% (worst 19 days).

Do MSTR and BTC crash together on bad days?

On shared dates (n=249), when BTC has a 2σ down day, MSTR also does 60.0% (3/5 days). In the other direction, when MSTR has one, BTC also does 37.5% (3/8 days).

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

MSTR showed better risk-adjusted performance with a Sharpe ratio of 2.34 versus BTC's 2.25 During 2023.

Could MSTR and BTC have been combined in a portfolio?

Yes, though allocation sizing mattered. Their strong correlation provided limited risk reduction since they tended to move together. MSTR's higher volatility (73.1%) meant even small allocations can materially impact overall portfolio risk.

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