Volatility of btc vs MSTR

Key Points

  • Research suggests BTC has a Sharpe ratio of approximately 1.30, while MSTR’s is around 1.49, based on recent data from Portfoliolab.
  • It seems likely that MSTR has a higher Sharpe ratio than BTC over the past year, though calculations can vary due to different methodologies.
  • The evidence leans toward MSTR offering better risk-adjusted returns, but this is controversial given observed price drops, suggesting potential discrepancies in data or time periods.

Sharpe Ratio Overview

The Sharpe ratio measures how much return an investment generates for the risk taken, calculated as (Expected Return – Risk-Free Rate) / Standard Deviation. For BTC and MSTR, this helps compare their performance over the past year, considering their volatility.

Comparison

Based on recent data from Portfoliolab (MSTR vs. BTC-USD comparison tool), BTC’s Sharpe ratio is approximately 1.30, while MSTR’s is around 1.49. This suggests MSTR has provided better risk-adjusted returns, despite its price volatility.

Unexpected Detail: Discrepancy in Calculations

Despite the higher Sharpe ratio for MSTR from Portfoliolab, my calculations using price data from March 4, 2024, to March 4, 2025, show MSTR with a negative Sharpe ratio due to a significant price drop, highlighting potential differences in how returns and volatility are measured.

Survey Note: Detailed Analysis of Sharpe Ratio for BTC vs. MSTR

This note provides a comprehensive examination of the Sharpe ratio comparison between Bitcoin (BTC) and MicroStrategy (MSTR), drawing from recent data and market analyses as of March 4, 2025. The Sharpe ratio, a measure of risk-adjusted return, is calculated as the difference between the expected return and the risk-free rate, divided by the standard deviation of the returns. This metric is crucial for investors assessing whether the returns of an asset justify its volatility, particularly for high-risk assets like BTC and MSTR.

Background and Context

Bitcoin, a decentralized cryptocurrency, and MicroStrategy, a company heavily invested in Bitcoin, both exhibit significant volatility, making the Sharpe ratio a valuable tool for comparison. MSTR’s strategy of leveraging debt and equity to acquire Bitcoin amplifies its price movements, potentially affecting its risk-adjusted returns compared to BTC. The analysis focuses on the past year of trading data to ensure relevance to current market conditions.

Sharpe Ratio Calculation and Data Sources

The Sharpe ratio is given by the formula:

[ \text{Sharpe Ratio} = \frac{\text{Expected Return} – \text{Risk-Free Rate}}{\text{Standard Deviation of Return}} ]

To calculate this, we need the expected return (typically the average return over a period), the risk-free rate (often the yield on a 1-year US Treasury bill), and the standard deviation (a measure of volatility). Data was sourced from financial platforms like Portfoliolab, TradingView, and MacroTrends, with cross-referencing to ensure accuracy.

Bitcoin (BTC) Sharpe Ratio Analysis

For BTC, the expected return over the past year was estimated based on price data. On March 4, 2024, BTC’s price was approximately $67,385.25, and by March 4, 2025, it was around $88,000, yielding a return of approximately 30.6%. The risk-free rate, based on the current 1-year US Treasury bill rate of around 4.2% (MacroTrends 1 Year Treasury Rate), was used. The standard deviation (volatility) was initially calculated using Bitbo.io’s 30-day volatility of 2.09%, annualized to approximately 33.1% (σ_annual = σ_daily * sqrt(252), where σ_daily = 0.0209 and sqrt(252) ≈ 15.87). This gave a Sharpe ratio of (30.6% – 4.2%) / 33.1% ≈ 0.80.

However, Portfoliolab (Bitcoin (BTC-USD) Stock Analysis) reports a Sharpe ratio of 1.14 for BTC over the past year, implying a standard deviation of approximately 23.16% (calculated as (30.6% – 4.2%) / 1.14 ≈ 23.16%). This discrepancy suggests Portfoliolab may use a different methodology, possibly monthly returns or a different time frame, leading to a lower volatility estimate.

MicroStrategy (MSTR) Sharpe Ratio Analysis

For MSTR, the expected return was calculated using historical stock prices. On March 1, 2024, MSTR’s price was approximately $577, and by March 4, 2025, it was around $260, indicating a return of approximately -54.94%. Using the same risk-free rate of 4.2%, the initial calculation required the standard deviation. Portfoliolab (MicroStrategy Incorporated (MSTR) Stock Analysis) reports a 1-year volatility of 72.14%, leading to a Sharpe ratio of (-54.94% – 4.2%) / 72.14% ≈ -0.82, reflecting the significant price drop.

However, Portfoliolab’s comparison tool (MSTR vs. BTC-USD comparison tool) shows MSTR’s Sharpe ratio as 1.49 and BTC’s as 1.30, suggesting a positive return for MSTR over their chosen period. This inconsistency may arise from different time frames or calculation methods, as their individual MSTR page from November 8, 2024, reports a Sharpe ratio of 3.60, further complicating the comparison.

Comparison and Discrepancies

The table below summarizes the Sharpe ratios from different sources:

AssetSharpe Ratio (My Calculation)Sharpe Ratio (Portfoliolab Comparison)Sharpe Ratio (Portfoliolab Individual)
BTC0.801.301.14
MSTR-0.821.493.60

This table highlights significant variations. My calculations, based on price data, show BTC with a Sharpe ratio of 0.80 and MSTR with -0.82, aligning with observed price movements. However, Portfoliolab’s data suggests MSTR has a higher Sharpe ratio (1.49 or 3.60), which contradicts the price drop from $577 to $260, indicating potential differences in data periods or methodologies.

Implications for Investors

For investors, a higher Sharpe ratio indicates better risk-adjusted returns. Based on Portfoliolab’s comparison tool, MSTR (1.49) outperforms BTC (1.30), suggesting MSTR compensates for its higher volatility with returns. However, my calculations suggest MSTR’s negative Sharpe ratio reflects its risk, given the price decline. This discrepancy underscores the importance of understanding the time frame and calculation method, as market conditions can significantly impact results.

Unexpected Detail: Leverage Impact

An interesting aspect is MSTR’s leverage strategy, using debt to acquire Bitcoin, which amplifies both returns and volatility. This could explain Portfoliolab’s higher Sharpe ratio for MSTR if their data captures periods of significant Bitcoin price increases, offsetting the recent drop. This complexity adds layers to MSTR’s risk profile, not fully mirrored by BTC’s direct exposure.

Conclusion

Based on Portfoliolab’s recent comparison tool, MSTR has a Sharpe ratio of 1.49 and BTC has 1.30, suggesting MSTR offers better risk-adjusted returns. However, my calculations using price data from March 4, 2024, to March 4, 2025, show MSTR with a negative Sharpe ratio, highlighting potential discrepancies. Investors should consider multiple sources and understand the specific time frames and methodologies, as these can significantly affect the Sharpe ratio, especially for volatile assets like BTC and MSTR.

Key Citations

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