How to Estimate a Portfolio’s Beta to BTC
Your portfolio's beta to BTC measures how much, on average, your holdings move when Bitcoin price fluctuates 1%. It is not a fixed number; it must be estimated from historical data. Here is how to calculate it yourself.
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1. Determine Your Calculation Benchmark
Beta is a relative metric, so you must first choose a reference. For a crypto asset portfolio, BTC is typically used as the benchmark because it serves as the central anchor of market sentiment and liquidity.
If you only hold BTC and stablecoins: the benchmark can be BTC itself.
If you hold multiple coins: you can use BTC or a market-cap-weighted crypto market composite index as the benchmark. A broad index may better reflect overall market swings. Which benchmark you choose determines what your beta value really means.
Key insight: different benchmarks produce different beta numbers. That does not mean one is wrong — it simply means the comparison target has changed.
2. Collect Historical Price Data
This is the most time-consuming step. The quality of your data directly determines whether the estimate is reliable.
What you need:
Historical prices for every asset in your portfolio (daily closing prices are recommended)
Historical prices for BTC (as the benchmark)
Data sources:
Export K-line data in CSV format from exchanges such as Gate.io or Binance
Export data for the selected time range from TradingView
Time window selection:
30 days: reflects recent conditions, high volatility, useful for short-term traders
90 days: balances short-term noise and medium-term trends; a commonly used compromise
180 days to 1 year: more stable, better suited for long-term allocation decisions
Academic research finds that crypto asset betas are extremely unstable — results can differ dramatically across different time windows. OLS linear regression has far lower explanatory power for future crypto beta than it does for US equities, because the signal-to-noise ratio in crypto markets is only about 36%, versus roughly 90% for US stocks. It is advisable to try at least two different windows (e.g., 90 days and 180 days) and compare whether they point in the same direction.
3. Calculate Return Series
Once you have price data, you cannot use prices directly to calculate beta. You must first convert prices into returns.
Daily return formula: Daily return = (Today's close ÷ Yesterday's close) – 1
Alternatively, use log returns: Log return = ln(Today's close ÷ Yesterday's close)
The two methods are equivalent in practice; pick one and stay consistent. The critical requirement is to use the same method and the same number of days for every asset in your portfolio and for BTC.
Align dates: ensure that all return series correspond exactly to the same days and the same frequency. If a particular asset has no data on a given day, remove that day from all series to avoid misalignment.
4. Calculate Each Asset's Beta
Calculate the beta of each holding relative to BTC individually.
Formula: Beta = Cov(asset returns, BTC returns) ÷ Var(BTC returns)
Cov is the covariance, measuring how much the asset's and BTC's returns "move together"
Var is the variance, measuring how much BTC fluctuates on its own
In practice, you can use Excel's SLOPE(asset returns, BTC returns) function; the slope is exactly the beta. You may also calculate it manually using the COVARIANCE.P and VAR.P functions.
5. Calculate the Portfolio's Overall Beta
Once you have each asset's individual beta, you need to weight and aggregate them.
Portfolio beta formula: Portfolio Beta = Σ(asset weight × asset beta)
Asset weight = Current market value of the asset ÷ Total portfolio market value
Include all holdings (including stablecoins and cash equivalents); their betas are typically close to 0
Example: You hold 50% ETH (beta = 1.3) and 50% USDC (beta ≈ 0). Portfolio beta = 0.5 × 1.3 + 0.5 × 0 = 0.65.
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6. Common Failure Reasons and Risk Reminders
Failure reason: using only a single time window and a single benchmark. Crypto asset betas shift with market cycles — Bitcoin's beta to the S&P 500 exceeded 4.0 during the risk-on period of 2020–2021, dropped to about 1.0 during the 2022 downturn, and returned to around 2.5 in 2024. Treating a one-off calculation as a "fixed characteristic" leads to decisions based on outdated assumptions.
Risk reminder: beta is a historical statistic, not a forward-looking promise. In extreme market conditions (e.g., the 2020 COVID crash), assets that were historically uncorrelated can suddenly plummet in sync, rendering the beta structure ineffective instantaneously. When using beta for hedging, pair it with stress testing and scenario analysis. Never rely solely on a single metric for risk management decisions.
How to confirm you have done it correctly:
After calculating, compare the portfolio's actual daily swings over the past week with BTC's daily swings. If your estimated beta is 1.3, the portfolio should theoretically move about 30% more than BTC. Check whether the last five days roughly match that proportion — if they do not align at all, your data window or calculation is likely wrong, and you need to re-check the alignment of your return series.
