Beta Coefficient Calculator — Crypto vs Benchmark
Measure how strongly a crypto asset moves with a benchmark — solve β from covariance and variance, or paste your own return or price history for a full regression with a scatter plot.
The line's slope is β. Dashed line: a β = 1 asset that moves one-for-one with the benchmark.
Each dot is one period (returns in %). The amber line is the fitted regression; its slope is β.
How to Use This Calculator
- Basic: choose β, Cov or Var to solve for, and enter the other two values (in %² or decimal²).
- Advanced: paste paired asset and benchmark data — returns or prices — one period per line.
- Set the data type and basis — percent returns, decimal returns or prices; sample or population statistics.
- Optionally add a risk-free rate and expected benchmark return to see the CAPM expected return.
- Read the graphs and tables — the response line, scatter plot, conversions and regression statistics.
What This Tool Offers
- ✓Solve for β, Cov or Var from the same relationship.
- ✓Paste real data — returns or prices — for any crypto and any benchmark.
- ✓Unit conversion between %² and decimal², plus % move tables.
- ✓Two graphs — asset response line and a scatter plot with regression fit.
- ✓Full statistics — correlation, R², alpha, standard error, t-stat and CAPM return.
What is beta?
Beta measures how sensitive an asset's returns are to the returns of a benchmark. A β of 1 means the asset tends to move one-for-one with the benchmark, above 1 means it amplifies the benchmark's moves, and below 1 means it dampens them. A negative β means it tends to move the opposite way. For crypto, common benchmarks are Bitcoin (for altcoins) or a broad equity index (for Bitcoin itself).
Formula
Equivalently β = ρ · σₐ / σₘ, where ρ is the correlation between the two return series. Beta is also the slope of the regression of asset returns on benchmark returns.
| Symbol | Meaning |
|---|---|
| β | Beta coefficient — sensitivity of the asset to the benchmark |
| Cov(Rₐ, Rₘ) | Covariance between asset and benchmark returns |
| Var(Rₘ) | Variance of the benchmark's returns |
| ρ | Correlation between asset and benchmark returns |
| σₐ, σₘ | Standard deviations of asset and benchmark returns |
| α | Alpha — return unexplained by the benchmark (regression intercept) |
Reference: interpreting beta
| β | Interpretation |
|---|---|
| < 0 | Tends to move opposite to the benchmark |
| 0 | No linear relationship with the benchmark |
| 0 – 1 | Moves with the benchmark, but less strongly |
| 1 | Moves in step with the benchmark |
| > 1 | Amplifies benchmark moves (higher risk and potential return) |
Reference: unit conversion
| From | To | Factor |
|---|---|---|
| Return in % | Return in decimal | ÷ 100 |
| Variance / covariance in %² | decimal² | ÷ 10,000 |
| Standard deviation in % | decimal | ÷ 100 |
Frequently asked questions
It depends on the question. Bitcoin is a common benchmark for altcoins, a broad crypto index measures market-wide sensitivity, and an equity index shows how the asset relates to traditional markets. The same asset can have very different betas against different benchmarks.
Yes. Beta estimated from daily, weekly or monthly returns, or over different windows, can differ a lot — especially in crypto, where relationships shift quickly. Use the same frequency for both series and check the standard error.
No. Correlation only measures how tightly the two series move together (−1 to +1); beta also scales by the asset's volatility relative to the benchmark: β = ρ·σₐ/σₘ.
For education and analysis only — not investment advice. Historical beta does not guarantee future behaviour.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| β | Beta coefficient | |
| Cov(Asset, Benchmark) | Covariance between asset and benchmark returns | |
| Var(Benchmark) | Variance of benchmark returns |
What it means
Beta measures an asset’s volatility relative to a benchmark (e.g., Bitcoin or a market index). A β > 1 means the asset moves more than the benchmark; β < 1 means less. This is used to assess systematic risk and to set target allocations. Understanding beta helps investors manage portfolio risk and to understand how assets behave in relation to the market.
Worked example
Beta Coefficient – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| Covariance | 0.045 |
| Benchmark Variance | 0.030 |
| Parameter | Value |
|---|---|
| Cov | 0.020 |
| Var | 0.030 |
Common mistakes
- Beta: Measures asset’s volatility relative to a benchmark (e.g., BTC).
- Cov(Asset, Benchmark): Covariance between asset and benchmark returns.
- Var(Benchmark): Variance of benchmark returns.
- β >1: More volatile than benchmark; β <1: less volatile.
Applications
Beta coefficient (crypto vs benchmark) measures the sensitivity of an asset's returns to the market benchmark. A beta > 1 indicates higher volatility than the market, and < 1 indicates lower. Investors use beta to assess systematic risk and to build diversified portfolios. In crypto, beta relative to Bitcoin or an index is common. Understanding beta helps in risk management and in asset allocation.
- Assessing the systematic risk of a crypto asset
- Constructing diversified portfolios with target beta
- Hedging strategies and risk reduction
- Comparing asset volatility to the broader market
- Educational understanding of market sensitivity
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