Beta Calculator
Calculate a stock or asset beta from its correlation with the market, standard deviation, and market volatility.
Beta (β)
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Asset Move per 10% Market Change
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R² (Market Explanation)
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Calculation Details
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How to use this calculator
Enter the Correlation between the asset and the market (a number between −1.0 and +1.0), the Asset Standard Deviation (annual volatility of the asset’s returns), and the Market Standard Deviation (use ~15% for the S&P 500 as a baseline).
The calculator returns:
- Beta (β): the asset’s systematic market sensitivity
- Asset Move per 10% Market Change: practical interpretation of beta
- R²: how much of the asset’s variance is explained by the market
A growth stock: correlation 0.80 with S&P 500, asset SD 25%, market SD 15%
Beta = 0.80 × (25% / 15%) = 0.80 × 1.667 = 1.333
A 10% market move implies a ~13.3% move in this stock. R² = 0.80² = 64%, meaning 64% of the stock’s volatility is market-driven; 36% is company-specific.
The beta formula
Where:
- ρ (rho) = Pearson correlation between asset and market returns
- σ_asset = Standard deviation of the asset’s returns
- σ_market = Standard deviation of the market’s returns
This is mathematically equivalent to:
The two forms are identical because: Cov(X,Y) = ρ × σ_X × σ_Y, and Var(Y) = σ_Y²
The correlation × volatility ratio form is more intuitive: it separates how related the asset is to the market (correlation) from how volatile it is relative to the market (volatility ratio).
The two components of beta
Correlation (ρ): Ranges from −1.0 to +1.0. Measures the direction and strength of the market relationship. High correlation: moves are mostly in the same direction. Near zero: moves are largely unrelated. Negative: tends to move opposite to the market.
Volatility ratio (σ_asset / σ_market): Amplifies or dampens the correlation signal. A stock with twice the market’s volatility and correlation 0.8 has beta = 1.6. A bond with the same volatility but correlation 0.1 has beta = 0.1.
Building intuition:
| Correlation | Volatility Ratio | Beta | Asset Type Example |
|---|---|---|---|
| 0.9 | 1.5 | 1.35 | High-beta tech stock |
| 0.8 | 1.0 | 0.80 | Blue-chip stock |
| 0.5 | 0.8 | 0.40 | Utility stock |
| 0.1 | 0.5 | 0.05 | Investment-grade bond |
| −0.1 | 0.5 | −0.05 | Gold |
| 0.7 | 2.0 | 1.40 | Leveraged sector ETF |
How R-squared tells you whether your beta is worth trusting
R-squared (R²) = correlation² tells you what fraction of the asset’s variance is explained by the market. It is the quality metric for beta.
| R² Value | Interpretation |
|---|---|
| 90–100% | Almost all movement is market-driven; beta is highly reliable |
| 70–89% | Strong market relationship; beta is reliable |
| 50–69% | Moderate relationship; beta is meaningful but not dominant |
| 30–49% | Weak relationship; company-specific factors matter as much |
| Below 30% | Poor market fit; beta is unreliable as a risk measure |
Index ETFs: R² near 100% (they track the market by design) Large-cap stocks: R² typically 60–85% Small-cap stocks: R² typically 40–65% Individual commodities: R² typically 5–25%
A beta of 1.5 with R² of 0.90 is a reliable, interpretable number; 90% of the asset's movement is explained by the market. The same beta 1.5 with R² of 0.25 is nearly meaningless; the market explains only 25% of movements. Always check R² before acting on beta.
How CAPM uses beta to calculate expected return
Beta is the central risk parameter in the Capital Asset Pricing Model (CAPM):
Where (Rm − Rf) is the equity risk premium, the excess market return above the risk-free rate. Historically this has averaged about 5–7% per year for U.S. equities.
Expected return by beta (assuming Rf = 5%, Rm = 11%, premium = 6%):
| Beta | Expected Return | Interpretation |
|---|---|---|
| 0.0 | 5.0% | Risk-free asset; no market exposure |
| 0.5 | 8.0% | Half market exposure (e.g., balanced fund) |
| 1.0 | 11.0% | Market return (S&P 500) |
| 1.3 | 12.8% | 30% more than market exposure |
| 1.7 | 15.2% | Aggressive; significant amplification |
| 2.0 | 17.0% | 2× market exposure (2× ETF) |
| −0.5 | 2.0% | Inverse exposure; hedging |
An asset earning above its CAPM-predicted return has positive alpha. An asset earning below has negative alpha.
Levered and unlevered beta
Financial leverage (debt) amplifies beta. A company with significant debt is more sensitive to the market because debt creates fixed obligations that make equity more volatile.
Why this matters:
- Unlevered beta (asset beta) reflects only business risk, useful for comparing companies in the same industry with different capital structures
- When comparing a heavily-leveraged company to a debt-free peer, unlever both betas first, then compare
| Company | Levered Beta | D/E Ratio | Tax Rate | Unlevered Beta |
|---|---|---|---|---|
| Co. A | 1.4 | 0.5 | 25% | 1.07 |
| Co. B | 1.2 | 0.2 | 25% | 1.07 |
Both companies have the same business risk (unlevered beta 1.07). Co. A looks riskier only because of its higher leverage, not its underlying operations.
How to find correlation and standard deviation
To calculate beta from historical data:
- Download monthly closing prices for the asset and the S&P 500 (or relevant market benchmark) over 36–60 months
- Calculate monthly returns: (Price_t / Price_t-1) − 1
- Compute the standard deviation of both return series (Excel STDEV or =STDEV.S)
- Compute the correlation: Excel CORREL(asset_returns, market_returns)
- Enter these values into the calculator
Alternatively, use publicly available beta figures:
- Yahoo Finance: Stock page → Statistics tab → Beta (5Y monthly)
- Bloomberg: BEQ BETA command
- Morningstar: Stock quote → Ratings & Risk tab
Note that published betas typically use 5-year monthly data vs. the S&P 500. For some purposes (short-term risk), using 1-year or 2-year data gives a more current beta.
The bottom line
Beta is the most widely used single number in institutional finance for measuring systematic risk. It powers CAPM expected return calculations, portfolio construction decisions, and alpha attribution.
Understand its limits:
- Beta is backward-looking; it changes as the company’s business and leverage change
- Low R² means beta is unreliable for that specific asset
- Beta measures one type of risk (market sensitivity), not tail risk, credit risk, or liquidity risk
Use beta alongside the Portfolio Beta Calculator (to see whole-portfolio sensitivity) and the Alpha Calculator (to see whether returns adequately compensate for the beta taken).
Frequently Asked Questions
What is beta in finance?
Beta (β) measures how much an asset moves relative to the market. A beta of 1.0 means it moves in sync with the market. Beta 1.5 means 50% more volatile. Beta 0.5 means half as volatile. Beta −1.0 means it moves in the opposite direction.
What is a normal market standard deviation?
The S&P 500 has historically had an annual standard deviation of about 15–17% over long periods. In calm years it may be 10–12%; in volatile years (2008, 2020) it can exceed 25–30%. Use 15% as a baseline assumption for long-run modeling.
How do I find the correlation of a stock with the market?
Gather monthly returns for both the stock and the S&P 500 over 36–60 months. Calculate the Pearson correlation coefficient: ρ = Cov(X,Y) / (σ_X × σ_Y). Excel's CORREL() function, Google Sheets, and financial data sites can compute this directly.
Can correlation be negative?
Yes. Gold, utility stocks, and some defensive assets often have low or negative correlation with the S&P 500. A negative correlation (e.g., −0.3) with high asset volatility produces negative beta — the asset tends to rise when the market falls.
What is the difference between this calculator and the Portfolio Beta Calculator?
This calculator computes beta for an individual asset using correlation and volatility inputs. The Portfolio Beta Calculator computes the weighted average beta of a multi-asset portfolio from individual asset betas and their allocation weights.
What does R-squared mean for beta?
R² (R-squared) equals correlation². It represents the fraction of the asset's return variance explained by market movements. R² = 0.85 means 85% of the stock's volatility comes from market-wide factors; 15% is company-specific. Low R² makes beta unreliable as a risk predictor.
Is beta calculated on historical data?
Yes — published betas are always historical, typically using 3–5 years of monthly returns. Historical beta may not perfectly predict future beta, especially for companies undergoing major changes (mergers, spinoffs, business pivots, leverage changes).
What beta do different sectors typically have?
Technology: 1.2–1.8. Energy: 0.8–1.5 (varies with oil prices). Consumer Staples: 0.4–0.7. Utilities: 0.2–0.5. Healthcare: 0.6–0.9. Financials: 1.0–1.5. Gold miners: 0.5–1.0 (or negative). These are typical ranges and vary by company and time period.
Does beta change over time?
Yes. As a company's business model, financial leverage, size, and industry exposure change, its beta changes. Young high-growth tech companies often have high betas that moderate as they mature. Companies adding debt typically see rising beta.
What is levered vs. unlevered beta?
Levered beta (equity beta) reflects the risk of a company including its debt load. Unlevered beta (asset beta) removes the effect of financial leverage to reflect just the business risk. Unlevered β = Levered β / (1 + (1−tax rate) × Debt/Equity). This is used in WACC calculations.
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