What is Beta? Definition, Formula, and Example

What is beta?

Beta (β) measures how much a security's price moves when the broad market moves. A beta of 1.0 means the stock has historically moved one-for-one with its benchmark. A beta of 1.5 means a 1% market move has been associated with a 1.5% move in the stock. A beta of 0.5 means the stock moves half as much. Negative betas — rare outside of inverse ETFs, gold miners, and some volatility products — indicate a security that moves opposite the market. Beta is the single number that captures a stock's market-risk exposure and is the core input to the Capital Asset Pricing Model (CAPM).

How beta is calculated

Beta is the slope coefficient of a linear regression of the security's returns against the benchmark's returns:

β = Cov(R_asset, R_market) / Var(R_market)

Equivalently:

β = ρ × (σ_asset / σ_market)

where ρ is the return correlation and σ is the standard deviation of returns. The standard computation uses 60 monthly returns (5 years) regressed against the S&P 500 or a total-market index. Short-window daily betas (1 year of trading days) are more current but noisier and far more regime-sensitive.

Worked example

Using 5 years of monthly returns through March 2026:

• NVDA vs. SPY: β ≈ 1.68, R² ≈ 0.44. A 1% SPY move maps to a 1.68% expected NVDA move, but only 44% of NVDA's variance is explained by the market — the other 56% is idiosyncratic (AI demand, product cycles, export-control rules).
• DUK (Duke Energy) vs. SPY: β ≈ 0.43. Regulated utility cash flows damp market moves.
• TSLA vs. SPY: β drifted from ≈2.3 in 2022 to ≈1.5 by 2025 as the float expanded and speculative flows normalized.

In a $100,000 portfolio split evenly between the three, portfolio beta = (1.68 + 0.43 + 1.50) / 3 ≈ 1.20 — roughly 20% more market-sensitive than SPY alone.

When traders use beta

• Portfolio construction: target a portfolio beta (aggressive 1.3, defensive 0.7) by weighting high- and low-beta holdings.
• CAPM expected return: E(R) = R_f + β × (R_m − R_f). The 10-year Treasury supplies R_f; the market-risk premium runs ~5–6% historically.
• Beta-weighted delta for options books: expressing delta in SPY-equivalent units lets a trader hedge a mixed book with a single SPX or ES position.
• Relative-value screens: stocks with low beta and high alpha (positive regression intercept) are the quant holy grail.

Limitations and common misconceptions

Beta is backward-looking and unstable. TSLA's beta halving in three years illustrates that the number you regress today may not hold tomorrow. Beta also assumes linear sensitivity — during crashes, correlations spike toward 1 and high-beta names fall far more than their linear beta predicts. Single-stock R² is usually under 0.5, meaning most of a stock's variance is *not* market-driven and beta-hedging leaves substantial residual risk. Fama-French and Carhart models extend beta with size, value, and momentum factors precisely because single-factor beta under-specifies the exposure. Finally, "low beta = low risk" is wrong: a stock with β = 0.3 but 60% annualized idiosyncratic volatility is far riskier than a β = 1.0 index ETF.

Related terms

• What is the VIX? — aggregate market-volatility expectation
• What is Implied Volatility? — forward-looking single-stock volatility measure
• What is Average True Range? — absolute volatility in price units
• What is the Yield Curve? — source of the risk-free rate used in CAPM
• What is a Moving Average? — often paired with beta in regime filters