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Category Investments & Stocks

Stock Returns (%, comma or newline separated) Enter periodic percentage returns for the stock.

Market Returns (%, comma or newline separated) Enter matching periodic percentage returns for the benchmark index.

Risk-Free Rate (%) Annual risk-free rate (e.g., T-bill yield).

Characteristic Line (Stock vs Market Returns)

Interpretation

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About

A stock's beta coefficient (β) quantifies its systematic risk relative to a benchmark index. Miscalculating β leads to mispriced assets, flawed hedge ratios, and incorrect cost-of-equity inputs for DCF models. This tool computes β via ordinary least squares (OLS) regression of periodic stock returns against market returns, outputting covariance, variance, correlation (ρ), R², standard error, and the Bloomberg-style adjusted beta. It also derives the CAPM expected return using the user-supplied risk-free rate R_f. Results assume returns are stationary and linearly related; fat tails, structural breaks, or survivorship bias are not modeled.

Practitioners should note that β is sensitive to the observation window and return frequency. A 5-year monthly window (standard for Bloomberg terminals) yields different estimates than 1-year daily data. This calculator accepts any period count but does not interpolate missing observations. Pro tip: compare your result against at least two window lengths before committing to a cost-of-capital assumption.

Formulas

The beta coefficient is derived from ordinary least squares regression of the stock's periodic returns on the market's periodic returns. The slope of the fitted line is β.

β = Cov(R_s, R_m)Var(R_m)

Where covariance and variance expand to:

Cov(R_s, R_m) = 1n n∑i=1 (R_s,i − R_s)(R_m,i − R_m)

Var(R_m) = 1n n∑i=1 (R_m,i − R_m)²

The Pearson correlation coefficient:

ρ = Cov(R_s, R_m)σ_s ⋅ σ_m

The coefficient of determination:

R² = ρ²

The Bloomberg adjusted beta regresses raw beta toward the market mean of 1.0:

β_adj = 23 ⋅ β_raw + 13

CAPM expected return:

E(R_s) = R_f + β ⋅ (E(R_m) − R_f)

Where R_s = stock return per period, R_m = market return per period, R_s = mean stock return, R_m = mean market return, n = number of observations, σ_s = standard deviation of stock returns, σ_m = standard deviation of market returns, R_f = risk-free rate (e.g., T-bill yield), E(R_m) = expected market return (mean of R_m).

Reference Data

Beta Range	Classification	Risk Profile	Typical Sectors	Portfolio Implication
β < 0	Inverse	Moves opposite to market	Gold miners, inverse ETFs	Natural hedge
β = 0	Zero-beta	No market correlation	Risk-free assets, some alternatives	Pure diversifier
0 < β < 0.5	Very Low	Minimal systematic risk	Utilities, consumer staples	Defensive allocation
0.5 ≤ β < 0.8	Low	Below-market volatility	Healthcare, telecoms, REITs	Income-oriented
0.8 ≤ β ≤ 1.2	Market-like	Tracks benchmark closely	Large-cap diversified, index funds	Core holding
1.2 < β ≤ 1.5	Moderate-High	Amplifies market moves	Industrials, financials	Growth tilt
1.5 < β ≤ 2.0	High	Significant amplification	Tech growth, biotech, small-cap	Aggressive growth
β > 2.0	Very High	Extreme sensitivity	Leveraged ETFs, speculative stocks	Tactical / short-term only
Common Benchmark Indices
S&P 500	β = 1.00	US large-cap baseline	500 companies	Most common benchmark
NASDAQ-100	β ≈ 1.15	Tech-heavy	100 non-financial	Growth benchmark
Russell 2000	β ≈ 1.25	Small-cap premium	2000 small-caps	Size factor exposure
MSCI World	β ≈ 0.95	Global diversified	23 developed markets	International core
MSCI EM	β ≈ 1.10	Emerging market risk	24 emerging markets	EM allocation
Typical Sector Betas (vs S&P 500, 5Y Monthly)
Technology	1.20 - 1.40	High growth sensitivity	Software, semis, hardware	Cyclical growth
Financials	1.10 - 1.30	Rate-sensitive	Banks, insurance, asset mgmt	Macro-linked
Healthcare	0.65 - 0.85	Defensive	Pharma, medtech, services	Low-vol allocation
Consumer Staples	0.55 - 0.75	Recession-resistant	Food, beverage, household	Defensive anchor
Energy	0.90 - 1.30	Commodity-linked	Oil, gas, renewables	Inflation hedge
Utilities	0.30 - 0.55	Very defensive	Electric, water, gas	Income / low-vol
Real Estate	0.70 - 0.95	Rate-sensitive defensive	REITs, development	Yield play
Materials	1.00 - 1.20	Cyclical	Mining, chemicals, metals	Commodity exposure
Industrials	1.00 - 1.15	Economic cycle proxy	Aerospace, transport, machinery	Cyclical core
Communication Services	0.85 - 1.10	Mixed	Media, telecom, social	Blend growth/defensive

Frequently Asked Questions

Shorter windows (e.g., 1 year of daily returns) capture recent regime shifts but introduce noise from transient events. Longer windows (5 years monthly, the Bloomberg default of 60 observations) smooth out anomalies but may include structural breaks where the company's risk profile changed materially (M&A, spin-offs, leverage changes). There is no universally correct window. Compare estimates from at least two periods before using β in a cost-of-equity calculation.

The Bloomberg-adjusted beta applies a Bayesian shrinkage toward 1.0 using the formula β_adj = (2/3)β_raw + (1/3). This reflects the empirical observation that betas mean-revert over time. High-beta stocks tend to see their betas decline, and low-beta stocks tend to see theirs rise. Use adjusted beta for forward-looking CAPM estimates and raw beta for historical attribution.

R² measures the fraction of the stock's return variance explained by the market. A low R² (e.g., below 0.20) means the stock's returns are driven primarily by idiosyncratic factors, not systematic market movements. The beta may still be statistically significant, but it explains little of the total risk. For such stocks, single-factor CAPM is a poor model; multi-factor approaches (Fama-French 3 or 5 factor) are more appropriate.

Yes. A negative beta means the asset moves inversely to the market benchmark on average. Gold mining stocks and certain put-option-heavy strategies may exhibit negative beta. In portfolio construction, a negative-beta asset acts as a natural hedge, reducing overall portfolio beta. However, negative betas estimated from short sample windows can be unstable. Verify with longer data or alternative benchmarks before relying on the hedge property.

The standard error quantifies the precision of the beta estimate. A 95% confidence interval is approximately β ± 1.96 × SE(β). If this interval spans a wide range (e.g., 0.6 to 1.8), the estimate is unreliable for decision-making. Standard error decreases with more observations and higher R². To improve precision, increase the sample size or use a higher-frequency return series.

Significantly. Beta is always relative to the chosen benchmark. A US tech stock measured against the S&P 500 might show β = 1.3, but against the NASDAQ-100 it could be β = 0.9 because the benchmark itself is tech-heavy. For global stocks, using a domestic index versus MSCI World produces different results. Always match the benchmark to the investor's actual opportunity set or the relevant asset pricing model.