Concept

Beta

Beta is a Statistics concept. The Library holds 1 implementation — a working definition you can pull into Quant.

Top Beta indicator

The top custom implementation, built on the original standard Beta formula.

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The Beta implementation below can become a backtested trading strategy, built in plain English with no code.

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Beta

Indicator

What is Beta?

Beta measures how strongly an asset's returns move with a benchmark's. Formally it is the covariance of the asset's returns with the benchmark's returns divided by the variance of the benchmark's returns, which is the same thing as the slope of a linear regression of asset returns on benchmark returns. A beta of 1 means the asset has historically moved in line with the index; above 1, amplified; between 0 and 1, damped; negative, tending to move opposite.

Beta and correlation answer different questions. Correlation says how reliably two series move together; beta says how much, because beta equals correlation multiplied by the ratio of the asset's volatility to the benchmark's. A volatile, loosely correlated asset can still print a large beta. And beta is a windowed estimate, not a fixed attribute: it drifts with regime, lookback, and return frequency.

Estimation choices shape the number more than most users appreciate. Convention in equity analytics runs from one to two years of daily returns up to five years of monthly ones, and the same stock can print materially different betas across those recipes. Refinements exist for the known failure modes: rolling windows expose drift, up-market and down-market betas estimated separately expose asymmetry that a single slope averages away, and shrinkage adjustments in the Blume tradition pull raw estimates toward 1 to counter the tendency of extreme betas to mean-revert. None of them fixes the underlying truth that beta is a description of a past window, applied forward on faith.

For traders the number is a workhorse with known limits. Screeners rank names by beta and alpha together, the paired outputs of one regression; crypto substitutes Bitcoin for the index and reads altcoin betas the same way; and portfolio bookkeeping nets position betas into one aggregate market sensitivity. The known limits: slopes estimated on calm windows understate crisis behavior, since co-movement strengthens in stress; a low R-squared makes the slope decorative; and fat-tailed return distributions let single days own the estimate, which is why regression diagnostics belong next to the number.

How to identify and estimate beta

Beta is one regression slope; the craft is in the recipe choices around it.

  1. 1Choose the benchmark deliberately: the index the strategy actually hedges with or compares against, not a default.
  2. 2Align the data: matching return frequencies and windows, with dividends and corporate actions handled consistently on both series.
  3. 3Regress asset returns on benchmark returns: the slope is beta, the intercept is alpha.
  4. 4Check the fit before trusting the slope: low correlation or R-squared means the beta describes little of the asset's movement.
  5. 5Roll the window and watch the drift: a beta that swings across subperiods is telling you the relationship is regime-dependent, which is information in itself.

How it's calculated

Beta measures how many units the asset's return moves per unit move in the benchmark's return over a chosen window.

Rat=Pat−Pat−1Pat−1\mathrm{Ra}_t = \frac{\mathrm{Pa}_t - \mathrm{Pa}_{t-1}}{\mathrm{Pa}_{t-1}}
Rmt=Pmt−Pmt−1Pmt−1\mathrm{Rm}_t = \frac{\mathrm{Pm}_t - \mathrm{Pm}_{t-1}}{\mathrm{Pm}_{t-1}}
Beta=Cov⁡(Ra,Rm)Var⁡(Rm)\mathrm{Beta} = \frac{\operatorname{Cov}(\mathrm{Ra}, \mathrm{Rm})}{\operatorname{Var}(\mathrm{Rm})}
Cov⁡(Ra,Rm)=1n×∑t=1n(Rat−Ra‾)×(Rmt−Rm‾)\operatorname{Cov}(\mathrm{Ra}, \mathrm{Rm}) = \frac{1}{n} \times \sum_{t=1}^{n} (\mathrm{Ra}_t - \overline{\mathrm{Ra}}) \times (\mathrm{Rm}_t - \overline{\mathrm{Rm}})
Var⁡(Rm)=1n×∑t=1n(Rmt−Rm‾)2\operatorname{Var}(\mathrm{Rm}) = \frac{1}{n} \times \sum_{t=1}^{n} (\mathrm{Rm}_t - \overline{\mathrm{Rm}})^2
Equivalent: Beta=r×σa/σm\text{Equivalent: } \mathrm{Beta} = r \times \sigma_a / \sigma_m
Beta: beta of the asset relative to the benchmark
Pa_t: asset price (close) at period t
Pm_t: benchmark price (close) at period t
Ra_t: asset return over period t
Rm_t: benchmark return over period t
Ra_bar: mean of Ra over the n periods
Rm_bar: mean of Rm over the n periods
n: number of return observations (commonly 60 monthly or 252 daily)
t: period index
Cov(): covariance of the two return series
Var(): variance of the benchmark returns
r: correlation coefficient between Ra and Rm
σ_a: standard deviation of the asset returns
σ_m: standard deviation of the benchmark returns

Beta is the slope of the least-squares regression of asset returns on benchmark returns: 1 moves in line with the benchmark, above 1 amplifies its moves, below 1 dampens them, and negative values move opposite.

Population and sample divisors (n vs n - 1) cancel in the ratio, so both conventions give the same beta.

Log returns are an accepted alternative to the simple returns shown.

How traders use it

  • Hedging and sizing: index hedges are scaled by beta so the hedge notional actually offsets the position's measured market sensitivity rather than its raw dollar size.
  • Regime-fit screening: leaning into high-beta names when the index trend is the engine of the trade, rotating toward low-beta names when the goal is to mute index chop.
  • Beta-adjusted performance reads: a stock up 1% while its index is up 2% is lagging once beta is accounted for; alpha is the formal name for what remains after that adjustment.
  • Relative-value construction: long-short pairs are sized beta-neutral rather than dollar-neutral, so the spread expresses the relative view instead of a hidden market bet.
  • Crypto positioning: altcoin betas against Bitcoin quantify amplification, informing rotation between majors and high-beta alts as conviction about the benchmark leg changes.

Beta vs. neighboring measures

Correlation: Correlation measures how reliably two return series move together, bounded between -1 and 1. Beta measures how much the asset moves per unit of benchmark move, scaling correlation by relative volatility. Tight correlation with small moves gives a low beta; loose correlation with violent moves can still produce a high one.

Alpha: Both come from the same return regression. Beta is the slope, the market-linked component of returns; alpha is the intercept, the residual return left after the beta-scaled market contribution is removed. Exposure versus excess.

Linear Regression: Beta is one application of the general machine: regress returns on returns and read the slope. Everything the statistics teach about regression, sensitivity to outliers, fit diagnostics, unstable slopes on short windows, applies verbatim to beta, and gets forgotten exactly as often.

Concept family

Statistics

46 concepts mapped · 46 in the Library

Beta FAQ

What does a beta of 1.5 mean?

Over the measurement window, the asset moved on average about 1.5% for every 1% move in the benchmark. It is a regression slope, not a promise: on any single day the relationship can fail completely, and betas drift as regimes change, so a beta estimated on the past quarter may describe the next one poorly.

Is high beta the same as high volatility?

No. Volatility describes an asset on its own; beta describes only the index-linked component of its movement. Because beta combines correlation with relative volatility, an extremely volatile asset that barely tracks the index can carry a low beta, while a moderately volatile asset that tracks it tightly can carry a high one.

What window should beta be estimated over?

There is no single right recipe, only conventions: one to two years of daily returns for a responsive estimate, five years of monthly returns for a stable one, with the two frequently disagreeing. Shorter windows track regime change and inhale noise; longer ones smooth noise and average across regimes that no longer apply. Matching the window to the intended holding period, then checking stability by rolling it, is the defensible procedure.

Can beta be negative, and what does that mean?

Yes: a negative slope means the asset tended to move opposite the benchmark over the window, the profile of natural hedges. Persistent negative equity betas are rare and precious, which is why genuinely negatively correlated assets anchor hedging strategies. Transient negative betas on short windows are usually estimation noise or one-off events rather than durable structure, and deserve suspicion.

Why did a beta-matched hedge still lose money?

Several honest reasons. Beta is an average slope, and any single episode can deviate wildly from it; a low R-squared means most of the asset's movement was never index-linked to begin with, so the hedge addressed a minority of the risk; and co-movement itself shifts in stress, typically strengthening just as hedges are tested. Beta scales the hedge correctly on average, and averages are exactly what crises ignore.

How does beta work in crypto?

The same regression with Bitcoin, or occasionally a broad crypto index, as the benchmark. Altcoin betas above 1 are common in risk-on phases, quantifying the familiar amplification of Bitcoin's moves, and the estimates are even less stable than equity betas because regimes rotate faster and return distributions are heavier-tailed. The screening and hedging logic transfers; the confidence intervals deserve to be wider.

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