What does a beta of 1.5 mean?

That the asset historically moved about one and a half times as much as the benchmark, in both directions. It is a description of the past, not a forecast.

Why does R squared matter?

Because it says how much of the asset movement the benchmark explains at all. A precise-looking beta with an R squared of 0.2 is fitted to noise.

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Beta and Alpha Calculator

Beta and Jensen alpha from a return history, with the R squared that says whether the beta means anything. A beta fitted against a benchmark the asset barely tracks is a number without content, and the fit statistic is the only way to see that.

Also called: stock beta calculator, jensen alpha calculator.

Beta

1.59

Beta of 1.59 and annual alpha of 2.93% against the benchmark, on 12 observations with an R squared of 1. A beta of 1.59 means the asset moved about 1.6 times as far as the benchmark, in both directions. The extra return in a rising market is the same mechanism as the extra loss in a falling one. An R squared of 1 means the benchmark explains most of the movement, so the beta is meaningful. Note that 12 observations is still a small sample for a regression.

Annual alpha

2.93%

R squared

Correlation

Annualised asset return

20.9%

Annualised benchmark return

13.7%

Return CAPM expected from that beta

17.97%

Observations

On the beta

A beta of 1.59 means the asset moved about 1.6 times as far as the benchmark, in both directions. The extra return in a rising market is the same mechanism as the extra loss in a falling one.

On the fit

An R squared of 1 means the benchmark explains most of the movement, so the beta is meaningful. Note that 12 observations is still a small sample for a regression.

How this is calculated

An estimate, not an offer or a guarantee. Projected returns assume the rate you entered holds for the whole term, which no market does.

Method and background

This is what the calculation gives for the numbers you entered. It is an estimate, not advice, and it knows nothing about your situation beyond those numbers. Rules for United States change on a published schedule; the effective date is shown on every rule-based tool.

How this is calculated

Beta is the covariance of the asset with the benchmark divided by the variance of the benchmark, which is the slope of a regression through the two series. Alpha is the residual: the return earned above what the risk free rate plus beta times the market premium would have produced. The R squared matters more than either. At an R squared of 0.9 the benchmark explains most of the movement and the beta is meaningful; at 0.3 it explains almost nothing and both figures are artefacts of a poor fit. Twelve observations is a small sample for a regression, and the estimate should be treated as indicative rather than settled.

beta is the slope of the asset against the benchmark, and alpha is what is left after the return that slope alone would have produced

β: Sensitivity to the benchmark
α: Return unexplained by the benchmark

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

a high beta asset against its benchmark

Asset returns, in percent: 4.1, -2.8, 5.6, 1.2, -3.4, 6.1, 2.0, -4.9, 4.4, 0.6, 2.8, 5.2
Benchmark returns, in percent: 2.6, -1.9, 3.4, 1.0, -2.1, 3.8, 1.4, -3.0, 2.9, 0.5, 1.8, 3.3
Periods per year: 12
Risk free rate, annual: 6.5%

Beta1.59

twelve monthly pairs, regression slope of the asset on the benchmark

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an asset identical to its benchmark

Asset returns, in percent: 2, -1, 3, 4
Benchmark returns, in percent: 2, -1, 3, 4
Periods per year: 12
Risk free rate, annual: 6.5%

Beta1

boundary: perfect tracking gives beta 1 and no alpha

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Method and limits

What it assumes

Both series cover the same periods in the same order.

What it deliberately does not model

Beta is unstable over time and estimates from different windows disagree materially.
A low R squared makes both beta and alpha unreliable regardless of how precise they look.
Alpha measured against the wrong benchmark measures the benchmark choice, not skill.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

What does a beta of 1.5 mean?: That the asset historically moved about one and a half times as much as the benchmark, in both directions. It is a description of the past, not a forecast.
Why does R squared matter?: Because it says how much of the asset movement the benchmark explains at all. A precise-looking beta with an R squared of 0.2 is fitted to noise.