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Paired-return beta and intercept calculator

Enter matched return percentages to calculate a descriptive slope, intercept and defined fit measures.

Omni Finance AcademyBy Omni Finance Academy
Matched periods
5
Slope (benchmark beta)
2.1
Fitted intercept per period
1.2 %
Residual standard error
0.6325 percentage points
Benchmark sample variance
2.5 percentage points²
Sample covariance
5.25 percentage points²
In-sample R²
97.351 %
Sample correlation
0.9867

Equal-weight matched period returns; least squares includes an intercept. The fitted intercept is not automatically Jensen alpha or evidence of skill. No significance test, prediction interval, causation or future-return estimate is supplied.

Observed returns and fitted line-3.721.56.72Period 1: benchmark -2%, asset -3%Period 2: benchmark -1%, asset -0.5%Period 3: benchmark 0%, asset 1%Period 4: benchmark 1%, asset 2.5%Period 5: benchmark 2%, asset 6%-202Asset return (%)Benchmark return (%)-3.721.56.72Period 1: benchmark -2%, asset -3%Period 2: benchmark -1%, asset -0.5%Period 3: benchmark 0%, asset 1%Period 4: benchmark 1%, asset 2.5%Period 5: benchmark 2%, asset 6%-202Asset return (%)Benchmark return (%)Residuals versus benchmark returns-0.912-0.10.712Period 1: benchmark -2%, residual 0%Period 2: benchmark -1%, residual 0.4%Period 3: benchmark 0%, residual -0.2%Period 4: benchmark 1%, residual -0.8%Period 5: benchmark 2%, residual 0.6%-202Residual (percentage points)Benchmark return (%)-0.912-0.10.712Period 1: benchmark -2%, residual 0%Period 2: benchmark -1%, residual 0.4%Period 3: benchmark 0%, residual -0.2%Period 4: benchmark 1%, residual -0.8%Period 5: benchmark 2%, residual 0.6%-202Residual (percentage points)Benchmark return (%)

Dots are the supplied paired observations. The solid line is the least-squares fit with an intercept; the dashed line marks zero residual. Points are not joined as a time path. The table retains period order and duplicate observations. This is an in-sample descriptive fit.

View paired observations and residuals
Supplied periods and fitted values
PeriodBenchmark (%)Asset (%)Fitted (%)Residual (percentage points)
1-2-3-30
2-1-0.5-0.90.4
3011.2-0.2
412.53.3-0.8
5265.40.6
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Use matched compatible returns

Enter 3–100 comma-separated observations for each series in matching period order. Both use percentages and the same period, currency and income/cost basis. The calculator uses equal observation weights and fits asset return on the chosen benchmark with an intercept.

Read the original default record

Benchmark returns −2/−1/0/1/2 percent and asset returns −3/−0.5/1/2.5/6 percent give slope 2.1, intercept 1.2% per supplied period and residual standard error approximately 0.632456 percentage points. They are hypothetical observations.

Inspect both graphical views

The scatter plots actual observations and the fitted line within the observed benchmark range. The residual view plots signed deviations against benchmark returns. Points are not connected as a time path. The expandable table retains input period order, repeated observations, fitted values and residuals.

Handle non-identifiable or constant records

A constant benchmark cannot identify a slope and is rejected. A constant asset record can give slope zero and a defined intercept, but its correlation and R² ratios are undefined and omitted.

Retain the descriptive model scope

The tool does not choose a market proxy, infer matching dates, subtract a risk-free series or perform significance/causality/prediction analysis. A raw fitted intercept is not automatically Jensen alpha or proof of skill. Use the record and model appropriate to the learning task.

Further references