Investment Beta and Alpha Calculator
Regress matched asset and benchmark simple returns and show market sensitivity, alpha and tracking error.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Calculate sample covariance divided by benchmark sample variance. Subtract the benchmark-related excess return from asset excess mean for Jensen alpha.
β=cov(asset,benchmark)/var(benchmark); α=mean(asset)−rf−β(mean(benchmark)−rf)
Worked example
Asset 3%, −1%, 5%, 1% versus benchmark 1%, −1%, 2%, 0% has beta 2 and alpha 1% per period at a zero risk-free return.
Assumptions and input details
Lists must have equal length and matched dates/intervals. Benchmark variance must be positive. Alpha annualization is arithmetic alpha×frequency and is labeled as such, not compounded excess wealth. Correlation and R² are undefined for a constant asset. Tracking error is sample SD of asset minus benchmark, annualized by √frequency. No live market data or national tax rules are inferred. Enter consistent amounts in one currency unless explicitly stated otherwise.
References: CFA Institute: risk-adjusted performance measures
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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