Alpha Calculator (Investment)

Alpha measures the portion of a portfolio or asset return that is not explained by market movements or a benchmark model. Different alpha calculations exist for single-period comparisons, regression-based estimates, and multi-period annualized excess returns.

This tool supports multiple validated methods so you can choose the calculation that matches your data: single-period CAPM comparison, Jensen-style calculations using regression summary statistics, or annualized excess from cumulative returns. It includes guidance on input formats and accuracy considerations.

Updated Nov 1, 2025QA PASS — golden 25 / edge 120Run golden-edge-2026-01-23

Governance

Record bd609233793b • Reviewed by Fidamen Standards Committee

Calculation method

Calculates alpha as actual asset return minus the CAPM-expected return using a supplied beta. Enter percentage values (e.g., 8 for 8%).

Inputs

Asset return (%) — single-period (enter as percent, e.g., 8 for 8%)

Min -100 · Max 100

Market return (%) — single-period (enter as percent, e.g., 6 for 6%)

Min -100 · Max 100

Risk-free rate (%) (enter as percent, e.g., 1.5 for 1.5%)

Min -100 · Max 100

Beta (β) — use 1 for market-level sensitivity

Min -10 · Max 10

Mean asset return (%) — e.g., average periodic return (enter as percent, e.g., 0.8 for 0.8% if using monthly)

Min -100 · Max 100

Mean market return (%) — same periodicity as mean asset return

Min -100 · Max 100

Estimated beta from regression (β̂) — supply regression output if available

Min -10 · Max 10

Cumulative asset total return (decimal, e.g., 0.35 for 35%)

Min -0.999 · Max 100

Cumulative benchmark total return (decimal, e.g., 0.28 for 28%)

Min -0.999 · Max 100

Number of years (for annualization)

Min 1 · Max 100

Results

Updates as you type

Alpha (CAPM) (%)

2.00%

Output	Value	Unit
Alpha (CAPM) (%)	2.00%	%

Primary result2.00%

Visualization

Points

Methodology

CAPM single-period alpha is the observed return minus the CAPM-expected return: Alpha = R_p - [R_f + β (R_m - R_f)]. Use this when you have a single observed asset return, a market return, a risk-free rate, and a beta.

Jensen-style alpha here uses supplied summary regression outputs (estimated beta and mean periodic returns). For rigorous regression-based inference, perform a time-series regression of asset excess returns on market excess returns and supply the estimated beta and mean returns from that analysis.

Annualized excess alpha converts cumulative total returns to annualized returns using geometric annualization and reports the difference. This is appropriate when comparing multi-period total returns across different horizons.

Key takeaways

Choose the method that matches your data: single-period CAPM for point-in-time comparisons, Jensen-style for regression-derived estimates, and annualized excess for multi-period cumulative returns.

Ensure periodicity alignment and data provenance. For formal reporting and trading or advisory decisions, retain regression diagnostics and data lineage, and follow organizational validation and control processes.

Worked examples

Example 1 (CAPM single-period): Asset return = 12%, Market = 7%, Risk-free = 1.5%, Beta = 1.2. Expected CAPM return = 1.5% + 1.2*(7% - 1.5%) = 8.7%. Alpha = 12% - 8.7% = 3.3%.

Example 2 (Annualized): Asset cumulative return = 0.50 (50%) over 4 years, Benchmark cumulative = 0.30 (30%). Annualized asset = (1.50)^(1/4)-1 = 10.67%. Annualized benchmark = (1.30)^(1/4)-1 = 6.78%. Annualized alpha = 3.89%.

F.A.Q.

What input formats should I use?

For single-period and mean returns, enter percentage numbers (e.g., 8 for 8%). For cumulative multi-period returns used in annualized mode, enter decimal fractions (e.g., 0.35 for 35%). Beta and estimated regression coefficients are plain numeric values (e.g., 1.05).

When should I use the Jensen-style method?

Use Jensen-style when you have regression outputs (estimated beta and mean periodic returns) from a time-series regression of asset excess returns on market excess returns. That preserves statistical estimation steps and standard error reporting in your source regression.

Does this tool run regressions on raw time-series data?

No. This tool accepts summary statistics and single-period figures. For full regression analysis, use a statistical package, export the estimated beta and summary statistics, then input the estimates here. Methodology guidance in this page explains required steps.

How accurate are the results?

Calculations are deterministic given your inputs, but accuracy depends on data quality, correct periodicity alignment, and appropriate model choice. See the accuracy and validation section and consult time-series regression diagnostics for inference.

Are there regulatory or standards considerations?

Use documented procedures for data handling, model validation, and controls. Follow applicable standards for data integrity and process controls cited below for traceability and reproducibility.

Sources & citations

NIST — Frameworks and best practices for data integrity and controls — https://www.nist.gov
ISO — Standards overview (quality and information security controls) — https://www.iso.org
IEEE — Best practices for measurements and reporting — https://www.ieee.org
OSHA — Operational risk controls and workplace safety guidance (for operational alpha contexts) — https://www.osha.gov
SEC — Investor.gov Educational Resources — https://www.investor.gov/
CFA Institute — Global Investment Performance Standards (GIPS) — https://rpc.cfainstitute.org/gips-standards
FINRA — Investment Products — https://www.finra.org/investors/investing/investment-products

Further resources

Related tools

External guidance

Versioning & Change Control

Audit record (versions, QA runs, reviewer sign-off, and evidence).

Record ID: bd609233793b

What changed (latest)

v1.0.0 • 2025-11-01 • MINOR

Initial publication and governance baseline.

Why: Published with reviewed formulas, unit definitions, and UX controls.

Public QA status

PASS — golden 25 + edge 120

Last run: 2026-01-23 • Run: golden-edge-2026-01-23

Engine

v1.0.0

Data

Baseline (no external datasets)

Content

v1.0.0

Governance

Last updated: Nov 1, 2025

Reviewed by: Fidamen Standards Committee (Review board)

Credentials: Internal QA

Risk level: low

Reviewer profile (entity)

Fidamen Standards Committee

Review board

Internal QA

Entity ID: https://fidamen.com/reviewers/fidamen-standards-committee#person

Semantic versioning

MAJOR: Calculation outputs can change for the same inputs (formula, rounding policy, assumptions).
MINOR: New features or fields that do not change existing outputs for the same inputs.
PATCH: Bug fixes, copy edits, or accessibility changes that do not change intended outputs except for previously incorrect cases.

Review protocol

Verify formulas and unit definitions against primary standards or datasets.
Run golden-case regression suite and edge-case suite.
Record reviewer sign-off with credentials and scope.
Document assumptions, limitations, and jurisdiction applicability.

Assumptions & limitations

Uses exact unit definitions from the Fidamen conversion library.
Internal calculations use double precision; display rounding follows the unit's configured decimal places.
Not a substitute for calibrated instruments in regulated contexts.
Jurisdiction-specific rules may require official guidance.

Change log

v1.0.0 • 2025-11-01 • MINOR

Initial publication and governance baseline.

Why: Published with reviewed formulas, unit definitions, and UX controls.

Areas: engine, content, ui • Reviewer: Fidamen Standards Committee • Entry ID: c00e0b29ff64