Jensen’s Alpha Calculator: Measure Your Investment Performance

How to use the tool

• Return from Investment (R_i)
  Enter your total gain or loss as a percentage.
  Sample 1: 9.75 % Sample 2: 4.10 %
• Market Index Return (R_m)
  Key in the comparable benchmark’s return.
  Sample 1: 6.20 % Sample 2: 5.50 %
• Risk-Free Rate (R_f)
  Use the current 3-month U.S. T-bill or similar low-risk yield.
  Sample 1: 1.90 % Sample 2: 1.50 %
• Beta (β)
  Insert your asset’s beta versus the chosen index.
  Sample 1: 0.95 Sample 2: 1.20
• Press “Calculate” to view alpha and the detailed breakdown.

Formula

The calculator applies the Capital Asset Pricing Model:

$$ \alpha = R_i – \lbrace R_f + \beta (R_m – R_f) \rbrace $$

Example A — Positive Alpha

• Input values: 9.75 %, 6.20 %, 1.90 %, 0.95
• Market excess: 6.20 % − 1.90 % = 4.30 %
• Beta term: 0.95 × 4.30 % = 4.085 %
• Expected return: 1.90 % + 4.085 % = 5.985 %
• Alpha: 9.75 % − 5.985 % = 3.77 %

Example B — Negative Alpha

• Input values: 4.10 %, 5.50 %, 1.50 %, 1.20
• Market excess: 5.50 % − 1.50 % = 4.00 %
• Beta term: 1.20 × 4.00 % = 4.80 %
• Expected return: 1.50 % + 4.80 % = 6.30 %
• Alpha: 4.10 % − 6.30 % = −2.20 %

Quick-Facts

• Typical mutual-fund alpha ranges from −10 % to +10 % over one year (Morningstar, 2023).
• 3-month U.S. T-bill yield—common R_f proxy—stood at 5.41 % on 14 Jun 2024 (U.S. Treasury, 2024).
• Average beta for S&P 500 constituents is about 1.00 (Damodaran Dataset 2024, NYU).
• William Sharpe introduced CAPM in 1964 (Sharpe, 1964).

FAQ

What does a positive alpha tell you?

A positive alpha shows your investment outperformed its risk-adjusted benchmark, signalling skill or superior strategy (Investopedia “Jensen’s Alpha”).

Can alpha be negative?

Yes. Negative alpha means your return fell short of the level justified by the risk you assumed (CFA Institute, 2022).

How often should you recalculate alpha?

Quarterly or annually keeps noise low while capturing shifts in beta and market trends (Malkiel & Elton, 2014).

Which rate counts as risk-free?

Analysts usually adopt the 3-month Treasury bill because of minimal default risk and high liquidity (Federal Reserve FAQ).

Does alpha account for total risk?

No. Alpha isolates systematic risk via beta; unsystematic risk remains your responsibility (Sharpe, 1964).

Is alpha useful for fixed-income funds?

It works, but beta estimation for bonds relies on duration-adjusted regression, complicating accuracy (Fabozzi “Bond Markets”).

What is an acceptable tracking period?

At least 36 monthly observations improves statistical confidence in beta and alpha calculations (Morningstar Methodology V5).

Expert view on alpha?

“Alpha isolates manager skill from market movements,” states the GIPS Standards handbook (CFA Institute, 2022).