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Jensen’s Alpha Calculator

Estimate alpha relative to CAPM expected return using portfolio return, beta, market return, and risk-free rate.

Jensen's Alpha Engine

Quantify the "Abnormal Return" of a portfolio relative to the Security Market Line

Mathematical Ground Truth

Jensen's Measure

The Alpha Equation

αp = Rp - [Rf + βp(Rm - Rf)]

Where **[Rf + βp(Rm - Rf)]** represents the expected return dictated by the Capital Asset Pricing Model (CAPM).

Parameter Architecture

Portfolio Beta (β)

The systematic risk coefficient. A Beta of 1.0 means the portfolio moves with the market. A Beta of 1.5 implies 50% more volatility than the benchmark in the same direction.

Risk-Free Rate (Rf)

Usually the yield on a 10-year Government Treasury bond. It represents the "hurdle" return expected with zero default risk.

Why Alpha Matters?

Passive investing captures 100% of Beta. Active investing only justifies its existence (and higher fees) by producing persistent, positive **Jensen's Alpha**. Without positive alpha, you are simply paying active fees for passive results.

Quantitative Audit Series

The Alpha
Detective

"Market Beta is a gift from the economy; Jensen's Alpha is a prize for the skilled manager. This guide teaches you how to tell the difference."

Study Roadmap

"Price is what you pay; value (and Alpha) is what you get."

In finance, Jensen's Alpha is the forensic tool used to verify if a manager's high returns are a result of genuine value-added or simply aggressive risk-taking.

The CAPM Threshold

Jensen's Alpha measures the difference between a portfolio's actual return and the return it **should have earned** according to the Capital Asset Pricing Model (CAPM).

"If you have a Beta of 2.0, you are taking twice the market risk. You don't have Alpha unless you return more than twice the risk premium."

The Logic Chain

  • Market Return - Risk Free = Risk Premium
  • Risk Premium × Beta = Your Required Return
  • Actual Return - Required Return = Your Alpha

The Security Market Line

Visualizing Alpha means plotting a point relative to the Security Market Line (SML).

Above the Line

Positive Alpha. This is where stock pickers and elite hedge funds aim to live. Every point above the line represents return gained without adding systematic exposure.

Below the Line

Negative Alpha. The portfolio is 'leakier' than the index. You are paying for risk that is not showing up in the returns.

Alpha Audit Checklist

Demystifying the returns of the 1%

Active Management Toolkit

Treynor Ratio

Performance per unit of Beta

Sharpe Ratio

Total risk efficiency

Information Ratio

Quantifying tracking error alpha

Beta Calculator

Market sensitivity audit

Quantitative Performance Summary

"Jensen's Alpha provides the ultimate truth in performance reporting. By stripping away the contribution of the market, it reveals the true value-add (or drain) of a manager's decisions. In a world of market beta, Alpha is the only true prize."

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Jensen’s Alpha Calculator

Estimate alpha relative to CAPM expected return using portfolio return, beta, market return, and risk-free rate.

How to use Jensen’s Alpha Calculator

Step-by-step guide to using the Jensen’s Alpha Calculator:

  1. Enter your values. Input the required values in the calculator form
  2. Calculate. The calculator will automatically compute and display your results
  3. Review results. Review the calculated results and any additional information provided

Frequently asked questions

How do I use the Jensen’s Alpha Calculator?

Simply enter your values in the input fields and the calculator will automatically compute the results. The Jensen’s Alpha Calculator is designed to be user-friendly and provide instant calculations.

Is the Jensen’s Alpha Calculator free to use?

Yes, the Jensen’s Alpha Calculator is completely free to use. No registration or payment is required.

Can I use this calculator on mobile devices?

Yes, the Jensen’s Alpha Calculator is fully responsive and works perfectly on mobile phones, tablets, and desktop computers.

Are the results from Jensen’s Alpha Calculator accurate?

Yes, our calculators use standard formulas and are regularly tested for accuracy. However, results should be used for informational purposes and not as a substitute for professional advice.