Jensen's Alpha Calculator (Portfolio CAPM
### Capital Asset Pricing Model (CAPM) & Jensen's Alpha Theory Developed by Michael Jensen in 1968, Jensen's Alpha quantifies the excess return generated by an investment portfolio beyond the return.
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📐 Formula
💡 Practical Example
A mutual fund generates a 15.00% annual return with Beta = 1.20. Given a 4.00% T-bill risk-free rate and 11.00% S&P 500 return: CAPM expected return is 12.40% [4.00 + 1.20 × (11.00 - 4.00)], resulting in a +2.60% positive Jensen's Alpha.
📖 About Jensen's Alpha Calculator (Portfolio CAPM
Capital Asset Pricing Model (CAPM) & Jensen's Alpha Theory
Developed by Michael Jensen in 1968, Jensen's Alpha quantifies the excess return generated by an investment portfolio beyond the return predicted by the Capital Asset Pricing Model (CAPM).
Core Investment Formulas
- CAPM Expected Return: R_expected = R_f + β × (R_m - R_f)
- Market Risk Premium: Premium = R_m - R_f
- Jensen's Alpha Formula: α = R_p - R_expected = R_p - [ R_f + β × (R_m - R_f) ]
Interpreting Jensen's Alpha
- α > 0.00%: Portfolio beat the market benchmark on a risk-adjusted basis.
- α = 0.00%: Portfolio earned exactly the return expected for its level of systematic risk.
- α < 0.00%: Portfolio underperformed its risk-adjusted benchmark, destroying capital value.
How to Use This Calculator
Enter your Actual Portfolio Total Return (Rp) (e.g. e.g. 15.0 in %), Risk-Free Rate of Return (Rf) (e.g. e.g. 4.0 in %), Portfolio Systematic Risk (Beta β) (e.g. e.g. 1.2 in β), and Market Benchmark Return (Rm) (e.g. e.g. 11.0 in %). Results update instantly as you type — adjust any value to compare scenarios.
The Formula
CAPM Expected Return = R_f + β * (R_m - R_f)
Worked Example
A mutual fund generates a 15.00% annual return with Beta = 1.
- Given a 4.00% T-bill risk-free rate and 11.00% S&P 500 return: CAPM expected return is 12.40% [4.00 + 1.20 × (11.00 - 4.00)], resulting in a +2.60% positive Jensen's Alpha.
Understanding Your Result
Chemical calculations require careful attention to significant figures — your result is only as precise as your least precise input. For laboratory work, verify that temperature, pressure, and concentration conditions match the formula's assumed standard state (typically 25°C and 1 atm). Compare your result against published reference values for the specific compound or reaction. Safety note: laboratory chemical calculations should always be verified by a qualified chemist before practical application.
💡 Mathematical Rigor & Applied Context
- This calculator applies exact mathematical definitions following conventions established by NIST and international standards bodies.
- Rounding errors accumulate across multi-step calculations. For precision-critical work, maintain extra significant figures through all intermediate steps.
- Many mathematical concepts have multiple valid formulations — if a result seems unexpected, verify which convention or definition applies to your context.
- Dimensional analysis (unit tracking) is the fastest way to catch formula errors. Every term in an equation must have consistent, compatible units.
- Numerical methods used in digital calculators introduce floating-point precision limits (~15 significant digits for IEEE 754 double precision).
- For statistical and probabilistic calculations, always specify whether you are working with population parameters or sample statistics — formulas differ.
- Visualizing a problem geometrically or testing with known boundary values (zero, infinity, negative) reveals hidden errors faster than algebraic checking.
- When in doubt, validate your result against a simplified hand calculation or a published worked example from a textbook or standards document.
Results are for informational and educational purposes only. Always verify critical decisions with a qualified professional.