Risk & Performance

Alpha

The excess return of an investment compared to what a risk model (like CAPM) predicts it should earn.

01 / Formula

Formula

α = Rₚ − [Rf + βₚ(Rₘ − Rf)]

02 / Variables

Variables

Rₚ: Portfolio return
Rf: Risk-free rate
βₚ: Portfolio beta
Rₘ: Market return

03 / Worked Example

Worked Example

Scenario: Portfolio returning 11%, risk-free rate 3%, beta 1.2, market return 8%: expected return = 3% + 1.2(8% − 3%) = 9%; alpha = 11% − 9% = 2%.

Steps:

Calculate expected return = risk-free rate + beta × (market return − risk-free rate)
Calculate expected return = 3% + 1.2 × 5% = 9%
Subtract expected from actual: 11% − 9% = 2% alpha

04 / When to Use

When to Use This Formula

Evaluate manager skill or strategy outperformance
Compare value added beyond systematic risk
Decompose return into market and skill components

05 / Limitations

Limitations & Assumptions

Depends entirely on model choice (CAPM is just one model)
Short histories create unstable estimates
Positive alpha may reflect luck rather than skill
Multiple model choices create multiple alpha results

06 / Questions

Common Questions

Can positive return have negative alpha?

Yes. The portfolio may be up, but below what the model predicted given its risk exposure.

Does alpha prove skill?

Not by itself. Over long periods with many observations, positive alpha suggests skill; short-term alpha may be luck.