E(R) = Rf + Beta x (Rm - Rf)
Alpha = Rp - E(R)
Where Rp is actual return, Rf is risk-free rate, Rm is market return, and Beta measures market sensitivity.
Jensen's Alpha, named after economist Michael Jensen, measures the excess return that a portfolio generates over its expected return as predicted by the Capital Asset Pricing Model (CAPM). A positive alpha indicates that the portfolio manager has added value beyond what could be explained by the portfolio's market risk exposure, while a negative alpha suggests underperformance.
Alpha is widely used in the investment industry to evaluate fund manager skill. A consistently positive alpha suggests genuine investment skill, while negative alpha may indicate poor stock selection, high fees, or unfavorable market timing. However, past alpha does not guarantee future performance.
Beta measures the sensitivity of a portfolio's returns to market movements. A beta of 1.0 means the portfolio moves in lockstep with the market. A beta greater than 1.0 indicates higher volatility -- when the market rises 10%, a portfolio with beta 1.5 would be expected to rise 15%, but it would also fall 15% when the market drops 10%.
Conversely, a beta below 1.0 suggests lower volatility than the market, which may be desirable for conservative investors. Negative beta (rare) indicates an inverse relationship with the market, meaning the asset tends to rise when the market falls. Understanding your portfolio's beta helps you gauge how much market risk you're taking on.
Both alpha and beta are backward-looking measures based on historical data and may not predict future performance. Beta assumes a linear relationship between portfolio and market returns, which may not hold during extreme market conditions. Alpha calculations depend on the choice of benchmark -- using an inappropriate benchmark can lead to misleading alpha values.
The CAPM model itself has well-documented limitations, including its assumption that all investors can borrow at the risk-free rate and that markets are perfectly efficient. Multi-factor models like the Fama-French three-factor model address some of these shortcomings by accounting for additional risk factors beyond market exposure alone.