Alpha and Beta

Beta and alpha split a portfolio's returns into two parts: the part explained by market movements and the part that is not. Beta measures sensitivity to the market: a beta of 1.5 means the portfolio tends to move 1.5% when the market moves 1%. Alpha is the return left over after accounting for that market exposure, often treated as a sign of skill. A fund that beats the market simply by holding riskier stocks has high beta, not high alpha. Separating the two is essential for judging whether a manager or strategy truly adds value.

Beta#

Beta = Covariance(portfolio returns, market returns) / Variance(market returns)

Equivalently, beta equals the correlation between the portfolio and the market, multiplied by the portfolio's volatility divided by the market's volatility. See Covariance and Correlation.

Alpha and CAPM#

The Capital Asset Pricing Model (CAPM) says the expected return for a given beta is:

Expected return = Risk free rate + Beta × (Market return - Risk free rate)
Alpha = Actual return - Expected return

This version is often called Jensen's alpha, after Michael Jensen, who used it in 1968 to evaluate mutual funds.

Estimating with regression#

In practice, alpha and beta are estimated by regressing the portfolio's excess returns on the market's excess returns:

Portfolio excess return = Alpha + Beta × Market excess return + Error

The slope is beta, the intercept is alpha (per period, so annualise it), and R squared shows how much of the portfolio's movement the market explains. See Regression Analysis and R-Squared.

Multi factor alpha#

CAPM uses only the market. Many returns that look like alpha are actually exposure to other known factors, such as small companies, cheap value stocks or momentum. Multi factor models, such as the Fama French models, estimate alpha after controlling for these factors. A manager whose alpha disappears after adding factors is delivering factor beta, which can often be bought cheaply in funds. See Factor Models and Factor Investing Explained.

Pitfalls#

Why it matters for traders#

• Hedging: knowing beta tells you how many index futures to sell to hedge market risk. See Hedging.
• Evaluating strategies: a strategy that only earns money when the market rises may simply be long beta.
• Portfolio construction: combining low beta, high alpha strategies improves diversification. See Diversification.

Frequently asked questions#

What is beta in investing?#

A measure of how much a portfolio or stock tends to move relative to the market; a beta of 1.5 means it moves about 1.5 times as much.

What is alpha in investing?#

The return beyond what is explained by market exposure, or by several risk factors in multi factor models.

Can alpha be negative?#

Yes. Negative alpha means a portfolio earned less than expected for its risk, which is common after fees.

Next, learn how consistently a manager beats a benchmark in Information Ratio and Tracking Error.