# What does alpha and beta signify in portfolio analysis?

Jan 22, 2016

Alpha is a measure of an investment’s performance on a risk-adjusted basis. It takes the volatility (price risk) of a security or fund portfolio and compares its risk-adjusted performance to a benchmark index. The excess return of the investment relative to the return of the benchmark index is its alpha.

Simply stated, alpha is often considered to represent the value that a portfolio manager adds or subtracts from a fund portfolio’s return. A positive alpha of 1 means the fund has outperformed its benchmark index by 1%. Correspondingly, a similar negative alpha would indicate an underperformance of 1%. For investors, the more positive an alpha is, the better it is.

Beta, also known as the beta coefficient, is a measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole. Beta is calculated using regression analysis, and you can think of it as the tendency of an investment’s return to respond to swings in the market. By definition, the market has a beta of 1 Individual security and portfolio values are measured according to how they deviate from the market.

A beta of 1.0 indicates that the investment’s price will move in lock-step with the market. A beta of less than 1 indicates the investment will be less volatile than the market, and correspondingly, a beta of more than 1 indicates the investment’s price will be more volatile than the market. For example, if a fund portfolio’s beta is 1.2, it’s theoretically 20% more volatile than the market.

The mathematical construct for this is:

${y}_{i} = \alpha + {\beta}_{i} {x}_{i} + {e}_{i}$

Typically this solved through a linear regression. The interpretation is: $\alpha =$ intercept; $\beta =$ slope