What it is:
The very existence of alpha is controversial, however, because those who believe in the efficient market hypothesis (which says, among other things, that it is impossible to beat the market) attribute alpha to luck instead of skill, and base this belief on the fact that most managers fail to beat the market over the long-term.
How it works/Example:
Mathematically speaking, alpha is the rate of return that exceeds what was expected or predicted by models like the capital asset pricing model (CAPM). To understand how it works, consider the CAPM formula:
r = Rf + beta * (Rm - Rf ) + alpha
The main part of the CAPM formula (except the excess-return factor) calculates what the rate of return on a certain security or portfolio ought to be under certain market conditions. Note that two similar portfolios might carry the same amount of risk (same beta) but because of different alphas, it's possible for one to generate higher returns than the other. This is a fundamental quandary for investors, who always want the highest return for the least amount of risk.