Let's assume you are a portfolio manager who expects your client's portfolio to return 15% next year. The year goes by and the portfolio actually returns 16%. In its most basic sense, the *alpha* of the portfolio = 16% - 15% = 1%.

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 = R*_{f} + beta * (R_{m} - R_{f} ) + alpha

*where:*

r = the security's or portfolio's return

R_{f} = the risk-free rate of return

beta = the security's or portfolio's price volatility relative to the overall market

R_{m} = the market return

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.