The α (alpha) of a security or fund is its out-performance over the return adjusted for risk, with risk measured by β (beta).
α= (r - rf) - (β×(rm - rf))
where rf is the risk free rate
rm is the (forecast) market rate of return
and r the return on a fund or security.
This uses the same risk adjustment as CAPM
Financial engineering can produce portable alpha, separating alpha and beta so investors can add alpha to portfolios without affecting beta.
The advantage of alpha over simply comparing absolute return to market (or benchmark index) performance is that it adjusts for the level of risk taken. Investors usually look at returns compared to a benchmark (usually the market index) which is more visible, receives more publicity, and is not susceptible in any inaccurate estimates.
Alpha is also used as a label by fund management companies to indicate funds that are more aggressive in trying to outperform the market. However, most so called alpha funds are simply trying to out-perform rather than maximise alpha.