The first letter of the Greek alphabet is used in finance as a measure of the return on an investment after comparing it to an appropriate market index that functions as a benchmark.
Alpha is a function of time and is measured over a specific period. For example if a fund has an alpha of x% over last year, it means that it exceeded the benchmark during that year by x%.
A typical benchmark for equities investments in the U.S. is the S&P 500 whereas equity investments in international markets can be mapped onto an appropriate index – typically a prevailing ETF.
The realized returns can also be compared to the theoretical expected returns by utilizing an asset pricing model (e.g. Fama-French model or CAPM) – this alpha is called Jensen’s alpha. Moreover, a regression analysis of the actual returns against the Fama-French returns for instance can provide useful information on the persistence of alpha and the fraction that is not explained by any of the factors.
The realized returns which are calculated after applying trading and execution fees are compared to the benchmark in order to conclude if the strategy over or under performed and reflect things on a relative scale. An extreme example is that during a year that S&P 500 had a negative return of y% by not investing at all you essentially beat the market by |y| %.