Alpha is the measurement of a fund's actual return and its expected return given its beta. Alpha is the excess return given the risk taken. Alpha is often used to measure a fund manager's performance. The higher the alpha is the more likely he is thought as a genius.
A positive alpha means that the fund has over performed, a negative alpha means the fund has under performed. A fund can also get a negative alpha when the expenses of a fund is considered.
The mathematical definition of alpha that Morningstar uses is below. Morningstar deducts the current return of the 90-day T-bill from the total return of both the fund and the benchmark index. The difference is called the fund's excess return.
Alpha = Excess Return -- ((Beta x (Benchmark - Treasury))
Benchmark = Total Return of Benchmark Index
Treasury = Return on Three-month Treasury Bill