What is Alpha?

Legal Definition
Alpha is a measure of the active return on an investment, the performance of that investment compared to a suitable market index. An alpha of 1% means the investment's return on investment over a selected period of time was 1% better than the market during that same period, an alpha of -1 means the investment underperformed the market. Alpha, along with beta, is one of two key coefficients in the capital asset pricing model used in modern portfolio theory and is closely related to other important quantities such as standard deviation, R-squared and the Sharpe ratio.

In modern financial markets, where index funds are widely available for purchase, alpha is commonly used to judge the performance of mutual funds and similar investments. As these funds include various fees normally expressed in percent terms, the fund has to maintain an alpha greater than its fees in order to provide positive gains compared to an index fund. Historically, the vast majority of traditional funds have had negative alphas, which has led to a flight of capital to index funds and non-traditional hedge funds.

It is also possible to analyze a portfolio of investments and calculate a theoretical performance, most commonly using the capital asset pricing model (CAPM). Returns on that portfolio can be compared to the theoretical returns, in which case the measure is known as Jensen's alpha. This is useful for non-traditional or highly focused funds, where a single stock index might not be representative of the investment's holdings.
-- Wikipedia
Legal Definition
1. in the UK a classification of london stocks on the stock exchange in a normal market. 2. in the US it measures the change in prices of stocks in the market. The change uses movements of a stock agaist the market focusing on growth. The higher the alpha