Define "alpha" in investment terms.

Alpha is a key concept in investment performance measurement, specifically representing the excess return of an investment relative to the return of a benchmark index or risk-adjusted expectation. When investors or portfolio managers refer to alpha, they are usually assessing how well an investment has performed compared to what would be anticipated based on its risk profile and the performance of the market as a whole.

For instance, if a fund generates a return of 12% while its benchmark index returns 10%, the fund would have an alpha of 2%. This positive alpha indicates that the manager has added value beyond what could be explained by market movements alone and is thus a measure of skill in active management. Investors often seek investments with positive alpha, as this suggests better-than-expected performance.

In contrast, the other definitions provided do not capture the essence of alpha. The risk-free rate of return represents a standard or comparison for investments, but does not relate to a benchmark of performance. The correlation of a security with the market pertains to the degree of co-movement between the security and the market, which affects risk but does not directly measure performance against a benchmark. A fixed return rate refers to an agreement on returns, which could apply to certain types of investments but does not encompass the comparative