Alpha is a measurement of the residual risk that an investor takes as a result of investing in a fund rather than in a market index. It represents the difference between a mutual fund's actual performance and the performance that would be expected based on the level of risk taken by the fund's manager.

If a fund produced the expected return for the level of risk assumed, the fund is said to have an Alpha of zero. A positive Alpha indicates a return greater than expected for the risk taken. A negative Alpha indicates the manager has not adequately rewarded investors for the risks taken.

where:

Alpha =

[

(sum of y) - {b * (sum of x)} n

]

n = number of observations
b = Beta of the fund
x = rate of return for the benchmark index (often, but not always, the S&P 500)
y = rate of return for the fund