The Capital Asset Pricing Model (CAPM) is a method for pricing risky assets such as publicly traded stocks. The formula solves for the expected return on investment by using data about an asset’s past performance and its risk relative to the market. Alpha is a measurement used to determine how well an asset or portfolio performed relative to its expected return on investment with a given amount of risk. In efficient markets alpha is assumed to be zero, but if an asset over- or under-performs its expected return relative to risk, it could receive a positive or negative alpha respectively.
Set up the CAPM equation using data relevant to a particular asset; for stocks much of this data can be found online through services like Google Finance. The formula for CAPM: Ei = Rf + Bi(Em - Rf) Where Ei = expected return on an investment, Rf = the return on a risk-free asset such as US Treasury bills, Bi = beta of an investment, or the volatility of an investment relative to the overall market, and Em = the expected market return.
Solve for Ei by multiplying beta and the difference between the expected market return and the risk-free asset return, then add that number with the risk-free asset return to obtain an asset’s expected return.
Take the value for expected asset return found in step two and the actual observed return of that asset and solve for alpha using the formula: alpha = return on investment – expected return on investment. An alpha greater than zero means the investment outperformed its expected return.
If you already have an asset's expected return, you can skip steps one and two and just solve for alpha by finding the difference between the actual return and the expected return.