Beta equation (security)

The market beta of a security is determined as follows: Regress excess returns of stock y on excess returns of the market. The slope coefficient is beta. Define n as number of observation numbers.

• Beta=
• [(n) (sum of [xy]) ]-[ (sum of x) (sum of y)]/
• [(n) (sum of [xx]) ]-[ (sum of x) (sum of x)]
• where: n = # of observations (usually 36 to 60 months)
• x = rate of return for the S&P 500 index
• y = rate of return for the security.
• Related: Alpha