The beta of an investment strategy corresponds to its relation with the systematic moves of the prices, i.e. the one driven by very common factors. Typically market indexes are benchmarks used to measure the beta against.

The beta of an investment strategy corresponds to its relation with the systematic moves of the prices, i.e. the one driven by very common factors. Typically market indexes are benchmarks used to measure the beta against.

The more beta, the more directional risk the portfolio is taking, as opposed to the "alpha" that is meant to be idiosyncratic. Borrowing the common notation of econometrics, the alpha and beta of a portfolio is obtained regressing its returns $r^p$ against the of of common indexes $r^b$: $$r^p = \alpha + \beta\, r^b + \epsilon.$$

Writing this requires assumptions, like the stationarity of $r^p$ and $r^b$, the choice of a time scale (daily, weekly, monthly?). Most questions come from trying to relax these assumptions, giving birth to interesting problems.