text: how to calculate risks for investments? (beta, covariance, systematic vs unsystematic risk, etc...). risk might be equated to uncertainty: uncertainty about achieving your investing goals. usually, proffesional aproximmate uncertainty with standard deviation. basically that's all behind risk perception. now, covariance is a measure about how returns on one assets might be relate to ohters'. in order to calculate the standard deviation of a portolio , you need a covariance matrix: se = sqrt( x'cx) where se is standard deviation of the return, sqrt stands for square root, x is a vector of portfolio holdings and c is a covariance matrix. beta is the regression coefficient of one asset's returns with respect to the market returns. it an easy and dirty way to approximate the std deviation of given asset. however, its not much more difficult to express assets returns as a linear function of several factors. that is called multivariate analysis or, in financial jargon, apt (arbitrage pricing theory).  if the returns are expressed as linear combinations of factors and f is factor weighting matrix (entries being securities and factors), c can be calculated as  c=f'm f where m is the factor covariance matrix.  now, we have been talking about absolute risk. what is relevant, however is risk relative to goal (benchmark) for doing that you have to measure tracking error, which is de std dev of the differences in return between the benchmark and the portfolio. systematic risk is the risk that can be avoided by diversifiing de portfolio. unsystematic risk is the risk that is inherent to the underlying market