Editing Multivariate random variable (section)

===Portfolio theory===
In [[portfolio theory]] in [[finance]], an objective often is to choose a portfolio of risky assets such that the distribution of the random portfolio return has desirable properties. For example, one might want to choose the portfolio return having the lowest variance for a given expected value.  Here the random vector is the vector <math>\mathbf{r}</math> of random returns on the individual assets, and the portfolio return ''p'' (a random scalar) is the inner product of the vector of random returns with a vector ''w'' of portfolio weights — the fractions of the portfolio placed in the respective assets. Since ''p'' = ''w''<sup>T</sup><math>\mathbf{r}</math>, the expected value of the portfolio return is ''w''<sup>T</sup>E(<math>\mathbf{r}</math>) and the variance of the portfolio return can be shown to be ''w''<sup>T</sup>C''w'', where C is the covariance matrix of <math>\mathbf{r}</math>.