Studdridge International is a high-end consulting firm specialized in estimating large-dimensional covariance matrices, and in exploiting the information they contain to make optimal decisions.

A covariance matrix of a set of variables contains the variances (of all variables) as well as the covariances (between all pairs of variables). Say there are ten variables. Then there are ten variances and 45 distinct covariances; this is because the covariance between two variables does not depend on the ordering. The covariance matrix collects these numbers in a ten by ten matrix: the diagonal contains the variances and the off diagonals contain the covariances (where each distinct covariance appears twice, one above the diagonal and once below).

The covariance matrix is intimately linked to the correlation matrix. The difference between the two is a multiplicative adjustment that captures the magnitude of the random swings in each variable, called the standard deviation (and mathematically obtained as the square root of the variance). From the covariance matrix, we can thus back out all the correlations.

We only accept assignments where the number of correlated variables is at least 30. Another critical quantity is the ratio of the number of variables to sample size, called the concentration. Studdridge International delivers significant performance boosts when the concentration ratio is at least 1/10.