In insurance, the analyst is often faced with a large number of inter-related variables for which correlations need to be estimated. Clearly, all correlations lie in the interval [-1, 1], but the numbers cannot be assigned independently. Here, the choices left to the analyst are considered from both a geometric and a probabilistic viewpoint. In practice, the underwriter or risk manager may fix some of the correlations and this paper considers, from both these viewpoints, what effect this has on the analyst's choice of correlations between the remaining variables.