I am trying to construct a covariance matrix between a set of demands $t \in T$. The only information I have of the demands are the mean and the standard deviation. I intend to apply Cholesky Decomposition to this covariance matrix and the resulting values shall then be used in an optimisation problem related to Gamma-robustness (Bertsimas, Sim) to be protected against a set of worst-case correlations on each demand.
I started with constructing a covariance matrix as follows:
$$cov(t,t^\prime) = SD(t) SD(t^\prime) \rho$$
where $\rho$ is the correlation coefficient. I set $\rho$ to different values to observe the impact of correlation between different demands on the optimisation problem. The problem I currently have is that when I generate such a covariance matrix the Cholesky decomposition always returns an error saying the matrix isn't positive definite. I thus want to ask you for some suggestions to construct such an artificial covariance matrix where the only information at hand is the SD values.