A decision maker faces two correlated risks and can obtain information on only one of them. Intuition suggests that the existence of a high correlation (in absolute value) between the risks should increase total information value. Indeed in such a case information about one risk induces a relevant information on the other one. Using a simple example, we show that this intuition is often correct, but that it can be mitigated by other factors.
Eeckhoudt, L., Thomas, A., & Treich, N. (2011). Correlated risks and the value of information. Journal of Economics, 102(1), 77-87. https://doi.org/10.1007/s00712-010-0169-5 (Original work published 2011)