This article studies a principal-agent problem with flexible information acquisition. The agent has to choose between investing in an innovative asset about which costly information can be acquired or in a conventional asset about which there is enough historical data and no information is acquired. In the first-best problem, the principal acquires information about the entire distribution of cash flow from the innovative asset. Contrarily, in the second-best problem, less information is acquired about the left tail of the distribution compared to the first-best. The optimal contract of the agent when the innovative asset is chosen pays zero wage below a cutoff value of cash flow and an increasing wage above the cutoff. As a consequence, the information intensity is zero for these low cash flows where no wage is paid. This results in investment in even those assets that have a thick left tail and thus a high likelihood of failure ex post. Our paper explains why agents make investments without learning about the left tail of the distribution which in turn may lead to a financial crisis.