The project risk manager should monitor risk thresholds closely, as they represent the organization's risk appetite. In a project with a low risk appetite, it is essential to ensure that risks are managed within the defined thresholds to address stakeholders' concerns and maintain their confidence in the project's success.
According to the PMI Risk Management Professional (PMI-RMP) Reference Materials, risk thresholds are the measure of acceptable variation around an objective that reflects the risk appetite of the organization1. Risk appetite is the degree of uncertainty an entity is willing to take on in anticipation of a reward2. In this case, the project has a significant impact on the organization and the stakeholders have a low risk appetite, meaning they are not willing to accept much deviation from the project objectives. Therefore, the project risk manager should monitor the risk thresholds closely to ensure that the project risks do not exceed the acceptable level of variation and impact the project performance negatively. By monitoring the risk thresholds, the project risk manager can also identify when risk responses are needed and evaluate their effectiveness.
References: 1: PMI, Practice Standard for Project Risk Management, 2009, p. 20 2: PMI, A Guide to the Project Management Body of Knowledge (PMBOK® Guide), Sixth Edition, 2017, p. 720