Final answer:
Controls in risk assessments for audits can be either directly or indirectly related to financial statement assertions. Direct controls aim at specific assertions, while indirect controls affect the overall control environment, influencing all assertions. Thus, controls are always related to assertions in some manner.
Step-by-step explanation:
In the context of an audit, risks assessments are a crucial part of the auditor's methodology to ensure that financial statements are free from material misstatements. To answer the question posed, controls related to assertions in financial statements can be linked in two key ways: directly and indirectly. The first option indicates that controls can certainly be directly related to an assertion when they address the accuracy and completeness of that assertion. An example of a direct control could be the authorization of transactions, which aims to ensure the occurrence and completeness assertions of revenue recognition are met. On the other hand, controls indirectly related to an assertion may not directly address the accuracy of a specific financial statement assertion but still impact the overall control environment, such as segregation of duties. Segregation of duties helps to prevent fraud, which indirectly maintains the integrity of all assertions. The third and fourth options are incorrect; controls are designed to be related to assertions in some manner, whether directly or indirectly.
Therefore, the correct answer to how controls can be related to an assertion is both directly and indirectly related. Controls cannot be unrelated to assertions within the purpose of an audit, as their primary role is to prevent or detect and correct material misstatements.