There is an inverse relationship between the assessed level of inherent and control risk and detection risk as set by the auditor.

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BlackTom AI · Accepted Answer

The statement revolves around the core components of the audit risk model and how they interact during planning.
First, recall the key elements: inherent risk is the susceptibility of an assertion to a material misstatement assuming no related controls; control risk is the risk that a misstatement could occur and not be prevented or detected by the client's internal controls; detection risk is the risk that the auditor will not detect a misstatement that exists. 
Next, the audit risk model ties these together: Audit Risk (AR) = Inherent Risk (IR) × Control Risk (CR) × Detection Risk (DR). For a given acceptable level of AR, if IR or CR increases, DR must decrease to keep the product at or below the target AR. This is the essence of the inverse relationship mentioned.
A common misconception is thinking detection risk is set independently of IR and CR; in fact, higher IR/CR typically leads to the auditor requiring more persuasive evidence, which corresponds to a lower DR (i.e., more evidence or higher-quality procedures). Conversely, if IR and CR are assessed as low, DR can be higher because less evidence may be sufficient to achieve the same overall AR.
Another angle to consider is the practical implication: as risk components rise, the auditor responds with more intensive procedures, more samples, or higher-quality testing to reduce detection risk, illustrating the inverse dynamic rather than a direct proportionality.
In sum, the statement that there is an inverse relationship between the assessed level of inherent and control risk and detection risk aligns with the structure of the audit risk model, and recognizing this relationship helps auditors plan appropriate procedures and evidence.

There is an inverse relationship between the assessed level of inherent and control risk and detection risk as set by the auditor.

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