What is the term for a risk characterized by unfavorable attributes that make it unacceptable to admitted insurers?

The term for a risk that has unfavorable attributes making it unacceptable to admitted insurers is "distressed risk." Distressed risks typically involve factors such as a high likelihood of loss, poor loss history, or unusual circumstances that render them uninsurable by standard insurance companies. Admitted insurers are those that are licensed and regulated within a particular state, and they often have strict underwriting guidelines that exclude risks perceived as too high or problematic.

In contrast, the other terms do not accurately encapsulate this specific type of risk. Unique risk may refer to risks that are different from typical standards, but not necessarily to the extent that they are deemed unacceptable. High-capacity risk is not a standard term in the insurance context and does not specifically relate to insurability by admitted insurers. Export risk usually pertains to international transactions and the factors affecting them rather than risks that are uninsurable by admitted insurers. Therefore, the choice of "distressed risk" aligns with the definition required in this context.