Dependence between risks reduces the benefits of diversification. Modem portfolio theory is based on correlation as a measure of dependence while the criterion presented here is based on the copula theory as a measure of the intrinsic relatedness of different risks. The dependencies are examined by fitting copulas, estimating the dependence parameters and lastly using distance matrices to cluster the risks together. The motivation of the study was driven by the fact that insurance companies have collapsed in the past, one reason being the type of business classes they engage in. It is therefore important to understand the dependencies between risks for better risk management. The study derives its data from the general insurance business in Kenya where the risks are classified by the Copula based approach. Five major classes stand out each with peculiar characteristics. The first cluster involves the rare but with a high probability of a huge claim amount lines: Engineering, Liability, Fire industrial and Theft. The second contain lines with moderate claim amounts as compared to the previous cluster but rather slightly more frequent: Fire domestic, Personal accident, Workman's compensation, Motor commercial and motor private. In the following cluster we have the less popular lines under the umbrella of the miscellaneous class. Marine and Transit which is completely erratic clusters alone while the Aviation line whose main business is exported to foreign countries forming the last cluster. Finally, it can be remarked that the choice of distance to apply is crucial.