The quantification of diversification benefits due to aggregation of risk plays a prominent role in the (regulatory) capital management of large firms within the financial industry. However, the complexity of today's risk landscape makes a quantifiable reduction of risk concentration a challenging task. We discuss some of the issues that may arise. The theory of second-order regular variation and second-order subexponentiality provides the ideal methodological framework to derive second-order approximations for diversification benefits. As a byproduct, this allows us to analyze the accuracy of the closed-form OpVaR approximation (Böcker-Klüppelberg).