For a static model of n individuals generated by heavy-tailed losses, under the assumption that there exist asymptotic independence and dependence structures between the losses, we derive asymptotic formulas for both the systemic expected shortfall and marginal expected shortfall based on higher-moment capital allocation rules. Our results indicate that systemic risk is asymptotically proportional to the value-at-risk of a representative random variable, and it is influenced by the risk aversion parameter p and the structure of asymptotic dependence, while the structure of asymptotic independence has a negligible effect. In addition, simulation studies are conducted to better illustrate our results.