Suppose X 1,X 2 are independent random variables satisfying a second-order regular variation condition on the tail-sum and a balance condition on the tails. In this paper we give a description of the asymptotic behaviour as t → ∞ for P(X 1 + X 2 > t). The result is applied to the problem of risk diversification in portfolio analysis and to the estimation of the parameter in a MA(1) model.