We consider the upper limit of Sn/n1/p where Sn are partial sums of iid random variables. Under the assumption of E(X+)p < ∞, we provide an integral test which determines the upper limit up to certain universal constant factors depending on p only. The problem is closely related to moment properties of ladder variables. We prove our theorem by considering the lower limit of Tk/kp where Tk is the k-th epoch of the random walk.