In this article we propose two new methods of portfolio allocation which are applicable for all return distributions. The properties of these new methods are compared with that of Markowitz's mean-variance method using extensive simulation. It is found that the new methods perform appreciably in terms of growth of wealth as well as protecting against the downside risk, in situations where the return distributions of one or more of the stocks is heavy-tailed. These methods can be effective substitutes for the mean-variance method which is not applicable for return distributions with heavy-tails having infinite expectation or variance.