This paper deals with certain concepts that are important to the decision maker in building a portfolio selection model. It is the purpose of this study to determine the upper and lower bounds of the risk associated with life assurance companies decision-making processes. In order to obtain an investment portfolio, the decision maker has to know a certain range of risk levels. In the knowledge of these two bounds for the risk, it will be an easier task to select the appropriate portfolio. In the following section we provide a statistical solution for determining the minimum and the maximum bounds of the risk associated with the investment problem. We consider the case where the risk is given by a quadratic form.