Return risk map in a fuzzy environment

Within the framework of Assets Liability Management, we understand that immunization is the main method to assure a certain yield in a future date departing from an initial portfolio. Although the objective of passive strategies is to design a portfolio that will achieve the performance of a predetermined benchmark, active bond management strategies rely on expectations of interest rate movements or changes in yield-spread relationships. However, the variation of the duration increases the risk of a portfolio, that why the decision maker will have to choose the combination of expected return (mid-point of the fuzzy number) and risk (width of the fuzzy number) which provides the higher utility. Finally, the construction of a fuzzy return risk map will allow the DM to know the over risk and the over return as regards immunization strategy for each duration and for each risk aversion of the DM. The construction of a risk return map presents the results in an appropriate way. This methodology will help the DM to choose the best duration for the DM interest rate forecast