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If the REF plots close to the MV frontier, are the portfolios different?   

 

Efficient frontier portfolios are graphed in terms of their mean and variance.  If you compare RE and MV portfolios at the same risk level, the allocations typically vary even though the risks and returns are similar.  The portfolio composition exhibits on the Charts Worksheet display the MV and RE optimal asset allocations from low risk on the left-hand side of the charts to high risk on the right-hand side.  Each color represents the weight of a particular asset in the optimization for a given level of portfolio risk risk.  The left panel provides the MV efficient frontier, the right panel the REF. 

 

The exhibits show that the two frontiers have different asset allocations for the same risk-return inputs.  The MV composition map displays sharp changes in allocations while the RE allocations reflect smooth transitions as risk is increased.  The RE exhibit includes allocations for all the assets in the optimization universe while MV excludes some assets.  The maximum return RE optimized portfolio (far right) is well diversified, while the MV maximum return portfolio is a single asset.  REF portfolios reflect better diversification and more investment intuitiveness whether or not the frontiers are close in mean-variance space.