Geometric mean variance

The concept of constructing an investment portfolio by maximising the mean return while minimising the variance of the return was first introduced by Markowitz (1952). Instead of focusing only on the prospects of each individual asset, the idea was that the correlations between the different assets could be used to enhance returns at any given level of risk. However, in practice the mean-variance concept is hard to apply, because it frequently implies highly leveraged portfolios with large long positions in some assets against large short positions in others. Such portfolios are usually unacceptable to portfolio managers in the real world, and the higher the correlations between the various assets, the more likely this is to happen.

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