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There are many assumptions on mean-variance portfolio theory and they seem to be very unrealistic, for example

1) investors have the same information at the same time:

calculating expected returns for assets and their covariance requires many statistical knowledge and the calculation may differ greatly from one forecasting method to the others.

2) investors make their decision solely on the means and covariances of asset returns:

Even if all investors have the same expected returns and covariances, some investors may make their decision based on their asset preferences for example: if you like apple, you may invest in apple without considering any of those statistical information. It seems to be very irrational but I saw some people doing in this way.

Apart from this, there are many counter-examples for underlying assumptions. So, can we actually make our decisions using mean-variance portfolio?

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Mean-variance (MV) is a framework rather than a prescription. This framework allows one to make, discuss, and defend his investment decision.

In practice, there are many ways to make adjustments to this framework, if you believe they will improve performance. E.g. you can adjust the framework by stating "I will MV-optimize weights subject to "0" if the weights fall below 2%" or you can incorporate your beliefs of the expected returns (Black-Litterman). Or, you can redefine volatility, only diversifying away negative deviations.

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It is well known that the MV-optimal portfolio has some very bad properties in practice:

  • Backtesting: The MV portfolio performs very bad in backtesting applications
  • Diversification: The MV portfolio tends to invest all funds into the best asset (highest sharpe ratio) of the past, leading to very low diversification.
  • Non-Normality: Return distributions are actually highly non-normal and asymmetric, which contradicts the assumptions of MV (there are other moments of the distribution which should be considered aswell).

The MV model has some important theoretical implications which cannot be shown as easily without its simplifying assumptions, however in practice MV is not recommended.

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