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What is the usual method of dealing with many uncertain mean returns in portfolio optimization?
For example say you have a 3 asset portfolio with assets A, B and C. All the correlations and variances are the same.
You can't reject the null that the assets have the same mean return for (A and B) and (B and C), but you can reject the null for (A and C).
It seems there is no nonbiased way to choose the means?
Your question accurately addresses of the practical problems of applying Modern Portfolio Theory (i.e. mean-variance optimization) in practice.
Generally the correlations are considered much more difficult to accurately estimate in this context.
I am not sure I understand the question. Isn't $E(r)$ is an unbiased estimator of $r$?
You may want to look at the Black-Litterman model. It is an optimization model developed to address the practical problems in applying portfolio optimization.
