Abstract
Assuming that the assets returns are normally distributed with a known covariance matrix, we derive a joint sampling distribution for the estimated optimal portfolio as well as for its mean and risk return. We show that the estimation error increases with the investor’s risk tolerance and the number of assets within the portfolio, while it decreases with the sample size. In addition, by deriving the portfolio joint distribution, we propose a new portfolio based on two step optimization framework that outperforms the conventional portfolio for high levels of estimation error. Moreover, we show that the proposed portfolio achieves a lower opportunity cost than the conventional one.
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