In this dissertation, we extend the ideas of Raymond Kan and Guofu Zhou for optimal portfolio construction under parameter uncertainty. Kan and Zhou proved analytically that under parameter uncertainty, investing in the sample tangency portfolio and the riskless is not optimal. Based on this idea we will approach the portfolio construction under parameter uncertainty in a different way. We will optimise the expected out-of-sample performance of a portfolio using a numerical approach. Using Monte Carlo simulations we will develop an algorithm that calculates the expected out-of-sample performance of any portfolio rule. We will then extend this algorithm in order to be able to input new portfolio rules and test their performance.\ud \ud The new portfolio rules we introduce are based on shrinkages for the mean and covariance matrix of the assets returns. These shrinkages will have some parameters that will be chosen so that we optimise the expected out-of-sample performance of the input portfolio rule. A comparison is then done between the portfolio rules we introduce and Kan and Zhou portfolio rules
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